<?PHP
/*
******************************************************
SATURN
Heliocentric Coords Module - VSOP 87 Theory - Series C3
Heliocentric rectangular X,Y,Z,R coordinates for the
mean dynamical ecliptic and equinox of the date.
Module Range: 1 AD to 4000 AD
Written in PHP v5.2.5
This source code is released to the public domain.
Jay Tanner
VSOP87@NeoProgrammics.com
******************************************************
*/
function Saturn_hXYZR($JDArg)
{
// Compute time in Julian millennia from J2000.0
$t = ($JDArg - 2451545.0) / 365250.0;
// Compute the heliocentric coordinates for time ($t).
$hX = Saturn_X0($t) + Saturn_X1($t) + Saturn_X2($t)
+ Saturn_X3($t) + Saturn_X4($t) + Saturn_X5($t);
$hY = Saturn_Y0($t) + Saturn_Y1($t) + Saturn_Y2($t)
+ Saturn_Y3($t) + Saturn_Y4($t) + Saturn_Y5($t);
$hZ = Saturn_Z0($t) + Saturn_Z1($t) + Saturn_Z2($t)
+ Saturn_Z3($t) + Saturn_Z4($t) + Saturn_Z5($t);
// Compute heliocentric radius vector (distance).
$hR = SqRt($hX*$hX + $hY*$hY + $hZ*$hZ);
// Return the heliocentric XYZR coordinates
// in a space-delimited data vector.
return "$hX $hY $hZ $hR";
}
/*
Saturn - VSOP87 Series Version C3 - Rectangular (X,Y,Z) Coordinates
X = X-Coordinate in AU (Astronomical Units)
Y = Y-Coordinate in AU
Z = Z-Coordinate in AU
R*R = (X*X + Y*Y + Z*Z)
HELIOCENTRIC DYNAMICAL ECLIPTIC AND EQUINOX OF THE DATE
PHP Language
VSOP87 Functions Source Code
Generated By NeoProgrammics VSOP87 Code Generator
(c) Jay Tanner 2008
Ref:
Astronomy & Astrophysics
vol. 202, p309-p315
Pierre Bretagnon, Gerard Francou
1988
*/
function Saturn_X0($t) // 2047 terms of order 0
{
$X0 = 9.52312533591*cos(0.87401491487 + 213.5429129215*$t);
$X0 += 0.79501390398*cos(4.76580713096 + 0.2438174835*$t);
$X0 += 0.26427074351*cos(0.12339999915 + 426.8420083595*$t);
$X0 += 0.06836881382*cos(4.14537914189 + 206.42936592071*$t);
$X0 += 0.06628914946*cos(0.75057317755 + 220.6564599223*$t);
$X0 += 0.02340967916*cos(2.01979283929 + 7.3573644843*$t);
$X0 += 0.01250581159*cos(2.17392657526 + 110.45013870291*$t);
$X0 += 0.01141539711*cos(3.03345312296 + 419.72846135871*$t);
$X0 += 0.01098217124*cos(5.65720860592 + 640.1411037975*$t);
$X0 += 0.00773784455*cos(3.50285419449 + 213.0552779545*$t);
$X0 += 0.00708587042*cos(2.70922969272 + 316.6356871401*$t);
$X0 += 0.00434227030*cos(0.71624098563 + 529.9347825781*$t);
$X0 += 0.00373110880*cos(0.00103492669 + 433.9555553603*$t);
$X0 += 0.00413446294*cos(5.12392705512 + 102.84895673509*$t);
$X0 += 0.00169743473*cos(6.19449424436 + 205.9417309537*$t);
$X0 += 0.00122184772*cos(4.36825124039 + 103.3365917021*$t);
$X0 += 0.00141571884*cos(4.84926431365 + 419.2408263917*$t);
$X0 += 0.00097840616*cos(1.01545569510 + 323.74923414091*$t);
$X0 += 0.00080586098*cos(5.62239507032 + 11.2895177474*$t);
$X0 += 0.00083840998*cos(0.62002007163 + 227.77000692311*$t);
$X0 += 0.00072499120*cos(2.42001514073 + 633.0275567967*$t);
$X0 += 0.00070188882*cos(0.88664463373 + 209.6107596584*$t);
$X0 += 0.00068920772*cos(4.01663904384 + 217.4750661846*$t);
$X0 += 0.00065633219*cos(2.76404999091 + 202.4972126576*$t);
$X0 += 0.00058340081*cos(2.16106790491 + 224.5886131854*$t);
$X0 += 0.00054036331*cos(4.90882849644 + 853.4401992355*$t);
$X0 += 0.00045670301*cos(1.87822014512 + 14.47091148511*$t);
$X0 += 0.00039957906*cos(4.29286414022 + 199.3158189199*$t);
$X0 += 0.00044623718*cos(5.61332771211 + 63.49208081989*$t);
$X0 += 0.00025182378*cos(0.37762569174 + 216.72430665921*$t);
$X0 += 0.00024597547*cos(4.52837189964 + 210.36151918381*$t);
$X0 += 0.00024755958*cos(5.60048517853 + 415.7963080956*$t);
$X0 += 0.00025518626*cos(1.63814026860 + 117.5636857037*$t);
$X0 += 0.00030420785*cos(4.58036001246 + 735.6326960483*$t);
$X0 += 0.00022261024*cos(5.81339199632 + 522.3336006103*$t);
$X0 += 0.00023384603*cos(5.53454487341 + 647.25465079831*$t);
$X0 += 0.00019921860*cos(2.52438740442 + 426.3543733925*$t);
$X0 += 0.00023368080*cos(0.18801837763 + 149.8070146181*$t);
$X0 += 0.00024816783*cos(5.50044242809 + 75.0254160508*$t);
$X0 += 0.00015057730*cos(4.67637379107 + 277.2788112249*$t);
$X0 += 0.00013291291*cos(0.78826176081 + 309.0345051723*$t);
$X0 += 0.00012028365*cos(1.02934559031 + 1059.6257476727*$t);
$X0 += 0.00012408238*cos(4.19692495275 + 490.5779066629*$t);
$X0 += 0.00012037260*cos(5.66358935866 + 352.06040979221*$t);
$X0 += 0.00007880259*cos(2.60324364809 + 743.23387801611*$t);
$X0 += 0.00007428823*cos(4.26427762571 + 6.86972951729*$t);
$X0 += 0.00006985779*cos(3.88380796193 + 309.5221401393*$t);
$X0 += 0.00009059376*cos(4.31626349433 + 1052.02456570489*$t);
$X0 += 0.00006626180*cos(5.53666910204 + 838.72547026689*$t);
$X0 += 0.00008285289*cos(2.03028865010 + 95.7354097343*$t);
$X0 += 0.00007908600*cos(2.91633632242 + 316.14805217309*$t);
$X0 += 0.00006284835*cos(1.10258326823 + 3.6883357796*$t);
$X0 += 0.00006078527*cos(6.15871885410 + 441.06910236111*$t);
$X0 += 0.00005628724*cos(2.47826941808 + 846.3266522347*$t);
$X0 += 0.00005274108*cos(3.40288166935 + 220.16882495529*$t);
$X0 += 0.00005584926*cos(3.11230524128 + 412.6149143579*$t);
$X0 += 0.00004423799*cos(0.00561711784 + 198.82818395289*$t);
$X0 += 0.00004849319*cos(0.26891980614 + 537.0483295789*$t);
$X0 += 0.00004179381*cos(0.45517914787 + 4.1759707466*$t);
$X0 += 0.00005772348*cos(5.30786967696 + 38.3768531213*$t);
$X0 += 0.00005198014*cos(4.54573443270 + 211.09523236671*$t);
$X0 += 0.00005154525*cos(0.34613786659 + 215.99059347631*$t);
$X0 += 0.00003792407*cos(5.99326135433 + 422.9098550964*$t);
$X0 += 0.00004380719*cos(1.15696233721 + 202.0095776906*$t);
$X0 += 0.00004838174*cos(2.03403080585 + 109.9625037359*$t);
$X0 += 0.00003765792*cos(3.72073369090 + 212.579705075*$t);
$X0 += 0.00003749721*cos(1.16925812858 + 214.506120768*$t);
$X0 += 0.00003116757*cos(0.84596173223 + 213.4947288117*$t);
$X0 += 0.00003115849*cos(4.04374864852 + 213.5910970313*$t);
$X0 += 0.00003119049*cos(0.50950816465 + 625.42637482889*$t);
$X0 += 0.00003235633*cos(1.36565416054 + 632.5399218297*$t);
$X0 += 0.00004077069*cos(5.95933511847 + 136.78920667889*$t);
$X0 += 0.00003290391*cos(0.32712024501 + 522.8212355773*$t);
$X0 += 0.00002828736*cos(0.73223929578 + 330.8627811417*$t);
$X0 += 0.00003365297*cos(1.42074759163 + 437.8877086234*$t);
$X0 += 0.00002888976*cos(1.14066267703 + 86.07111631471*$t);
$X0 += 0.00002748221*cos(5.42931189203 + 138.76131435421*$t);
$X0 += 0.00002742545*cos(0.93548005709 + 203.9816853659*$t);
$X0 += 0.00002636395*cos(5.40701545041 + 288.32451148881*$t);
$X0 += 0.00003170535*cos(5.76636557141 + 76.50988875911*$t);
$X0 += 0.00002530060*cos(5.09730517007 + 629.0954035336*$t);
$X0 += 0.00002985976*cos(4.15644325876 + 1066.7392946735*$t);
$X0 += 0.00002617358*cos(5.45160906944 + 127.22797912329*$t);
$X0 += 0.00002504577*cos(1.49069183275 + 9.8050450391*$t);
$X0 += 0.00002459199*cos(5.26431553671 + 1155.1173399235*$t);
$X0 += 0.00002429561*cos(3.97256605696 + 223.1041404771*$t);
$X0 += 0.00003133467*cos(4.05731806661 + 1368.4164353615*$t);
$X0 += 0.00002289072*cos(3.68644263049 + 430.7741616226*$t);
$X0 += 0.00002651422*cos(5.01550706453 + 412.12727939089*$t);
$X0 += 0.00002791618*cos(1.76104978670 + 3.42521122121*$t);
$X0 += 0.00002086473*cos(3.54266754065 + 423.66061462181*$t);
$X0 += 0.00002337517*cos(5.86744835115 + 388.70897272171*$t);
$X0 += 0.00001735774*cos(5.67596672079 + 736.1203310153*$t);
$X0 += 0.00001617760*cos(4.44174561688 + 96.2230447013*$t);
$X0 += 0.00001635420*cos(4.54438827357 + 12.77399045571*$t);
$X0 += 0.00001637578*cos(2.19935832842 + 213.0216480597*$t);
$X0 += 0.00001633497*cos(2.69143754521 + 214.0641777833*$t);
$X0 += 0.00001703439*cos(2.42595077461 + 529.44714761109*$t);
$X0 += 0.00001499174*cos(3.59977145410 + 52.446380556*$t);
$X0 += 0.00001462063*cos(5.92411007321 + 430.02340209721*$t);
$X0 += 0.00001975850*cos(2.02313657577 + 1.7282901918*$t);
$X0 += 0.00001422179*cos(4.89979449865 + 625.9140097959*$t);
$X0 += 0.00001539334*cos(4.78536735793 + 860.55374623631*$t);
$X0 += 0.00001400317*cos(3.72256803400 + 341.01470952831*$t);
$X0 += 0.00001337694*cos(6.25839826307 + 948.9317914863*$t);
$X0 += 0.00001427589*cos(5.41396429448 + 350.5759370839*$t);
$X0 += 0.00001149795*cos(0.20404714120 + 941.8182444855*$t);
$X0 += 0.00001112160*cos(0.47891380184 + 234.8835539239*$t);
$X0 += 0.00001015231*cos(4.99599119065 + 1471.50920958009*$t);
$X0 += 0.00001090238*cos(5.82704347671 + 363.1061100561*$t);
$X0 += 0.00001091460*cos(1.13704115272 + 174.1860370063*$t);
$X0 += 0.00001152320*cos(3.83459893564 + 201.01273994931*$t);
$X0 += 0.00000874317*cos(5.95988532860 + 515.2200536095*$t);
$X0 += 0.00001180011*cos(3.80422455282 + 1684.80830501809*$t);
$X0 += 0.00001058128*cos(1.29841878389 + 742.74624304909*$t);
$X0 += 0.00000850822*cos(4.55296025129 + 949.4194264533*$t);
$X0 += 0.00000869178*cos(3.23528200552 + 210.6221516147*$t);
$X0 += 0.00001119594*cos(3.46591203463 + 703.8770021009*$t);
$X0 += 0.00000868384*cos(1.65138396031 + 216.4636742283*$t);
$X0 += 0.00000830815*cos(0.58110190109 + 212.79215339611*$t);
$X0 += 0.00000825441*cos(4.30721839854 + 214.2936724469*$t);
$X0 += 0.00000881196*cos(1.46906794476 + 209.35012722751*$t);
$X0 += 0.00000866345*cos(3.41432821062 + 217.73569861551*$t);
$X0 += 0.00000789515*cos(0.23961241737 + 223.83785366*$t);
$X0 += 0.00001091862*cos(2.67346837599 + 340.52707456129*$t);
$X0 += 0.00001008329*cos(1.08917861648 + 226.07308589371*$t);
$X0 += 0.00000919088*cos(4.86163770046 + 565.35950523021*$t);
$X0 += 0.00000820108*cos(2.19486077696 + 88.6218627335*$t);
$X0 += 0.00000716162*cos(5.81233216238 + 1265.32366114289*$t);
$X0 += 0.00000860928*cos(3.70614582002 + 252.8997888367*$t);
$X0 += 0.00000710939*cos(3.41349088844 + 417.2807808039*$t);
$X0 += 0.00000701898*cos(1.91952059017 + 956.53297345411*$t);
$X0 += 0.00000918630*cos(4.57690637056 + 563.87503252191*$t);
$X0 += 0.00000711475*cos(0.90576159835 + 207.913838629*$t);
$X0 += 0.00000797153*cos(2.01469397505 + 208.1262869501*$t);
$X0 += 0.00000758732*cos(4.77442040057 + 728.5191490475*$t);
$X0 += 0.00000642018*cos(1.92693340665 + 639.6534688305*$t);
$X0 += 0.00000769629*cos(2.89427987517 + 218.9595388929*$t);
$X0 += 0.00000811029*cos(6.22246903964 + 1162.7185218913*$t);
$X0 += 0.00000692909*cos(3.97674040211 + 219.171987214*$t);
$X0 += 0.00000798757*cos(1.35424808982 + 22.3352180113*$t);
$X0 += 0.00000834309*cos(2.96244339722 + 160.852714882*$t);
$X0 += 0.00000655277*cos(0.92079690947 + 301.9209581715*$t);
$X0 += 0.00000762632*cos(1.72094446975 + 21.5844584859*$t);
$X0 += 0.00000576036*cos(3.10166158268 + 99.40443843901*$t);
$X0 += 0.00000615654*cos(2.27550746905 + 845.8390172677*$t);
$X0 += 0.00000578589*cos(0.80405181178 + 265.745475994*$t);
$X0 += 0.00000626782*cos(2.79771540666 + 18.40306474821*$t);
$X0 += 0.00000589499*cos(3.90740268282 + 554.31380496631*$t);
$X0 += 0.00000700182*cos(0.40018815531 + 62.0076081116*$t);
$X0 += 0.00000697691*cos(0.57105547911 + 124.6772327045*$t);
$X0 += 0.00000613843*cos(4.42239495907 + 218.2087793675*$t);
$X0 += 0.00000581263*cos(2.07871172739 + 231.70216018621*$t);
$X0 += 0.00000666749*cos(2.82369459311 + 425.35753565121*$t);
$X0 += 0.00000516903*cos(0.38857203410 + 414.31183538731*$t);
$X0 += 0.00000499031*cos(2.54039255853 + 408.68276109481*$t);
$X0 += 0.00000502357*cos(6.19770250859 + 1258.21011414209*$t);
$X0 += 0.00000531983*cos(2.53130210328 + 215.0273856298*$t);
$X0 += 0.00000643415*cos(1.39270825866 + 64.97655352819*$t);
$X0 += 0.00000518385*cos(2.70002198759 + 142.6934676173*$t);
$X0 += 0.00000550972*cos(0.47047442681 + 208.8770464755*$t);
$X0 += 0.00000469313*cos(0.32930418795 + 71.09326278771*$t);
$X0 += 0.00000456002*cos(4.67119057391 + 203.247972183*$t);
$X0 += 0.00000592362*cos(1.86789317281 + 266.233110961*$t);
$X0 += 0.00000465459*cos(5.40811702089 + 654.3681977991*$t);
$X0 += 0.00000444956*cos(4.73192251220 + 1787.9010792367*$t);
$X0 += 0.00000502683*cos(4.37046140723 + 251.6759485593*$t);
$X0 += 0.00000522764*cos(2.19701769819 + 212.05844021321*$t);
$X0 += 0.00000422458*cos(2.13565038243 + 479.532206399*$t);
$X0 += 0.00000437134*cos(1.32836524720 + 1589.3167127673*$t);
$X0 += 0.00000414039*cos(3.63548652605 + 148.32254190981*$t);
$X0 += 0.00000398994*cos(1.64973433253 + 213.6547875061*$t);
$X0 += 0.00000398994*cos(3.23989183406 + 213.4310383369*$t);
$X0 += 0.00000373088*cos(5.46010584090 + 1581.7155307995*$t);
$X0 += 0.00000469097*cos(3.55737355039 + 2001.2001746747*$t);
$X0 += 0.00000361258*cos(4.90274855427 + 302.40859313851*$t);
$X0 += 0.00000345920*cos(5.01286731480 + 198.5650593945*$t);
$X0 += 0.00000350777*cos(5.86079095869 + 98.6561710411*$t);
$X0 += 0.00000335274*cos(1.03009229022 + 213.7553612426*$t);
$X0 += 0.00000335274*cos(3.85953387637 + 213.3304646004*$t);
$X0 += 0.00000367346*cos(5.91088479684 + 750.3474250169*$t);
$X0 += 0.00000369973*cos(5.39933070480 + 151.2914873264*$t);
$X0 += 0.00000399230*cos(1.04833113678 + 1059.1381127057*$t);
$X0 += 0.00000318144*cos(6.15035386620 + 228.5207664485*$t);
$X0 += 0.00000315586*cos(5.68724533460 + 831.6119232661*$t);
$X0 += 0.00000337834*cos(0.66798086530 + 175.40987728371*$t);
$X0 += 0.00000313433*cos(3.54547785742 + 2.20386307129*$t);
$X0 += 0.00000330040*cos(1.38038349450 + 276.79117625789*$t);
$X0 += 0.00000383783*cos(2.57160924287 + 56.3785338191*$t);
$X0 += 0.00000350135*cos(4.75975448170 + 114.38229196601*$t);
$X0 += 0.00000401239*cos(4.28930925743 + 178.11819026941*$t);
$X0 += 0.00000404631*cos(6.03696917524 + 1479.11039154791*$t);
$X0 += 0.00000404539*cos(1.52309497166 + 311.9552664791*$t);
$X0 += 0.00000304876*cos(6.11535489175 + 195.38366565681*$t);
$X0 += 0.00000289344*cos(4.48279316993 + 192.2022719191*$t);
$X0 += 0.00000270250*cos(5.14035236650 + 636.2089505344*$t);
$X0 += 0.00000271661*cos(1.28934639885 + 278.76328393321*$t);
$X0 += 0.00000283573*cos(0.04390160982 + 191.45151239371*$t);
$X0 += 0.00000294112*cos(1.97767959737 + 1162.23088692429*$t);
$X0 += 0.00000266932*cos(5.65493346800 + 205.46615807421*$t);
$X0 += 0.00000269475*cos(2.14597987484 + 327.68138740401*$t);
$X0 += 0.00000348053*cos(0.61890667474 + 248.9676355736*$t);
$X0 += 0.00000296599*cos(1.51525625285 + 10.538758222*$t);
$X0 += 0.00000252084*cos(1.67555502838 + 213.80354535241*$t);
$X0 += 0.00000252084*cos(3.21407113821 + 213.28228049061*$t);
$X0 += 0.00000250282*cos(2.61655820302 + 433.46792039329*$t);
$X0 += 0.00000294321*cos(2.01870159642 + 106.5179854398*$t);
$X0 += 0.00000270973*cos(4.53462056041 + 1044.9110187041*$t);
$X0 += 0.00000263820*cos(3.76320728541 + 63.9797157869*$t);
$X0 += 0.00000238275*cos(5.91316475830 + 1574.6019837987*$t);
$X0 += 0.00000305244*cos(1.10529286976 + 483.4643596621*$t);
$X0 += 0.00000241411*cos(5.74870980326 + 221.61966776881*$t);
$X0 += 0.00000314980*cos(4.37056119892 + 479.044571432*$t);
$X0 += 0.00000223277*cos(4.01771641783 + 13.9832765181*$t);
$X0 += 0.00000292846*cos(3.86376968180 + 424.39432780471*$t);
$X0 += 0.00000304942*cos(1.75360932249 + 6283.3196674749*$t);
$X0 += 0.00000237167*cos(4.96019200454 + 235.6343134493*$t);
$X0 += 0.00000240608*cos(5.75032033143 + 275.7943385166*$t);
$X0 += 0.00000263455*cos(5.51056104098 + 70.6056278207*$t);
$X0 += 0.00000211236*cos(0.02154252782 + 544.1618765797*$t);
$X0 += 0.00000205878*cos(4.46555623121 + 842.3944989716*$t);
$X0 += 0.00000282395*cos(3.56598534931 + 404.7506078317*$t);
$X0 += 0.00000203077*cos(4.47228022052 + 2104.2929488933*$t);
$X0 += 0.00000267955*cos(3.49559055839 + 121.4958389668*$t);
$X0 += 0.00000238411*cos(4.99775321682 + 138.2736793872*$t);
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$X0 += 0.00000002701*cos(5.31018762949 + 300.854684461*$t);
$X0 += 0.00000002653*cos(0.61839059390 + 56.8661687861*$t);
$X0 += 0.00000002732*cos(4.84630107056 + 244.30176912761*$t);
$X0 += 0.00000002275*cos(3.01865971091 + 4002.64416683289*$t);
$X0 += 0.00000002952*cos(2.31378455663 + 645.77017809*$t);
$X0 += 0.00000002509*cos(4.52000559703 + 125.42799222991*$t);
$X0 += 0.00000002253*cos(2.22689163450 + 310.41591201661*$t);
$X0 += 0.00000002632*cos(5.22086889296 + 416.79314583689*$t);
$X0 += 0.00000002307*cos(5.65143265211 + 3164.1625140495*$t);
$X0 += 0.00000002532*cos(5.13544500097 + 90.3187837629*$t);
$X0 += 0.00000002434*cos(2.93786049007 + 769.0973731126*$t);
$X0 += 0.00000002819*cos(4.33639017787 + 34.9202727377*$t);
$X0 += 0.00000002827*cos(5.81289553813 + 782.59075393131*$t);
$X0 += 0.00000002409*cos(6.23011689079 + 621.4942215658*$t);
$X0 += 0.00000002533*cos(5.04860084233 + 631.54308408841*$t);
$X0 += 0.00000002542*cos(2.08891387679 + 176.63371756111*$t);
$X0 += 0.00000002171*cos(0.62533559840 + 1891.4814884223*$t);
$X0 += 0.00000002552*cos(1.71107443815 + 12566.3955174663*$t);
$X0 += 0.00000002811*cos(1.38980153585 + 641.62557650581*$t);
$X0 += 0.00000002910*cos(4.77695576046 + 330.9658470057*$t);
$X0 += 0.00000002345*cos(5.85946991886 + 2104.7805838603*$t);
$X0 += 0.00000002188*cos(5.37105971182 + 1457.2821155785*$t);
$X0 += 0.00000002591*cos(0.63794997691 + 170.41394243761*$t);
$X0 += 0.00000002615*cos(0.54729482995 + 143.6903053586*$t);
$X0 += 0.00000002434*cos(0.55328244480 + 183.486632131*$t);
$X0 += 0.00000003003*cos(0.06003858313 + 739.30172475301*$t);
$X0 += 0.00000002177*cos(2.60567333935 + 67.6366824041*$t);
$X0 += 0.00000002774*cos(1.24195655197 + 1048.58004740881*$t);
$X0 += 0.00000002462*cos(5.75946440696 + 247.2707145442*$t);
$X0 += 0.00000002386*cos(4.37257867425 + 430.98660994371*$t);
$X0 += 0.00000002988*cos(4.23764191275 + 1802.12817323829*$t);
$X0 += 0.00000002810*cos(5.72676129521 + 140.721359942*$t);
$X0 += 0.00000002255*cos(0.26165543800 + 6681.46867088311*$t);
$X0 += 0.00000002483*cos(5.73996136268 + 375.9517972134*$t);
$X0 += 0.00000002123*cos(0.34275870459 + 610.93615626891*$t);
$X0 += 0.00000002154*cos(1.01602323535 + 444.1074837469*$t);
$X0 += 0.00000002497*cos(0.09006336245 + 17.91542978119*$t);
$X0 += 0.00000002073*cos(5.08154035810 + 218.4719039259*$t);
$X0 += 0.00000002063*cos(4.77672198594 + 616.56523056141*$t);
$X0 += 0.00000002250*cos(5.37793469323 + 366.2875037938*$t);
$X0 += 0.00000002750*cos(1.30459159563 + 485.63685357099*$t);
$X0 += 0.00000002252*cos(2.78563182902 + 49.26498681829*$t);
$X0 += 0.00000002813*cos(0.73865142296 + 837.4534458797*$t);
$X0 += 0.00000002062*cos(0.67146633927 + 2634.47154895491*$t);
$X0 += 0.00000002822*cos(3.09009791052 + 162.6527017754*$t);
$X0 += 0.00000002611*cos(0.55025625817 + 927.5911504839*$t);
$X0 += 0.00000002212*cos(5.64460551330 + 193.4115579815*$t);
$X0 += 0.00000002182*cos(5.06007050383 + 335.38563523581*$t);
$X0 += 0.00000002403*cos(2.26991708124 + 452.4448710251*$t);
$X0 += 0.00000002564*cos(3.29999345582 + 427.73578023681*$t);
$X0 += 0.00000002111*cos(5.24419959900 + 422.6974067753*$t);
$X0 += 0.00000002308*cos(3.09970342539 + 155.2236405895*$t);
$X0 += 0.00000002054*cos(1.10667438189 + 883.5513617802*$t);
$X0 += 0.00000002713*cos(0.18767262914 + 6.3484646555*$t);
$X0 += 0.00000002692*cos(2.83455718298 + 1040.97886544099*$t);
$X0 += 0.00000002007*cos(3.46492872207 + 529.1840230527*$t);
$X0 += 0.00000002282*cos(4.82626097470 + 173.9254045754*$t);
$X0 += 0.00000002783*cos(3.97708739470 + 165.3610147611*$t);
$X0 += 0.00000002346*cos(5.96960035551 + 447.448936179*$t);
$X0 += 0.00000002376*cos(1.10753711310 + 945.48727319021*$t);
$X0 += 0.00000002081*cos(2.10189023227 + 90.57941619379*$t);
$X0 += 0.00000002489*cos(5.97615262196 + 2487.1722274643*$t);
$X0 += 0.00000002124*cos(0.24199244027 + 133.34468838281*$t);
$X0 += 0.00000002000*cos(1.71637966221 + 419.1926422819*$t);
$X0 += 0.00000001998*cos(1.38456498657 + 518.62844988331*$t);
$X0 += 0.00000001969*cos(0.87882959914 + 530.68554210351*$t);
$X0 += 0.00000002467*cos(1.16140871474 + 429.81095377611*$t);
$X0 += 0.00000001955*cos(2.64714107906 + 105.03351273151*$t);
$X0 += 0.00000002054*cos(4.07410590523 + 3789.34507139489*$t);
$X0 += 0.00000002425*cos(4.28534276753 + 180.40581212981*$t);
$X0 += 0.00000001995*cos(5.64222397445 + 409.5765329721*$t);
$X0 += 0.00000002035*cos(4.31478927336 + 437.40007365639*$t);
$X0 += 0.00000001990*cos(1.20144466178 + 2854.3965564267*$t);
$X0 += 0.00000002449*cos(3.51585269206 + 213.00709384469*$t);
$X0 += 0.00000002354*cos(5.70604510094 + 657.4065791849*$t);
$X0 += 0.00000002466*cos(1.21196311089 + 421.6885069465*$t);
$X0 += 0.00000001932*cos(3.95236750027 + 1062.80714141041*$t);
$X0 += 0.00000002448*cos(6.06475548762 + 205.98991506349*$t);
$X0 += 0.00000001912*cos(4.86893514364 + 419.28901050149*$t);
$X0 += 0.00000002647*cos(6.01524298699 + 747.1660312792*$t);
$X0 += 0.00000001873*cos(5.39710784329 + 345.08987514331*$t);
$X0 += 0.00000002199*cos(4.03618137033 + 681.7856015731*$t);
$X0 += 0.00000002386*cos(4.15979534815 + 25234.46294233869*$t);
$X0 += 0.00000001886*cos(4.74856771776 + 1096.8504572182*$t);
$X0 += 0.00000002200*cos(3.67398938648 + 784.28767496071*$t);
$X0 += 0.00000001859*cos(1.27634409007 + 535.6669227346*$t);
$X0 += 0.00000002123*cos(4.59517360138 + 418.2776185452*$t);
$X0 += 0.00000002326*cos(5.90565481193 + 166.58485503849*$t);
$X0 += 0.00000002007*cos(6.24913643216 + 527.01402127131*$t);
$X0 += 0.00000002162*cos(2.02542462393 + 420.2040342382*$t);
$X0 += 0.00000002185*cos(3.86722734363 + 110.189506272*$t);
$X0 += 0.00000002564*cos(0.08752711773 + 425.9482364822*$t);
$X0 += 0.00000001976*cos(3.27975163184 + 102.3276918733*$t);
$X0 += 0.00000001951*cos(3.80946898193 + 168.2963302829*$t);
$X0 += 0.00000001965*cos(2.72529355918 + 39.9162075838*$t);
$X0 += 0.00000001953*cos(4.34770725760 + 116.07921299541*$t);
$X0 += 0.00000002118*cos(0.16994068938 + 409.4335206202*$t);
$X0 += 0.00000002542*cos(0.28051618477 + 355.02935520881*$t);
$X0 += 0.00000002294*cos(5.31857052688 + 181.08713568601*$t);
$X0 += 0.00000002378*cos(0.97161359133 + 385.3005764479*$t);
$X0 += 0.00000001807*cos(4.30830792029 + 275.5818901955*$t);
$X0 += 0.00000001833*cos(2.25943126416 + 267.8776423637*$t);
$X0 += 0.00000002302*cos(5.74355401552 + 43.5328466618*$t);
$X0 += 0.00000002098*cos(0.08769001353 + 253.16042126761*$t);
$X0 += 0.00000002063*cos(5.99370738678 + 177.36743074401*$t);
$X0 += 0.00000002261*cos(1.40921864289 + 635.94831810351*$t);
$X0 += 0.00000002208*cos(0.06326079599 + 1194.21109128031*$t);
$X0 += 0.00000002053*cos(3.72658018441 + 103.37022159689*$t);
$X0 += 0.00000001966*cos(6.03016819317 + 835.5440765292*$t);
$X0 += 0.00000002346*cos(0.23030073846 + 222.6165055101*$t);
$X0 += 0.00000001855*cos(3.60752296582 + 23.1383671634*$t);
$X0 += 0.00000001855*cos(3.60752296582 + 22.6507321964*$t);
$X0 += 0.00000002017*cos(4.33634384614 + 243.599193712*$t);
$X0 += 0.00000002346*cos(5.76125045506 + 2957.9769656123*$t);
$X0 += 0.00000001781*cos(1.54883325886 + 220.9170923532*$t);
$X0 += 0.00000001781*cos(0.19920025414 + 206.1687334898*$t);
$X0 += 0.00000001851*cos(2.90153472874 + 1107.8961574821*$t);
$X0 += 0.00000001906*cos(0.30653739166 + 586.06949891369*$t);
$X0 += 0.00000002083*cos(6.04860095971 + 1037.7974717033*$t);
$X0 += 0.00000002271*cos(6.07739006315 + 234.0379661564*$t);
$X0 += 0.00000002271*cos(5.09542141062 + 193.0478596866*$t);
$X0 += 0.00000002373*cos(5.71475634706 + 281.4234128091*$t);
$X0 += 0.00000001873*cos(1.44953658425 + 1084.0047700609*$t);
$X0 += 0.00000002113*cos(4.95085993537 + 671.1605924345*$t);
$X0 += 0.00000001854*cos(5.40160586575 + 614.38067456499*$t);
$X0 += 0.00000001766*cos(0.87455416846 + 2.6769438233*$t);
$X0 += 0.00000001774*cos(3.12295108906 + 220.39582749141*$t);
$X0 += 0.00000001774*cos(4.90826773112 + 206.6899983516*$t);
$X0 += 0.00000002018*cos(2.80222834013 + 250.45210828191*$t);
$X0 += 0.00000001877*cos(0.86746878520 + 35.18090516859*$t);
$X0 += 0.00000002293*cos(6.18682503815 + 912.722679414*$t);
$X0 += 0.00000001775*cos(5.64171842529 + 228.7332147696*$t);
$X0 += 0.00000001775*cos(2.38950039489 + 198.3526110734*$t);
$X0 += 0.00000001908*cos(4.75541799866 + 3377.4616094875*$t);
$X0 += 0.00000001924*cos(0.05325859053 + 534.1275682721*$t);
$X0 += 0.00000001740*cos(3.73739180897 + 3362.74688051889*$t);
$X0 += 0.00000002154*cos(0.40104075464 + 666.96780674051*$t);
$X0 += 0.00000002288*cos(0.41986539828 + 103.597224133*$t);
$X0 += 0.00000001725*cos(5.50474519843 + 132.85705341579*$t);
$X0 += 0.00000001785*cos(4.98048380603 + 346.43133549971*$t);
$X0 += 0.00000002259*cos(2.60980626460 + 700.4204217173*$t);
$X0 += 0.00000001692*cos(5.01579761567 + 212.5340130927*$t);
$X0 += 0.00000001721*cos(5.21316754257 + 306.34074640161*$t);
$X0 += 0.00000002004*cos(4.26613787249 + 256.6718834054*$t);
$X0 += 0.00000002083*cos(2.24513842982 + 5216.33655531789*$t);
$X0 += 0.00000002234*cos(5.54983389111 + 799.36859435169*$t);
$X0 += 0.00000001980*cos(2.56001945144 + 451.97179027311*$t);
$X0 += 0.00000002071*cos(3.58320191234 + 549.8940167362*$t);
$X0 += 0.00000002071*cos(2.05739621883 + 45.49040012211*$t);
$X0 += 0.00000001998*cos(0.36777686598 + 1171.63205578549*$t);
$X0 += 0.00000002007*cos(0.88372371587 + 1364.4842820984*$t);
$X0 += 0.00000001836*cos(2.92694247168 + 644.8069702435*$t);
$X0 += 0.00000001687*cos(5.33007261538 + 520.37355502251*$t);
$X0 += 0.00000001705*cos(2.31286181244 + 2222.1004520805*$t);
$X0 += 0.00000002080*cos(1.45709625903 + 587.450905758*$t);
$X0 += 0.00000002061*cos(5.09975785401 + 337.5581291447*$t);
$X0 += 0.00000001674*cos(2.74515959016 + 207.6386519831*$t);
$X0 += 0.00000001723*cos(1.32784221906 + 6290.4332144757*$t);
$X0 += 0.00000001760*cos(2.25500156442 + 12.28635548869*$t);
$X0 += 0.00000001697*cos(4.20915600472 + 552.34169729099*$t);
$X0 += 0.00000001676*cos(2.04112487415 + 41.08516610701*$t);
$X0 += 0.00000001715*cos(2.13305723286 + 133.86844537209*$t);
$X0 += 0.00000001707*cos(2.05213240355 + 98.6012892869*$t);
$X0 += 0.00000001846*cos(0.24646975759 + 5849.1202946311*$t);
$X0 += 0.00000001707*cos(1.11053782306 + 895.0846970111*$t);
$X0 += 0.00000001821*cos(1.68122578438 + 9779.32999085069*$t);
$X0 += 0.00000002189*cos(0.22703640405 + 66.9486612035*$t);
$X0 += 0.00000002014*cos(5.22602330033 + 546.71262299849*$t);
$X0 += 0.00000001781*cos(1.68206567806 + 9772.21644384989*$t);
$X0 += 0.00000001685*cos(2.77209660580 + 10220.6429106953*$t);
$X0 += 0.00000001942*cos(0.62509516046 + 246.68001371321*$t);
$X0 += 0.00000002001*cos(2.79560236728 + 3.94896821049*$t);
$X0 += 0.00000001626*cos(5.14783884729 + 624.1543504417*$t);
$X0 += 0.00000001942*cos(3.67591631329 + 9146.54625153749*$t);
$X0 += 0.00000001802*cos(2.72673271293 + 1389.3509394536*$t);
$X0 += 0.00000001613*cos(3.84799104836 + 1144.0716396596*$t);
$X0 += 0.00000002160*cos(6.02089758599 + 336.5949212982*$t);
$X0 += 0.00000002090*cos(0.77231653699 + 629.35852809199*$t);
$X0 += 0.00000001968*cos(3.13421198037 + 118.3144452291*$t);
$X0 += 0.00000001822*cos(5.19742739470 + 1009.22317149361*$t);
$X0 += 0.00000001611*cos(0.79920795326 + 347.16754081009*$t);
$X0 += 0.00000001728*cos(1.00799863461 + 1091.3814416201*$t);
$X0 += 0.00000002055*cos(3.93160223679 + 1372.3485886246*$t);
$X0 += 0.00000001569*cos(4.53671161147 + 122.71967924421*$t);
$X0 += 0.00000001542*cos(5.32956278183 + 1166.1630401874*$t);
$X0 += 0.00000001878*cos(5.27282154972 + 133.82026126229*$t);
$X0 += 0.00000001628*cos(3.80471189414 + 46.22660543249*$t);
$X0 += 0.00000001987*cos(5.87487529487 + 913.5070688342*$t);
$X0 += 0.00000001542*cos(0.20693930936 + 551.3448595497*$t);
$X0 += 0.00000001643*cos(4.14805608546 + 196.3805033981*$t);
$X0 += 0.00000001715*cos(5.05123310391 + 709.29362807231*$t);
$X0 += 0.00000001803*cos(3.56272450751 + 58.0754548485*$t);
$X0 += 0.00000001620*cos(0.62227051964 + 700.2079733962*$t);
$X0 += 0.00000001584*cos(5.28418181170 + 3767.4544350593*$t);
$X0 += 0.00000002027*cos(3.91807332340 + 2118.5200428949*$t);
$X0 += 0.00000001660*cos(4.88325679293 + 318.43567403349*$t);
$X0 += 0.00000001695*cos(3.99389886352 + 327.19375243699*$t);
$X0 += 0.00000001617*cos(2.39206154532 + 83.6234357599*$t);
$X0 += 0.00000001522*cos(5.52616009652 + 406.39513923441*$t);
$X0 += 0.00000001847*cos(2.06358167839 + 488.6057989876*$t);
$X0 += 0.00000001505*cos(4.00358265141 + 447.28887748461*$t);
$X0 += 0.00000001747*cos(0.03102392120 + 173.6984020393*$t);
$X0 += 0.00000001511*cos(2.76524724862 + 414.09938706621*$t);
$X0 += 0.00000001932*cos(1.42317332409 + 40.59753113999*$t);
$X0 += 0.00000001512*cos(0.91625215222 + 1748.2810787631*$t);
$X0 += 0.00000001775*cos(2.24504797682 + 2707.58486990309*$t);
$X0 += 0.00000001830*cos(0.63475720612 + 259.7527034066*$t);
$X0 += 0.00000001574*cos(3.93642970138 + 322.3678272966*$t);
$X0 += 0.00000001477*cos(2.05303400646 + 355.2418035299*$t);
$X0 += 0.00000001498*cos(1.98604024579 + 174.9367965317*$t);
$X0 += 0.00000001487*cos(4.04993820708 + 141.4550731249*$t);
$X0 += 0.00000001676*cos(5.43783308850 + 3693.36584417709*$t);
$X0 += 0.00000001461*cos(1.38524899881 + 105.13657859549*$t);
$X0 += 0.00000001692*cos(3.46209472083 + 679.4979797127*$t);
$X0 += 0.00000001835*cos(5.85414378465 + 245.99869015701*$t);
$X0 += 0.00000001449*cos(5.42328914768 + 1159.0494931866*$t);
$X0 += 0.00000001661*cos(1.72245289890 + 736.59590389479*$t);
$X0 += 0.00000001443*cos(3.36134760735 + 466.5143984598*$t);
$X0 += 0.00000001476*cos(5.38971328268 + 3480.5543837061*$t);
$X0 += 0.00000001645*cos(5.17910426695 + 249.71839509901*$t);
$X0 += 0.00000001496*cos(3.22754175149 + 77623.56832092509*$t);
$X0 += 0.00000001890*cos(3.64866692511 + 764.6439549877*$t);
$X0 += 0.00000001480*cos(3.14944647582 + 262.77653057739*$t);
$X0 += 0.00000001937*cos(3.47338953300 + 757.5640378817*$t);
$X0 += 0.00000001587*cos(0.32048665561 + 6.9179136271*$t);
$X0 += 0.00000001683*cos(4.01550009219 + 6503.7323099137*$t);
$X0 += 0.00000001770*cos(5.08423811097 + 482.5011518156*$t);
$X0 += 0.00000001735*cos(2.28799872431 + 2435.3995475185*$t);
$X0 += 0.00000001457*cos(3.01927816891 + 256.18424843839*$t);
$X0 += 0.00000001471*cos(0.70642591223 + 1453.08683775701*$t);
$X0 += 0.00000001613*cos(1.78409994223 + 271.8621852535*$t);
$X0 += 0.00000001848*cos(2.55365760167 + 419.94090967981*$t);
$X0 += 0.00000001954*cos(4.83592161734 + 145.387226388*$t);
$X0 += 0.00000001662*cos(0.44336441806 + 25454.87558477749*$t);
$X0 += 0.00000001420*cos(6.11955516870 + 1354.18934135989*$t);
$X0 += 0.00000001390*cos(0.11880365257 + 544.7525774107*$t);
$X0 += 0.00000001679*cos(5.97438658773 + 285.1431177511*$t);
$X0 += 0.00000001607*cos(0.73844026178 + 544.2649424437*$t);
$X0 += 0.00000001536*cos(5.89479692757 + 3273.8812003019*$t);
$X0 += 0.00000001536*cos(5.89479692757 + 3274.36883526891*$t);
$X0 += 0.00000001587*cos(5.49922746524 + 148.5831743407*$t);
$X0 += 0.00000001794*cos(2.66160697296 + 754.5950924651*$t);
$X0 += 0.00000001407*cos(0.85219523429 + 316.1144222783*$t);
$X0 += 0.00000001658*cos(2.48037578229 + 415.0625949127*$t);
$X0 += 0.00000001512*cos(4.28907569036 + 428.4865397622*$t);
$X0 += 0.00000001501*cos(6.18750341180 + 5746.0275204125*$t);
$X0 += 0.00000001696*cos(2.90084876328 + 59.038662695*$t);
$X0 += 0.00000001590*cos(0.23710525653 + 349.6127292374*$t);
$X0 += 0.00000001827*cos(0.61806717369 + 230.3207533419*$t);
$X0 += 0.00000001891*cos(5.00801645038 + 1165.6392831981*$t);
$X0 += 0.00000001759*cos(4.58582597435 + 200.27902676641*$t);
$X0 += 0.00000001759*cos(3.44539284583 + 226.80679907661*$t);
$X0 += 0.00000001677*cos(4.23577119544 + 50.15875869559*$t);
$X0 += 0.00000001384*cos(4.27737882618 + 1176.9456158929*$t);
$X0 += 0.00000001600*cos(5.43870126795 + 10433.9420061333*$t);
$X0 += 0.00000001491*cos(1.31312182045 + 9676.23721663209*$t);
$X0 += 0.00000001400*cos(0.26007468679 + 1950.5344739372*$t);
$X0 += 0.00000001334*cos(0.72637373445 + 301.65783361311*$t);
$X0 += 0.00000001377*cos(0.86428517620 + 243.29037717131*$t);
$X0 += 0.00000001377*cos(4.02534099039 + 183.79544867171*$t);
$X0 += 0.00000001454*cos(3.28359870251 + 330.3751461747*$t);
$X0 += 0.00000001421*cos(4.52961540751 + 469.9709788434*$t);
$X0 += 0.00000001426*cos(3.01357344337 + 934.4415729263*$t);
$X0 += 0.00000001356*cos(5.87449410633 + 210.1345166477*$t);
$X0 += 0.00000001314*cos(2.71429002268 + 415.04804069769*$t);
$X0 += 0.00000001338*cos(3.51731603639 + 118.6299594142*$t);
$X0 += 0.00000001453*cos(0.57533096444 + 679.8134938978*$t);
$X0 += 0.00000001470*cos(3.81098724259 + 321.3015535861*$t);
$X0 += 0.00000001314*cos(2.08783972120 + 878.08234618209*$t);
$X0 += 0.00000001715*cos(6.08299477871 + 79.43065006591*$t);
$X0 += 0.00000001305*cos(2.73772701133 + 238.18505986809*$t);
$X0 += 0.00000001382*cos(0.52411582569 + 718.8548556279*$t);
$X0 += 0.00000001464*cos(1.92663592308 + 397.9001853893*$t);
$X0 += 0.00000001758*cos(3.53136981753 + 452.70550345601*$t);
$X0 += 0.00000001356*cos(4.56256930200 + 280.9357778421*$t);
$X0 += 0.00000001790*cos(2.61933789345 + 1357.3707350976*$t);
$X0 += 0.00000001578*cos(5.37892573514 + 383.5529791812*$t);
$X0 += 0.00000001464*cos(4.41309699814 + 360.1371646395*$t);
$X0 += 0.00000001375*cos(0.61137430521 + 535.56385687061*$t);
$X0 += 0.00000001620*cos(0.47405441337 + 109.0687318586*$t);
$X0 += 0.00000001663*cos(4.95313251291 + 102.73708215049*$t);
$X0 += 0.00000001314*cos(0.02379514725 + 1670.5812110165*$t);
$X0 += 0.00000001452*cos(0.95390444904 + 316.896319571*$t);
$X0 += 0.00000001302*cos(4.09749727380 + 116.6699138264*$t);
$X0 += 0.00000001421*cos(2.52300558725 + 166.84548746939*$t);
$X0 += 0.00000001339*cos(2.72026084734 + 5863.3473886327*$t);
$X0 += 0.00000001685*cos(6.07730679616 + 214.53975066279*$t);
$X0 += 0.00000001458*cos(3.04961044313 + 9352.73179997469*$t);
$X0 += 0.00000001341*cos(0.47332489447 + 1183.16539101641*$t);
$X0 += 0.00000001300*cos(3.88742356206 + 120.6020670895*$t);
$X0 += 0.00000001281*cos(4.57888575454 + 1108.3837924491*$t);
$X0 += 0.00000001652*cos(5.63517331024 + 165.8486497281*$t);
$X0 += 0.00000001259*cos(0.41488838005 + 2950.8634186115*$t);
$X0 += 0.00000001508*cos(1.65590855031 + 763.1931121742*$t);
$X0 += 0.00000001251*cos(0.56339346105 + 1055.2059594426*$t);
$X0 += 0.00000001416*cos(0.73841384971 + 1063.55790093581*$t);
$X0 += 0.00000001273*cos(0.60463815018 + 2207.8733580789*$t);
$X0 += 0.00000001755*cos(0.25702827395 + 557.75832326239*$t);
$X0 += 0.00000001665*cos(0.62988003125 + 163.82166029861*$t);
$X0 += 0.00000001330*cos(2.61784978340 + 156.02678974161*$t);
$X0 += 0.00000001472*cos(3.64179989725 + 346.1561488538*$t);
$X0 += 0.00000001472*cos(3.64179989725 + 346.64378382081*$t);
$X0 += 0.00000001283*cos(2.09085692852 + 4215.94326227089*$t);
$X0 += 0.00000001564*cos(1.45141699498 + 3391.68870348911*$t);
$X0 += 0.00000001232*cos(2.01286113512 + 767.1252654373*$t);
$X0 += 0.00000001339*cos(3.55159228628 + 419.7620912535*$t);
$X0 += 0.00000001471*cos(5.32263840566 + 2693.3577759015*$t);
$X0 += 0.00000001265*cos(3.33952901594 + 212.3045184291*$t);
$X0 += 0.00000001355*cos(3.06105542076 + 418.71956152989*$t);
$X0 += 0.00000001236*cos(1.64676624453 + 409.6795988361*$t);
$X0 += 0.00000001263*cos(4.89869307825 + 2090.06585489169*$t);
$X0 += 0.00000001580*cos(4.87533968051 + 1477.8383671607*$t);
$X0 += 0.00000001310*cos(5.18861487187 + 1012.66768978969*$t);
$X0 += 0.00000001245*cos(5.08294427560 + 748.9660181726*$t);
$X0 += 0.00000001565*cos(3.90450910087 + 1268.9926898476*$t);
$X0 += 0.00000001267*cos(5.32574708258 + 115.11600514891*$t);
$X0 += 0.00000001279*cos(1.12013287366 + 217.9481469366*$t);
$X0 += 0.00000001279*cos(0.62790063934 + 209.13767890641*$t);
$X0 += 0.00000001237*cos(3.25551290814 + 4112.8504880523*$t);
$X0 += 0.00000001208*cos(1.32712565413 + 116.12739710521*$t);
$X0 += 0.00000001358*cos(4.00471985016 + 973.7984488415*$t);
$X0 += 0.00000001406*cos(5.51451351576 + 959.45373476091*$t);
$X0 += 0.00000001365*cos(0.53588394734 + 988.28866740149*$t);
$X0 += 0.00000001189*cos(4.92462455483 + 1378.3052391897*$t);
$X0 += 0.00000001200*cos(0.49702267118 + 614.868309532*$t);
$X0 += 0.00000001537*cos(3.54508824305 + 170.72945662269*$t);
$X0 += 0.00000001449*cos(3.08273741016 + 1020.2688717575*$t);
$X0 += 0.00000001181*cos(1.33018054312 + 372.77040347569*$t);
$X0 += 0.00000001227*cos(5.69576717158 + 2421.1724535169*$t);
$X0 += 0.00000001504*cos(2.57217010618 + 2810.6776441217*$t);
$X0 += 0.00000001191*cos(1.49579907580 + 487.3965129252*$t);
$X0 += 0.00000001601*cos(1.72354458106 + 1151.1851866604*$t);
$X0 += 0.00000001207*cos(0.96898843462 + 3170.78842608329*$t);
$X0 += 0.00000001288*cos(4.69433760178 + 3149.44778508089*$t);
$X0 += 0.00000001277*cos(0.27655645720 + 217.24806364849*$t);
$X0 += 0.00000001276*cos(2.61558896767 + 94.7722018878*$t);
$X0 += 0.00000001451*cos(1.05411548466 + 514.95692905111*$t);
$X0 += 0.00000001451*cos(1.05411548466 + 514.46929408409*$t);
$X0 += 0.00000001235*cos(3.43297201820 + 173.43776960839*$t);
$X0 += 0.00000001353*cos(3.76027139434 + 530.0466571627*$t);
$X0 += 0.00000001464*cos(0.02257079027 + 746.15463932291*$t);
$X0 += 0.00000001246*cos(5.61078961339 + 424.8699006842*$t);
$X0 += 0.00000001236*cos(2.50843841662 + 1248.3857620281*$t);
$X0 += 0.00000001279*cos(0.03215301642 + 703.38936713389*$t);
$X0 += 0.00000001236*cos(4.30746328208 + 538.8483164723*$t);
$X0 += 0.00000001234*cos(4.16726551204 + 416.3200650849*$t);
$X0 += 0.00000001161*cos(1.82750814245 + 313.7149258333*$t);
$X0 += 0.00000001414*cos(1.60384951308 + 2648.6986429565*$t);
$X0 += 0.00000001177*cos(4.62142425135 + 643.5856220936*$t);
$X0 += 0.00000001187*cos(1.03828381736 + 1394.9800137461*$t);
$X0 += 0.00000001173*cos(1.60433079541 + 331.6135406671*$t);
$X0 += 0.00000001176*cos(2.90358611485 + 252.1490293113*$t);
$X0 += 0.00000001245*cos(4.65509615846 + 293.74113746021*$t);
$X0 += 0.00000001187*cos(3.72181414929 + 4105.7369410515*$t);
$X0 += 0.00000001274*cos(0.56033904615 + 165.10038233019*$t);
$X0 += 0.00000001391*cos(0.02309515967 + 5860.16599489499*$t);
$X0 += 0.00000001365*cos(5.22737241965 + 674.0813537413*$t);
$X0 += 0.00000001165*cos(1.16402753194 + 107.0417424291*$t);
$X0 += 0.00000001169*cos(1.54612792835 + 104.29979954861*$t);
$X0 += 0.00000001280*cos(2.60261684467 + 60.79832204921*$t);
$X0 += 0.00000001470*cos(0.46274502064 + 1147.7406683643*$t);
$X0 += 0.00000001243*cos(0.16760981697 + 945.7503977486*$t);
$X0 += 0.00000001211*cos(2.29834110056 + 271.05903610141*$t);
$X0 += 0.00000001378*cos(4.48082815431 + 880.26690217851*$t);
$X0 += 0.00000001141*cos(4.65662492035 + 1365.23504162379*$t);
$X0 += 0.00000001452*cos(3.82619301322 + 670.2522663422*$t);
$X0 += 0.00000001372*cos(3.12283015772 + 5852.3016883688*$t);
$X0 += 0.00000001152*cos(5.71979516304 + 253.2153030218*$t);
$X0 += 0.00000001145*cos(5.20900865265 + 3796.94625336271*$t);
$X0 += 0.00000001147*cos(5.23246594483 + 2048.1582325577*$t);
$X0 += 0.00000001139*cos(3.77606446333 + 227.81819103291*$t);
$X0 += 0.00000001139*cos(4.25515435685 + 199.26763481011*$t);
$X0 += 0.00000001350*cos(3.52660754473 + 25440.64849077589*$t);
$X0 += 0.00000001152*cos(5.11322028459 + 475.6000531359*$t);
$X0 += 0.00000001377*cos(0.50068712612 + 660.851097481*$t);
$X0 += 0.00000001324*cos(3.36678513643 + 101.3644840268*$t);
$X0 += 0.00000001189*cos(2.65397891656 + 1383.9343134822*$t);
$X0 += 0.00000001403*cos(3.67339271391 + 1699.0353990197*$t);
$X0 += 0.00000001177*cos(1.82821053485 + 303.3023650158*$t);
$X0 += 0.00000001164*cos(5.16928967595 + 1773.6739852351*$t);
$X0 += 0.00000001179*cos(5.67584375514 + 272.33775813299*$t);
$X0 += 0.00000001228*cos(6.14893570078 + 91.70019060721*$t);
$X0 += 0.00000001431*cos(3.53241753707 + 1467.3139317586*$t);
$X0 += 0.00000001142*cos(3.42129382875 + 656.9189442179*$t);
$X0 += 0.00000001157*cos(3.17352979808 + 469.6434025708*$t);
$X0 += 0.00000001157*cos(0.03193714449 + 470.1310375378*$t);
$X0 += 0.00000001459*cos(5.59118854590 + 1128.7782719475*$t);
$X0 += 0.00000001199*cos(3.32815503030 + 384.5161870277*$t);
$X0 += 0.00000001360*cos(6.23249225628 + 1560.3748897971*$t);
$X0 += 0.00000001399*cos(0.26308817006 + 1243.98302014049*$t);
$X0 += 0.00000001154*cos(3.90218563691 + 5539.8419719753*$t);
$X0 += 0.00000001290*cos(5.88751484616 + 1403.5780334552*$t);
$X0 += 0.00000001426*cos(0.71297202771 + 701.6924461045*$t);
$X0 += 0.00000001402*cos(5.49844037291 + 1112.3159457122*$t);
$X0 += 0.00000001097*cos(4.39996766325 + 735.6808801581*$t);
$X0 += 0.00000001431*cos(4.14934397552 + 388.9696051526*$t);
$X0 += 0.00000001187*cos(1.09475241758 + 6599.7115371315*$t);
$X0 += 0.00000001093*cos(6.27482624765 + 427.317581239*$t);
$X0 += 0.00000001537*cos(2.26997973747 + 2854.8841913937*$t);
$X0 += 0.00000001417*cos(0.74675814459 + 25557.96835899609*$t);
$X0 += 0.00000001238*cos(4.45159537738 + 559.94287925881*$t);
$X0 += 0.00000001473*cos(1.81109515353 + 2751.79141717511*$t);
$X0 += 0.00000001452*cos(2.08713835729 + 228.0331314815*$t);
$X0 += 0.00000001516*cos(5.88783767141 + 560.46663624809*$t);
$X0 += 0.00000001103*cos(4.63060901499 + 531.9405201482*$t);
$X0 += 0.00000001301*cos(1.44654929805 + 9790.37569111459*$t);
$X0 += 0.00000001099*cos(5.99645868304 + 527.929045008*$t);
$X0 += 0.00000001256*cos(1.98238644435 + 877.8192216237*$t);
$X0 += 0.00000001250*cos(3.85798606392 + 1226.45442019471*$t);
$X0 += 0.00000001113*cos(3.14740146804 + 124.18959773749*$t);
$X0 += 0.00000001072*cos(4.02039116236 + 206.2693072263*$t);
$X0 += 0.00000001072*cos(4.01082765782 + 220.8165186167*$t);
$X0 += 0.00000001335*cos(0.17870194529 + 121.0082039998*$t);
$X0 += 0.00000001282*cos(4.54628381109 + 9782.51138458839*$t);
$X0 += 0.00000001072*cos(0.62535496972 + 220.4964012279*$t);
$X0 += 0.00000001072*cos(1.12267854328 + 206.5894246151*$t);
$X0 += 0.00000001303*cos(3.69503246823 + 1096.48675892331*$t);
$X0 += 0.00000001397*cos(5.45476565968 + 1461.6848574661*$t);
$X0 += 0.00000001085*cos(2.72676641341 + 379.8839504765*$t);
$X0 += 0.00000001170*cos(2.12202833962 + 705.1008423783*$t);
$X0 += 0.00000001054*cos(3.95603977178 + 155.53915477459*$t);
$X0 += 0.00000001405*cos(4.62229591705 + 5436.7491977567*$t);
$X0 += 0.00000001097*cos(4.60268688107 + 476.56326098241*$t);
$X0 += 0.00000001241*cos(5.11295878390 + 2833.0559154243*$t);
$X0 += 0.00000001288*cos(0.42374008522 + 1340.8053429983*$t);
$X0 += 0.00000001129*cos(3.07767826513 + 1222.52226693161*$t);
$X0 += 0.00000001290*cos(0.79377005415 + 1082.2596649217*$t);
$X0 += 0.00000001166*cos(5.05925238169 + 2467.6428764329*$t);
$X0 += 0.00000001299*cos(5.43314879441 + 2509.5504987669*$t);
$X0 += 0.00000001321*cos(6.10687737458 + 9366.9588939763*$t);
$X0 += 0.00000001051*cos(4.35040361644 + 959.97749175019*$t);
$X0 += 0.00000001051*cos(4.35040361644 + 960.4651267172*$t);
$X0 += 0.00000001211*cos(2.80991523490 + 304.1055141679*$t);
$X0 += 0.00000001052*cos(3.86792125865 + 645.5577297689*$t);
$X0 += 0.00000001127*cos(0.31244064224 + 78477.25233764409*$t);
$X0 += 0.00000001258*cos(4.40841524052 + 5867.27954189579*$t);
$X0 += 0.00000001073*cos(2.88134377608 + 328.4845365561*$t);
$X0 += 0.00000001290*cos(4.48821585460 + 71.5688356672*$t);
$X0 += 0.00000001053*cos(4.63251123701 + 795.43644108859*$t);
$X0 += 0.00000001329*cos(5.03792511567 + 2740.7457169112*$t);
$X0 += 0.00000001352*cos(1.20612298463 + 1127.50624756031*$t);
$X0 += 0.00000001032*cos(5.79901826701 + 774.25336665311*$t);
$X0 += 0.00000001421*cos(0.04765558923 + 398.38782035631*$t);
$X0 += 0.00000001302*cos(0.47222793041 + 476.07562601539*$t);
$X0 += 0.00000001018*cos(1.52577563410 + 135.7923689376*$t);
$X0 += 0.00000001240*cos(0.29711496611 + 761.98382611181*$t);
$X0 += 0.00000001072*cos(4.40309497596 + 1257.9469895837*$t);
$X0 += 0.00000001044*cos(0.40386153641 + 304.36614659881*$t);
$X0 += 0.00000001166*cos(3.33113338762 + 613.6299150396*$t);
$X0 += 0.00000001025*cos(0.01753129634 + 121.59890483079*$t);
$X0 += 0.00000001321*cos(4.43670480817 + 323.48860171*$t);
$X0 += 0.00000001279*cos(4.51516906631 + 203.72105293501*$t);
$X0 += 0.00000001279*cos(3.51604975387 + 223.36477290801*$t);
$X0 += 0.00000001145*cos(6.17371704189 + 519.88592005549*$t);
$X0 += 0.00000001018*cos(2.91596221445 + 640.8918633229*$t);
$X0 += 0.00000001389*cos(5.24370269936 + 1115.7604640083*$t);
$X0 += 0.00000001343*cos(3.88682161226 + 108.26558270649*$t);
$X0 += 0.00000001195*cos(0.85808512318 + 99.1438060081*$t);
$X0 += 0.00000001008*cos(4.30738828647 + 102.5883243042*$t);
$X0 += 0.00000001143*cos(5.21944528509 + 256.3443071328*$t);
$X0 += 0.00000001019*cos(4.91718332635 + 6247.26929803929*$t);
$X0 += 0.00000001250*cos(5.68253927507 + 759.0148806952*$t);
$X0 += 0.00000001000*cos(2.13999178433 + 1939.4887736733*$t);
$X0 += 0.00000001110*cos(1.66567300271 + 1397.9489591627*$t);
$X0 += 0.00000001170*cos(1.26049852836 + 7.3909943791*$t);
$X0 += 0.00000001196*cos(4.77831019397 + 46.8173062635*$t);
$X0 += 0.00000001151*cos(2.51852068637 + 76.0222537921*$t);
$X0 += 0.00000001005*cos(5.76224230474 + 690.8591941617*$t);
$X0 += 0.00000001316*cos(1.32295596105 + 475.11241816889*$t);
$X0 += 0.00000000995*cos(4.20379456134 + 99.92819542829*$t);
$X0 += 0.00000001197*cos(1.26595437757 + 1392.5323331913*$t);
$X0 += 0.00000001110*cos(2.98882017733 + 523.2968084568*$t);
$X0 += 0.00000001088*cos(4.97175423832 + 824.23525170691*$t);
$X0 += 0.00000001015*cos(1.47228772360 + 634.98760238449*$t);
$X0 += 0.00000001012*cos(1.77286703845 + 689.86235642041*$t);
$X0 += 0.00000001381*cos(3.30442233560 + 97.4323307637*$t);
$X0 += 0.00000001276*cos(4.48973341413 + 465.7112493077*$t);
$X0 += 0.00000001233*cos(5.35220662775 + 1546.2908081474*$t);
$X0 += 0.00000001160*cos(6.23737046615 + 152.9884083558*$t);
$X0 += 0.00000001247*cos(3.58622778979 + 2434.9119125515*$t);
$X0 += 0.00000001201*cos(3.09828888291 + 528.71094230071*$t);
$X0 += 0.00000001045*cos(1.49017361423 + 608.0008407471*$t);
$X0 += 0.00000001034*cos(2.46164938759 + 540.49284787499*$t);
$X0 += 0.00000000988*cos(2.46330736551 + 967.8941879031*$t);
$X0 += 0.00000000973*cos(3.93273625700 + 173.38288785421*$t);
$X0 += 0.00000001081*cos(2.34160070624 + 560.9397170001*$t);
$X0 += 0.00000001105*cos(0.59883609919 + 227.7218228133*$t);
$X0 += 0.00000001105*cos(1.14919741381 + 199.3640030297*$t);
$X0 += 0.00000001022*cos(0.99655670520 + 599.40282103799*$t);
$X0 += 0.00000001176*cos(5.83186908907 + 9797.4892381154*$t);
$X0 += 0.00000001174*cos(0.61580453745 + 1680.87615175499*$t);
$X0 += 0.00000000980*cos(3.06958429681 + 944.99963822319*$t);
$X0 += 0.00000001194*cos(4.57575815213 + 725.0746307514*$t);
$X0 += 0.00000001045*cos(3.17246710740 + 343.49601997789*$t);
$X0 += 0.00000001227*cos(3.94543045845 + 1973.37663399041*$t);
$X0 += 0.00000001185*cos(2.30979572901 + 773.24197469681*$t);
$X0 += 0.00000001222*cos(3.21080779639 + 776.2109201134*$t);
$X0 += 0.00000000980*cos(2.09680719136 + 524.78128116509*$t);
$X0 += 0.00000001285*cos(2.51329534910 + 6.82154540749*$t);
$X0 += 0.00000001225*cos(2.82333756383 + 25344.66926355809*$t);
$X0 += 0.00000000985*cos(3.52739874813 + 913.24394427581*$t);
$X0 += 0.00000000995*cos(0.79227350270 + 557.2827503829*$t);
$X0 += 0.00000000983*cos(1.11328788816 + 550.3816517032*$t);
$X0 += 0.00000001005*cos(5.19307115578 + 301.17019864609*$t);
$X0 += 0.00000001208*cos(4.61381839173 + 2597.3785486837*$t);
$X0 += 0.00000000950*cos(2.91396525108 + 568.5408989679*$t);
$X0 += 0.00000001220*cos(4.63270249547 + 1458.71591204951*$t);
$X0 += 0.00000001171*cos(2.39322957185 + 2538.4923217371*$t);
$X0 += 0.00000001155*cos(1.80072310652 + 308.7713806139*$t);
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$X0 += 0.00000000716*cos(2.80780296922 + 4319.0360364895*$t);
$X0 += 0.00000000716*cos(5.94939562281 + 4319.5236714565*$t);
$X0 += 0.00000000797*cos(0.88312421788 + 529.9829666879*$t);
$X0 += 0.00000000729*cos(3.08861395930 + 1649.383582366*$t);
$X0 += 0.00000000803*cos(2.56866081755 + 151.0163006805*$t);
$X0 += 0.00000000765*cos(1.92150517901 + 1379.4621356254*$t);
$X0 += 0.00000000765*cos(5.06309783260 + 1379.9497705924*$t);
$X0 += 0.00000000749*cos(3.86728999613 + 785.772147669*$t);
$X0 += 0.00000000836*cos(4.09079447369 + 4010.24534880071*$t);
$X0 += 0.00000000727*cos(1.76200509604 + 608.1608994415*$t);
$X0 += 0.00000000727*cos(1.76200509604 + 608.64853440851*$t);
$X0 += 0.00000000719*cos(1.08122225861 + 467.68335698301*$t);
$X0 += 0.00000000709*cos(2.16805792847 + 103.5490400232*$t);
$X0 += 0.00000000709*cos(2.16805792847 + 103.0614050562*$t);
$X0 += 0.00000000920*cos(3.37948839250 + 870.7056746229*$t);
$X0 += 0.00000000716*cos(3.01984388520 + 664.78325074409*$t);
$X0 += 0.00000000857*cos(4.73776093669 + 2306.5463440674*$t);
$X0 += 0.00000000724*cos(4.70354725719 + 740.52556503041*$t);
$X0 += 0.00000000708*cos(4.72112546056 + 2431.4673942554*$t);
$X0 += 0.00000000706*cos(4.95679658990 + 102.63650841399*$t);
$X0 += 0.00000000706*cos(4.95679658990 + 103.12414338101*$t);
$X0 += 0.00000000824*cos(0.35265072853 + 1163.6817297378*$t);
$X0 += 0.00000000722*cos(3.07523457584 + 171.2170915897*$t);
$X0 += 0.00000000723*cos(0.74571067860 + 829.37669103239*$t);
$X0 += 0.00000000720*cos(1.80911156979 + 255.8687342533*$t);
$X0 += 0.00000000956*cos(1.61313021087 + 3068.1832868317*$t);
$X0 += 0.00000000800*cos(4.60599313494 + 279.72649177971*$t);
$X0 += 0.00000000800*cos(0.28363303165 + 147.3593340633*$t);
$X0 += 0.00000000868*cos(5.08886004770 + 669.4009330803*$t);
$X0 += 0.00000000769*cos(4.42409463602 + 3465.8396547375*$t);
$X0 += 0.00000000745*cos(4.41268882152 + 843.145258497*$t);
$X0 += 0.00000000848*cos(4.34921581475 + 103.3847758119*$t);
$X0 += 0.00000000703*cos(0.03980855697 + 4003.1318017999*$t);
$X0 += 0.00000000719*cos(2.96421431820 + 9988.69693302559*$t);
$X0 += 0.00000000818*cos(3.58195947060 + 311.48218572709*$t);
$X0 += 0.00000000901*cos(5.50487267537 + 937.8860912224*$t);
$X0 += 0.00000000783*cos(0.40400095682 + 199.83708378171*$t);
$X0 += 0.00000000783*cos(1.34403255618 + 227.24874206131*$t);
$X0 += 0.00000000909*cos(5.35487801471 + 4009.7577138337*$t);
$X0 += 0.00000000711*cos(0.19813010381 + 457.3738620295*$t);
$X0 += 0.00000000705*cos(1.55599502521 + 5653.98044645779*$t);
$X0 += 0.00000000712*cos(4.50433897135 + 354.2810878109*$t);
$X0 += 0.00000000733*cos(4.93048865178 + 37.6285857234*$t);
$X0 += 0.00000000708*cos(2.84637541601 + 840.6975779422*$t);
$X0 += 0.00000000708*cos(5.98796806961 + 840.2099429752*$t);
$X0 += 0.00000000695*cos(4.51136204527 + 812.70191647599*$t);
$X0 += 0.00000000695*cos(4.51136204527 + 813.189551443*$t);
$X0 += 0.00000000736*cos(1.20053248385 + 403.9474586796*$t);
$X0 += 0.00000000733*cos(0.72827400906 + 182.0357893175*$t);
$X0 += 0.00000000836*cos(3.44633331041 + 2331.8191383329*$t);
$X0 += 0.00000000928*cos(2.16436836139 + 842.13386654071*$t);
$X0 += 0.00000000768*cos(5.27501406783 + 1460.2003847578*$t);
$X0 += 0.00000000685*cos(5.86089797553 + 455.29619636271*$t);
$X0 += 0.00000000792*cos(1.62315871295 + 5422.5221037551*$t);
$X0 += 0.00000000837*cos(5.42340126188 + 570.7761312016*$t);
$X0 += 0.00000000682*cos(4.88563990270 + 3693.8534791441*$t);
$X0 += 0.00000000752*cos(2.13635874109 + 413.34862754081*$t);
$X0 += 0.00000000817*cos(1.53257391407 + 391.73279989249*$t);
$X0 += 0.00000000681*cos(2.40403440268 + 458.33457774851*$t);
$X0 += 0.00000000803*cos(5.00204662708 + 418.49006686629*$t);
$X0 += 0.00000000681*cos(0.38545629971 + 414.5749599457*$t);
return $X0;
}
function Saturn_X1($t) // 1023 terms of order 1
{
$X1 = 0.09285877988*cos(0.61678993503 + 0.2438174835*$t);
$X1 += 0.03086501680*cos(4.27493632359 + 426.8420083595*$t);
$X1 += 0.02728479923*cos(5.84476389020 + 206.42936592071*$t);
$X1 += 0.02644990371*cos(5.33256382404 + 220.6564599223*$t);
$X1 += 0.00629201988*cos(0.32457757988 + 7.3573644843*$t);
$X1 += 0.00256626023*cos(3.52453971595 + 640.1411037975*$t);
$X1 += 0.00312353889*cos(4.82956308970 + 419.72846135871*$t);
$X1 += 0.00189297041*cos(4.48614588896 + 433.9555553603*$t);
$X1 += 0.00204465020*cos(1.07744722386 + 213.5429129215*$t);
$X1 += 0.00118113185*cos(1.16350724193 + 110.45013870291*$t);
$X1 += 0.00067024295*cos(3.73239360544 + 316.6356871401*$t);
$X1 += 0.00066948413*cos(5.20221291915 + 227.77000692311*$t);
$X1 += 0.00031931062*cos(5.99122459014 + 199.3158189199*$t);
$X1 += 0.00024548187*cos(1.72318512907 + 205.9417309537*$t);
$X1 += 0.00030521021*cos(0.18185692767 + 14.47091148511*$t);
$X1 += 0.00022265017*cos(6.19403063806 + 103.3365917021*$t);
$X1 += 0.00018939520*cos(2.77554483793 + 853.4401992355*$t);
$X1 += 0.00018082904*cos(5.08903997736 + 209.6107596584*$t);
$X1 += 0.00017786477*cos(6.10321536300 + 217.4750661846*$t);
$X1 += 0.00016307253*cos(4.86906758451 + 216.72430665921*$t);
$X1 += 0.00016919177*cos(4.58471330942 + 633.0275567967*$t);
$X1 += 0.00015920273*cos(0.03453366907 + 210.36151918381*$t);
$X1 += 0.00016167186*cos(5.61042793206 + 323.74923414091*$t);
$X1 += 0.00014472589*cos(3.67415332596 + 647.25465079831*$t);
$X1 += 0.00011071575*cos(0.03003679044 + 117.5636857037*$t);
$X1 += 0.00009887534*cos(5.18637985637 + 202.4972126576*$t);
$X1 += 0.00008713930*cos(6.03455153122 + 224.5886131854*$t);
$X1 += 0.00006197025*cos(1.36464349110 + 213.0552779545*$t);
$X1 += 0.00005502258*cos(4.40320486328 + 441.06910236111*$t);
$X1 += 0.00005466098*cos(2.60358233388 + 11.2895177474*$t);
$X1 += 0.00003484091*cos(2.54141592195 + 6.86972951729*$t);
$X1 += 0.00003596198*cos(2.50280897492 + 309.0345051723*$t);
$X1 += 0.00003029001*cos(1.24873358475 + 522.3336006103*$t);
$X1 += 0.00003353859*cos(3.74904517566 + 95.7354097343*$t);
$X1 += 0.00002987715*cos(5.64325133005 + 309.5221401393*$t);
$X1 += 0.00002732424*cos(4.10964270304 + 149.8070146181*$t);
$X1 += 0.00003741808*cos(4.82356861468 + 412.6149143579*$t);
$X1 += 0.00002374342*cos(1.71597491607 + 198.82818395289*$t);
$X1 += 0.00002875345*cos(0.10934318294 + 426.3543733925*$t);
$X1 += 0.00002121841*cos(1.70223145921 + 220.16882495529*$t);
$X1 += 0.00002386687*cos(0.22569849869 + 109.9625037359*$t);
$X1 += 0.00001755551*cos(0.77463091610 + 277.2788112249*$t);
$X1 += 0.00001690652*cos(3.97638248269 + 422.9098550964*$t);
$X1 += 0.00001545396*cos(5.30260231719 + 330.8627811417*$t);
$X1 += 0.00001447492*cos(2.03498842518 + 4.1759707466*$t);
$X1 += 0.00001392451*cos(2.03410425344 + 1066.7392946735*$t);
$X1 += 0.00001331483*cos(5.06295810929 + 234.8835539239*$t);
$X1 += 0.00001452348*cos(6.21365122108 + 3.42521122121*$t);
$X1 += 0.00001285559*cos(2.40490814955 + 415.7963080956*$t);
$X1 += 0.00001159539*cos(4.60389667301 + 537.0483295789*$t);
$X1 += 0.00001128476*cos(5.45092270832 + 423.66061462181*$t);
$X1 += 0.00001131769*cos(6.00809348724 + 529.9347825781*$t);
$X1 += 0.00001127023*cos(2.88170875021 + 860.55374623631*$t);
$X1 += 0.00001101803*cos(4.07656502687 + 430.02340209721*$t);
$X1 += 0.00001061927*cos(4.38341564719 + 846.3266522347*$t);
$X1 += 0.00001343360*cos(2.98910861966 + 211.09523236671*$t);
$X1 += 0.00001331640*cos(1.90897752717 + 215.99059347631*$t);
$X1 += 0.00001287848*cos(2.08433845806 + 522.8212355773*$t);
$X1 += 0.00001050973*cos(0.41490086140 + 412.12727939089*$t);
$X1 += 0.00000900723*cos(0.97940540803 + 838.72547026689*$t);
$X1 += 0.00000882663*cos(5.41577217529 + 437.8877086234*$t);
$X1 += 0.00000924505*cos(0.31084816096 + 743.23387801611*$t);
$X1 += 0.00000876882*cos(6.15951573282 + 96.2230447013*$t);
$X1 += 0.00000905253*cos(3.37316127293 + 3.6883357796*$t);
$X1 += 0.00000820808*cos(4.74555854872 + 223.83785366*$t);
$X1 += 0.00000844907*cos(2.24191891660 + 625.42637482889*$t);
$X1 += 0.00000760731*cos(0.32645781021 + 625.9140097959*$t);
$X1 += 0.00000657423*cos(1.75192962523 + 316.14805217309*$t);
$X1 += 0.00000813631*cos(0.02636548240 + 21.5844584859*$t);
$X1 += 0.00000642768*cos(0.08669014735 + 1059.6257476727*$t);
$X1 += 0.00000657845*cos(3.90002282220 + 88.6218627335*$t);
$X1 += 0.00000715042*cos(6.12383205661 + 430.7741616226*$t);
$X1 += 0.00000596876*cos(5.09870868637 + 124.6772327045*$t);
$X1 += 0.00000472020*cos(3.60910799409 + 654.3681977991*$t);
$X1 += 0.00000467656*cos(1.37893062096 + 515.2200536095*$t);
$X1 += 0.00000472526*cos(0.17976235838 + 203.247972183*$t);
$X1 += 0.00000487417*cos(1.14265056645 + 736.1203310153*$t);
$X1 += 0.00000402114*cos(4.42612765272 + 86.07111631471*$t);
$X1 += 0.00000376954*cos(3.71201411962 + 76.50988875911*$t);
$X1 += 0.00000419410*cos(5.88905869137 + 742.74624304909*$t);
$X1 += 0.00000439384*cos(2.62527563052 + 301.9209581715*$t);
$X1 += 0.00000458871*cos(0.66305280938 + 529.44714761109*$t);
$X1 += 0.00000345395*cos(6.17484774422 + 192.2022719191*$t);
$X1 += 0.00000334209*cos(0.71189291081 + 1155.1173399235*$t);
$X1 += 0.00000330276*cos(0.35761199969 + 302.40859313851*$t);
$X1 += 0.00000339713*cos(2.73817515158 + 218.2087793675*$t);
$X1 += 0.00000304950*cos(0.18421276814 + 231.70216018621*$t);
$X1 += 0.00000312395*cos(2.36627641720 + 629.0954035336*$t);
$X1 += 0.00000311746*cos(1.93452684244 + 941.8182444855*$t);
$X1 += 0.00000299095*cos(2.15964302278 + 208.8770464755*$t);
$X1 += 0.00000299955*cos(0.17404785977 + 728.5191490475*$t);
$X1 += 0.00000271105*cos(2.70363094480 + 288.32451148881*$t);
$X1 += 0.00000260779*cos(0.87015911392 + 18.40306474821*$t);
$X1 += 0.00000278736*cos(5.35893413930 + 632.5399218297*$t);
$X1 += 0.00000335527*cos(3.07953134072 + 203.9816853659*$t);
$X1 += 0.00000259607*cos(6.00394254983 + 10.538758222*$t);
$X1 += 0.00000263983*cos(3.55443649812 + 363.1061100561*$t);
$X1 += 0.00000291544*cos(1.81131242466 + 223.1041404771*$t);
$X1 += 0.00000214376*cos(6.03151333634 + 208.1262869501*$t);
$X1 += 0.00000208551*cos(5.16427411899 + 218.9595388929*$t);
$X1 += 0.00000208257*cos(4.38726258110 + 408.68276109481*$t);
$X1 += 0.00000211653*cos(2.10642373554 + 138.76131435421*$t);
$X1 += 0.00000199845*cos(2.29578299708 + 13.9832765181*$t);
$X1 += 0.00000195781*cos(0.35428355710 + 52.446380556*$t);
$X1 += 0.00000192346*cos(6.21537031577 + 201.01273994931*$t);
$X1 += 0.00000191573*cos(0.44811077600 + 341.01470952831*$t);
$X1 += 0.00000185995*cos(4.78683696303 + 948.9317914863*$t);
$X1 += 0.00000168803*cos(1.10901900891 + 831.6119232661*$t);
$X1 += 0.00000170172*cos(1.18102994579 + 350.5759370839*$t);
$X1 += 0.00000167553*cos(5.00268725720 + 226.07308589371*$t);
$X1 += 0.00000177510*cos(4.94085831586 + 210.6221516147*$t);
$X1 += 0.00000177755*cos(6.22073652647 + 216.4636742283*$t);
$X1 += 0.00000157494*cos(1.71852514061 + 195.38366565681*$t);
$X1 += 0.00000162215*cos(6.01667468309 + 956.53297345411*$t);
$X1 += 0.00000160622*cos(2.21143597606 + 127.22797912329*$t);
$X1 += 0.00000147298*cos(0.31012308764 + 9.8050450391*$t);
$X1 += 0.00000177635*cos(6.27025545843 + 160.852714882*$t);
$X1 += 0.00000170308*cos(2.63474062872 + 207.913838629*$t);
$X1 += 0.00000158062*cos(5.63276958593 + 1059.1381127057*$t);
$X1 += 0.00000138665*cos(0.44735566636 + 1471.50920958009*$t);
$X1 += 0.00000150976*cos(3.13927888955 + 636.2089505344*$t);
$X1 += 0.00000136839*cos(4.51690712170 + 544.1618765797*$t);
$X1 += 0.00000163932*cos(2.23903496342 + 219.171987214*$t);
$X1 += 0.00000164921*cos(4.61861878322 + 22.3352180113*$t);
$X1 += 0.00000134204*cos(1.25807922003 + 703.8770021009*$t);
$X1 += 0.00000141934*cos(0.59018411736 + 202.0095776906*$t);
$X1 += 0.00000153018*cos(4.27626456939 + 56.3785338191*$t);
$X1 += 0.00000132722*cos(3.97656514012 + 750.3474250169*$t);
$X1 += 0.00000136617*cos(1.64500267431 + 1258.21011414209*$t);
$X1 += 0.00000124984*cos(4.28860125524 + 448.1826493619*$t);
$X1 += 0.00000138310*cos(4.40216198828 + 142.6934676173*$t);
$X1 += 0.00000121140*cos(0.16586240985 + 949.4194264533*$t);
$X1 += 0.00000146873*cos(0.47521375650 + 845.8390172677*$t);
$X1 += 0.00000135623*cos(0.85079579674 + 490.5779066629*$t);
$X1 += 0.00000114737*cos(0.83509600385 + 433.46792039329*$t);
$X1 += 0.00000107506*cos(2.74641093550 + 565.35950523021*$t);
$X1 += 0.00000105407*cos(3.58312013649 + 209.35012722751*$t);
$X1 += 0.00000123012*cos(2.85293627235 + 483.4643596621*$t);
$X1 += 0.00000104647*cos(1.30261134749 + 217.73569861551*$t);
$X1 += 0.00000123445*cos(4.85723767211 + 266.233110961*$t);
$X1 += 0.00000121327*cos(2.34436045601 + 618.3128278281*$t);
$X1 += 0.00000121539*cos(2.28006635810 + 515.70768857651*$t);
$X1 += 0.00000098330*cos(1.27153379840 + 1280.0383901115*$t);
$X1 += 0.00000123139*cos(1.72477244855 + 12.77399045571*$t);
$X1 += 0.00000106461*cos(6.21307355690 + 1044.9110187041*$t);
$X1 += 0.00000134338*cos(0.13238469429 + 419.2408263917*$t);
$X1 += 0.00000107530*cos(2.04781430457 + 424.39432780471*$t);
$X1 += 0.00000114356*cos(3.50494100764 + 270.1652642241*$t);
$X1 += 0.00000094347*cos(4.48494950953 + 1265.32366114289*$t);
$X1 += 0.00000104237*cos(3.80594641363 + 70.6056278207*$t);
$X1 += 0.00000088410*cos(2.09844529978 + 1073.85284167431*$t);
$X1 += 0.00000091547*cos(0.19575334067 + 106.5179854398*$t);
$X1 += 0.00000084219*cos(6.17220906984 + 113.6315324406*$t);
$X1 += 0.00000091641*cos(2.30922052677 + 497.69145366371*$t);
$X1 += 0.00000080939*cos(4.70817863540 + 651.1868040614*$t);
$X1 += 0.00000082304*cos(3.28548883281 + 643.32249753521*$t);
$X1 += 0.00000099237*cos(5.82968286033 + 639.6534688305*$t);
$X1 += 0.00000073063*cos(0.84493736921 + 1148.00379292269*$t);
$X1 += 0.00000079913*cos(3.01047372573 + 191.45151239371*$t);
$X1 += 0.00000070813*cos(2.40778621473 + 251.6759485593*$t);
$X1 += 0.00000072632*cos(1.31854571732 + 107.2687449652*$t);
$X1 += 0.00000075817*cos(1.44164476880 + 284.39235822571*$t);
$X1 += 0.00000072415*cos(1.87310857657 + 191.7146369521*$t);
$X1 += 0.00000084109*cos(1.77169250100 + 219.6932520758*$t);
$X1 += 0.00000066814*cos(4.85072561146 + 636.95971005981*$t);
$X1 += 0.00000064253*cos(4.88041745139 + 71.09326278771*$t);
$X1 += 0.00000073347*cos(4.31971264670 + 344.9468627914*$t);
$X1 += 0.00000061578*cos(5.13231029134 + 479.532206399*$t);
$X1 += 0.00000060447*cos(0.18657130674 + 1787.9010792367*$t);
$X1 += 0.00000063039*cos(3.97913628016 + 437.136949098*$t);
$X1 += 0.00000064265*cos(1.35985415674 + 1574.6019837987*$t);
$X1 += 0.00000058169*cos(3.07003751562 + 75.0254160508*$t);
$X1 += 0.00000065491*cos(5.37959870394 + 1375.52998236229*$t);
$X1 += 0.00000057055*cos(1.29146537045 + 98.6561710411*$t);
$X1 += 0.00000063072*cos(3.82756140289 + 359.173956793*$t);
$X1 += 0.00000076825*cos(0.26061032610 + 839.2131052339*$t);
$X1 += 0.00000065944*cos(3.15806762275 + 207.3925737672*$t);
$X1 += 0.00000065704*cos(0.38527237466 + 2.9375762542*$t);
$X1 += 0.00000059449*cos(4.25418200211 + 417.2807808039*$t);
$X1 += 0.00000066539*cos(0.19553179802 + 1162.23088692429*$t);
$X1 += 0.00000053194*cos(1.57281678134 + 227.2823719561*$t);
$X1 += 0.00000063890*cos(1.98911021042 + 235.6343134493*$t);
$X1 += 0.00000052968*cos(2.48775989817 + 175.40987728371*$t);
$X1 += 0.00000051480*cos(5.40158452623 + 416.547067621*$t);
$X1 += 0.00000053788*cos(0.70800398665 + 114.38229196601*$t);
$X1 += 0.00000052017*cos(2.01145465470 + 220.7046440321*$t);
$X1 += 0.00000048475*cos(0.16935246445 + 209.12312469139*$t);
$X1 += 0.00000048625*cos(0.32855808278 + 63.9797157869*$t);
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$X1 += 0.00000002352*cos(4.19836125385 + 479.044571432*$t);
$X1 += 0.00000002048*cos(1.46373921871 + 1788.38871420371*$t);
$X1 += 0.00000002647*cos(4.98237868701 + 2744.1902352073*$t);
$X1 += 0.00000001908*cos(3.37818588512 + 1368.9040703285*$t);
$X1 += 0.00000001900*cos(6.21516760726 + 271.6497369324*$t);
$X1 += 0.00000002178*cos(3.04872277319 + 254.5967098661*$t);
$X1 += 0.00000001894*cos(0.38526664490 + 1048.8431719672*$t);
$X1 += 0.00000001892*cos(4.53251590605 + 49.26498681829*$t);
$X1 += 0.00000001888*cos(0.97996534938 + 642.58878435231*$t);
$X1 += 0.00000002182*cos(4.42761937882 + 427.0544566806*$t);
$X1 += 0.00000001810*cos(6.24932174424 + 518.40144734719*$t);
$X1 += 0.00000001925*cos(6.21686018138 + 3156.5613320817*$t);
$X1 += 0.00000002022*cos(5.64661364195 + 4.4220489625*$t);
$X1 += 0.00000001793*cos(3.43045021055 + 419.6802772489*$t);
$X1 += 0.00000002336*cos(0.79346337330 + 10419.7149121317*$t);
$X1 += 0.00000001992*cos(2.92479817252 + 16.4309570729*$t);
$X1 += 0.00000001790*cos(4.60289486851 + 71.8440223131*$t);
$X1 += 0.00000001779*cos(2.30415626764 + 702.3925293926*$t);
$X1 += 0.00000001796*cos(3.79385866271 + 240.6302482954*$t);
$X1 += 0.00000001974*cos(0.40863452127 + 640.1892879073*$t);
$X1 += 0.00000001881*cos(2.58502310856 + 200.52510498229*$t);
$X1 += 0.00000001773*cos(0.91523739118 + 990.47322339791*$t);
$X1 += 0.00000002183*cos(0.33182574262 + 411.3765198655*$t);
$X1 += 0.00000002250*cos(0.80555474376 + 6077.1341190377*$t);
$X1 += 0.00000002182*cos(0.97387565779 + 426.6295600384*$t);
$X1 += 0.00000001835*cos(1.94831932983 + 163.1403367424*$t);
$X1 += 0.00000002428*cos(4.54827834066 + 2641.0974609887*$t);
$X1 += 0.00000001996*cos(1.88608745432 + 398.38782035631*$t);
$X1 += 0.00000001813*cos(1.03980179180 + 25.516611749*$t);
$X1 += 0.00000001980*cos(6.08475811682 + 206.54124050531*$t);
$X1 += 0.00000001940*cos(0.04753375650 + 774.7264474051*$t);
$X1 += 0.00000001910*cos(4.61558010626 + 175.6705097146*$t);
$X1 += 0.00000002379*cos(3.57535524190 + 594.8945211589*$t);
$X1 += 0.00000002068*cos(4.09042241645 + 183.85033042589*$t);
$X1 += 0.00000001733*cos(3.39710168703 + 705.36147480921*$t);
$X1 += 0.00000001824*cos(0.43158734549 + 420.2497262205*$t);
$X1 += 0.00000001804*cos(4.09117978828 + 9566.03089541269*$t);
$X1 += 0.00000002037*cos(3.95444170699 + 481.97988695381*$t);
$X1 += 0.00000001792*cos(1.26659627713 + 842.65762352999*$t);
$X1 += 0.00000001681*cos(2.53871998999 + 1575.08961876571*$t);
$X1 += 0.00000001732*cos(1.55363228273 + 692.34366686999*$t);
$X1 += 0.00000001698*cos(4.90525724103 + 355.50492808829*$t);
$X1 += 0.00000001828*cos(4.98959403756 + 484.9488323704*$t);
$X1 += 0.00000001713*cos(1.30182253021 + 457.8614969965*$t);
$X1 += 0.00000001808*cos(2.75209469281 + 622.2449810912*$t);
$X1 += 0.00000001911*cos(3.61821751946 + 5165.60650620771*$t);
$X1 += 0.00000001704*cos(6.23318457567 + 2538.00468677009*$t);
$X1 += 0.00000001688*cos(6.03910121927 + 267.22994870229*$t);
$X1 += 0.00000001665*cos(5.37698735936 + 1127.50624756031*$t);
$X1 += 0.00000002097*cos(2.22788409731 + 10007.3438152573*$t);
$X1 += 0.00000001691*cos(2.07854652969 + 789.7043009321*$t);
$X1 += 0.00000001699*cos(0.77916428304 + 760.4993534035*$t);
$X1 += 0.00000001783*cos(3.13574966388 + 2001.68780964171*$t);
$X1 += 0.00000001796*cos(4.27766403083 + 1194.21109128031*$t);
$X1 += 0.00000001619*cos(3.01440438125 + 189.47940471839*$t);
$X1 += 0.00000001652*cos(2.95148116143 + 152.77596003471*$t);
$X1 += 0.00000001707*cos(5.77147938366 + 3046.3550108623*$t);
$X1 += 0.00000001924*cos(0.43738095399 + 380.37158544351*$t);
$X1 += 0.00000001960*cos(3.34806236291 + 144.1779403256*$t);
$X1 += 0.00000001599*cos(5.99560668065 + 2008.8013566425*$t);
$X1 += 0.00000001804*cos(0.11881932366 + 353.5448825005*$t);
$X1 += 0.00000001586*cos(0.20398228990 + 6069.53293706989*$t);
$X1 += 0.00000001644*cos(1.16840005853 + 1112.3159457122*$t);
$X1 += 0.00000001572*cos(4.52460985815 + 91.54262404029*$t);
$X1 += 0.00000002123*cos(2.62748087622 + 1802.12817323829*$t);
$X1 += 0.00000001948*cos(4.60996708702 + 268.68079151581*$t);
$X1 += 0.00000001766*cos(4.90567167770 + 3333.7426971825*$t);
$X1 += 0.00000001565*cos(0.79981986869 + 97.9199657307*$t);
$X1 += 0.00000001602*cos(4.73221068440 + 490.09027169589*$t);
$X1 += 0.00000001546*cos(2.42254478872 + 258.78949556011*$t);
$X1 += 0.00000001724*cos(3.10736186704 + 26081.03341205689*$t);
$X1 += 0.00000001531*cos(4.39157176653 + 5216.33655531789*$t);
$X1 += 0.00000001619*cos(1.87855507272 + 784.28767496071*$t);
$X1 += 0.00000001871*cos(0.40711466948 + 206.3174913361*$t);
$X1 += 0.00000001734*cos(0.20470303542 + 304.84171947829*$t);
$X1 += 0.00000001732*cos(6.00632565407 + 1332.728588151*$t);
$X1 += 0.00000001517*cos(5.25218074419 + 1048.0924124418*$t);
$X1 += 0.00000001563*cos(3.46526834018 + 555.7982776746*$t);
$X1 += 0.00000001520*cos(3.35489835249 + 1101.2702454483*$t);
$X1 += 0.00000001687*cos(4.36557051418 + 3347.96979118411*$t);
$X1 += 0.00000001488*cos(1.67143354747 + 9999.7426332895*$t);
$X1 += 0.00000001587*cos(0.21300456338 + 372.77040347569*$t);
$X1 += 0.00000001662*cos(2.56954470179 + 26095.2605060585*$t);
$X1 += 0.00000001724*cos(1.33166239973 + 1037.7974717033*$t);
$X1 += 0.00000001477*cos(4.36052585434 + 208.3894115085*$t);
$X1 += 0.00000001657*cos(1.83865415601 + 552.829332258*$t);
$X1 += 0.00000001520*cos(2.73911257161 + 2318.0796792983*$t);
$X1 += 0.00000001443*cos(1.98940467508 + 910.0625505381*$t);
$X1 += 0.00000001446*cos(1.10349996175 + 204.9448932124*$t);
$X1 += 0.00000001446*cos(0.64453355125 + 222.14093263061*$t);
$X1 += 0.00000001850*cos(3.79242867450 + 699.94484883781*$t);
$X1 += 0.00000001439*cos(4.66881004427 + 393.70490756781*$t);
$X1 += 0.00000001452*cos(6.27116384237 + 1130.47519297691*$t);
$X1 += 0.00000001874*cos(2.34112858987 + 770.0605809591*$t);
$X1 += 0.00000001782*cos(1.54447498730 + 835.5440765292*$t);
$X1 += 0.00000001639*cos(5.07308302027 + 427.10264079041*$t);
$X1 += 0.00000001565*cos(0.60414645629 + 392.9017584157*$t);
$X1 += 0.00000001395*cos(5.81501189133 + 9146.54625153749*$t);
$X1 += 0.00000001516*cos(3.58009173951 + 397.9001853893*$t);
$X1 += 0.00000001684*cos(6.24638766723 + 1479.11039154791*$t);
$X1 += 0.00000001659*cos(1.59176755278 + 721.8932370137*$t);
$X1 += 0.00000001514*cos(5.91645211455 + 319.06881347989*$t);
$X1 += 0.00000001397*cos(2.98224235085 + 3163.6748790825*$t);
$X1 += 0.00000001747*cos(2.27656402390 + 37.88921815429*$t);
$X1 += 0.00000001492*cos(3.04531836360 + 263.9454891006*$t);
$X1 += 0.00000001354*cos(4.57495887478 + 140.2457870625*$t);
$X1 += 0.00000001506*cos(0.27404631561 + 251.4153161284*$t);
$X1 += 0.00000001365*cos(4.69515666017 + 694.31577454531*$t);
$X1 += 0.00000001352*cos(4.48933959673 + 60.79832204921*$t);
$X1 += 0.00000001352*cos(4.48933959673 + 60.3106870822*$t);
$X1 += 0.00000001531*cos(0.64877553761 + 907.0936051215*$t);
$X1 += 0.00000001783*cos(0.81801801901 + 185.08872491831*$t);
$X1 += 0.00000001550*cos(4.05055802538 + 170.51700830159*$t);
$X1 += 0.00000001524*cos(0.15234864850 + 921.3206991231*$t);
$X1 += 0.00000001541*cos(2.73990779933 + 31.73638687251*$t);
$X1 += 0.00000001578*cos(5.98549196472 + 190.6483632416*$t);
$X1 += 0.00000001578*cos(5.18731950905 + 236.4374626014*$t);
$X1 += 0.00000001732*cos(0.64736011209 + 1126.54303971381*$t);
$X1 += 0.00000001540*cos(0.36379616132 + 2833.0559154243*$t);
$X1 += 0.00000001323*cos(4.87522768351 + 460.7822583033*$t);
$X1 += 0.00000001312*cos(5.10594513264 + 448.98829064149*$t);
$X1 += 0.00000001724*cos(5.39037296555 + 78.4699343469*$t);
$X1 += 0.00000001472*cos(4.26339575699 + 34.1840674273*$t);
$X1 += 0.00000001296*cos(5.62129859108 + 2325.1932262991*$t);
$X1 += 0.00000001309*cos(5.45522580580 + 349.0914643756*$t);
$X1 += 0.00000001818*cos(4.16411482533 + 100.4012761803*$t);
$X1 += 0.00000001290*cos(2.36413128544 + 1176.9456158929*$t);
$X1 += 0.00000001334*cos(2.44221382511 + 282.9078855174*$t);
$X1 += 0.00000001287*cos(0.26504708130 + 286.8400387805*$t);
$X1 += 0.00000001392*cos(4.87830155415 + 69.12115511239*$t);
$X1 += 0.00000001515*cos(3.62072467848 + 12.28635548869*$t);
$X1 += 0.00000001247*cos(4.64664167702 + 187.67941782501*$t);
$X1 += 0.00000001247*cos(0.24298448957 + 239.40640801801*$t);
$X1 += 0.00000001246*cos(1.79539178116 + 2487.1722274643*$t);
$X1 += 0.00000001511*cos(1.66615367049 + 213.00709384469*$t);
$X1 += 0.00000001479*cos(0.68803218820 + 2516.66404576769*$t);
$X1 += 0.00000001233*cos(1.65114888447 + 2531.3787747363*$t);
$X1 += 0.00000001632*cos(2.90714941935 + 906.130397275*$t);
$X1 += 0.00000001387*cos(0.55195474062 + 401.569214094*$t);
$X1 += 0.00000001352*cos(0.63301755055 + 351.5727748252*$t);
$X1 += 0.00000001313*cos(0.13852930132 + 350.08830211689*$t);
$X1 += 0.00000001236*cos(3.39882375572 + 11926.01059618529*$t);
$X1 += 0.00000001227*cos(5.24375477429 + 4127.5652170209*$t);
$X1 += 0.00000001304*cos(0.28979853169 + 203.49405039889*$t);
$X1 += 0.00000001478*cos(4.80872386721 + 264.2610032857*$t);
$X1 += 0.00000001254*cos(6.19414707054 + 827.67977000299*$t);
$X1 += 0.00000001230*cos(2.44616325751 + 51535.66517935089*$t);
$X1 += 0.00000001385*cos(4.26128512958 + 41.2976144281*$t);
$X1 += 0.00000001364*cos(4.18584755012 + 65.46418849521*$t);
$X1 += 0.00000001395*cos(2.64686968582 + 629.35852809199*$t);
$X1 += 0.00000001284*cos(5.37115714123 + 168.2963302829*$t);
$X1 += 0.00000001435*cos(5.84382021042 + 617.5620683027*$t);
$X1 += 0.00000001411*cos(5.88687181276 + 188.270118656*$t);
$X1 += 0.00000001191*cos(0.70400726689 + 606.5163680388*$t);
$X1 += 0.00000001193*cos(1.77967286420 + 274.30986580831*$t);
$X1 += 0.00000001197*cos(2.05343251093 + 1062.80714141041*$t);
$X1 += 0.00000001356*cos(1.22316379022 + 50.6463936626*$t);
$X1 += 0.00000001356*cos(4.36475644381 + 50.15875869559*$t);
$X1 += 0.00000001276*cos(0.30928416823 + 2090.06585489169*$t);
$X1 += 0.00000001195*cos(2.85953206146 + 681.2979666061*$t);
$X1 += 0.00000001603*cos(1.64227556935 + 1560.3748897971*$t);
$X1 += 0.00000001191*cos(3.68583487315 + 9594.99527173989*$t);
$X1 += 0.00000001168*cos(1.08249837425 + 74.3947687319*$t);
$X1 += 0.00000001165*cos(4.67802137668 + 674.1844196053*$t);
$X1 += 0.00000001242*cos(5.63232378165 + 1902.5271886862*$t);
$X1 += 0.00000001330*cos(0.04908988755 + 200.27902676641*$t);
$X1 += 0.00000001330*cos(1.69894362545 + 226.80679907661*$t);
$X1 += 0.00000001154*cos(1.32466818176 + 2847.77064439291*$t);
$X1 += 0.00000001150*cos(5.63834183266 + 17.6523052228*$t);
$X1 += 0.00000001152*cos(1.92670632990 + 740.0524842784*$t);
$X1 += 0.00000001247*cos(5.13783491688 + 348.3913810875*$t);
$X1 += 0.00000001387*cos(5.73885801869 + 527.4871020233*$t);
$X1 += 0.00000001250*cos(1.98100336387 + 184.6010899513*$t);
$X1 += 0.00000001328*cos(4.49802504301 + 2957.48933064529*$t);
$X1 += 0.00000001587*cos(1.96187033145 + 1243.98302014049*$t);
$X1 += 0.00000001176*cos(1.80593057083 + 747.1660312792*$t);
$X1 += 0.00000001223*cos(0.59493067511 + 1773.6739852351*$t);
$X1 += 0.00000001161*cos(0.01398952175 + 2435.3995475185*$t);
$X1 += 0.00000001570*cos(4.69885872763 + 3060.5821048639*$t);
$X1 += 0.00000001303*cos(3.48272421278 + 393.2172726008*$t);
$X1 += 0.00000001126*cos(0.75321492124 + 305.10235190919*$t);
$X1 += 0.00000001534*cos(1.87537098734 + 81.9959506997*$t);
$X1 += 0.00000001117*cos(4.61546207470 + 526.00262931501*$t);
$X1 += 0.00000001307*cos(5.84787741027 + 72.090100529*$t);
$X1 += 0.00000001114*cos(0.00680453000 + 25234.46294233869*$t);
$X1 += 0.00000001118*cos(1.34292799669 + 511.7755353134*$t);
$X1 += 0.00000001242*cos(2.97258589350 + 145.387226388*$t);
$X1 += 0.00000001397*cos(4.30533366512 + 336.5949212982*$t);
$X1 += 0.00000001401*cos(2.28518305813 + 2118.5200428949*$t);
$X1 += 0.00000001139*cos(5.01671933650 + 1055.2059594426*$t);
$X1 += 0.00000001096*cos(3.93031837723 + 739.30172475301*$t);
$X1 += 0.00000001092*cos(1.72033976580 + 234.3959189569*$t);
$X1 += 0.00000001197*cos(0.70790588748 + 306.34074640161*$t);
$X1 += 0.00000001126*cos(5.90717690029 + 1144.0716396596*$t);
$X1 += 0.00000001351*cos(3.03970702934 + 179.6026629777*$t);
$X1 += 0.00000001165*cos(0.13814938960 + 746.67839631219*$t);
$X1 += 0.00000001167*cos(4.32162909656 + 634.7244778261*$t);
$X1 += 0.00000001121*cos(3.70393028752 + 366.2875037938*$t);
$X1 += 0.00000001051*cos(2.77078069512 + 383.81610373959*$t);
$X1 += 0.00000001053*cos(3.41928600573 + 2107.96197759801*$t);
$X1 += 0.00000001051*cos(2.99910636875 + 10000.23026825651*$t);
$X1 += 0.00000001288*cos(1.85993541573 + 247.4831628653*$t);
$X1 += 0.00000001045*cos(4.77749523511 + 1680.87615175499*$t);
$X1 += 0.00000001070*cos(5.83029249500 + 3472.9532017383*$t);
$X1 += 0.00000001043*cos(5.10256961747 + 151.5039356475*$t);
$X1 += 0.00000001033*cos(1.59445268426 + 6070.0205720369*$t);
$X1 += 0.00000001282*cos(3.59113162781 + 141.9427080919*$t);
$X1 += 0.00000001167*cos(5.76598251731 + 2920.8839653411*$t);
$X1 += 0.00000001100*cos(2.52155794298 + 2634.47154895491*$t);
$X1 += 0.00000001035*cos(5.30771361050 + 3369.8604275197*$t);
$X1 += 0.00000001091*cos(0.54826165686 + 1314.5693408863*$t);
$X1 += 0.00000001274*cos(3.38359403787 + 691.3468291287*$t);
$X1 += 0.00000001079*cos(4.20190952106 + 1044.6478941457*$t);
$X1 += 0.00000001085*cos(2.22740147584 + 141.208994909*$t);
$X1 += 0.00000001245*cos(5.83769374356 + 179.9181771628*$t);
$X1 += 0.00000001146*cos(0.33774172888 + 220.54458533771*$t);
$X1 += 0.00000001196*cos(3.17156910173 + 1460.2003847578*$t);
$X1 += 0.00000001136*cos(2.05466340621 + 480.00777927849*$t);
$X1 += 0.00000001119*cos(5.41354135574 + 1534.9819833251*$t);
$X1 += 0.00000001056*cos(3.62871723489 + 437.40007365639*$t);
$X1 += 0.00000001032*cos(2.32675902580 + 184.97110483931*$t);
$X1 += 0.00000001032*cos(2.56286714079 + 242.11472100371*$t);
$X1 += 0.00000001039*cos(2.32832376555 + 1791.0824729744*$t);
$X1 += 0.00000001061*cos(2.50615202413 + 938.63685074779*$t);
$X1 += 0.00000001123*cos(3.96404102873 + 25668.17468021549*$t);
$X1 += 0.00000001103*cos(5.86207947745 + 210.60759739969*$t);
$X1 += 0.00000001015*cos(4.05475486800 + 252.4121538697*$t);
$X1 += 0.00000000979*cos(5.22245385112 + 610.44852130189*$t);
$X1 += 0.00000000979*cos(2.08086119753 + 610.93615626891*$t);
$X1 += 0.00000001043*cos(3.45408554292 + 17.91542978119*$t);
$X1 += 0.00000001128*cos(3.92351069480 + 398.5308327082*$t);
$X1 += 0.00000001035*cos(3.02168366647 + 235.68919520349*$t);
$X1 += 0.00000001072*cos(4.53150424448 + 746.15463932291*$t);
$X1 += 0.00000001131*cos(3.37345520465 + 5481.9983758643*$t);
$X1 += 0.00000000986*cos(5.28602240316 + 192.448350135*$t);
$X1 += 0.00000001287*cos(1.95273113714 + 314.1880065853*$t);
$X1 += 0.00000000973*cos(3.85435039011 + 561.6904765255*$t);
$X1 += 0.00000001298*cos(1.08374685926 + 614.38067456499*$t);
$X1 += 0.00000001151*cos(1.20704230584 + 905.64276230799*$t);
$X1 += 0.00000001279*cos(5.88520431436 + 322.3678272966*$t);
$X1 += 0.00000000963*cos(3.50426087646 + 782.59075393131*$t);
$X1 += 0.00000001064*cos(5.75961632886 + 1372.3485886246*$t);
$X1 += 0.00000000973*cos(3.52289496745 + 24.6228398717*$t);
$X1 += 0.00000001096*cos(5.06936627625 + 731.92754532131*$t);
$X1 += 0.00000001080*cos(6.27980868199 + 2906.6568713395*$t);
$X1 += 0.00000001200*cos(2.31102641105 + 195.6467902152*$t);
$X1 += 0.00000000993*cos(1.95529510745 + 6062.9070250361*$t);
$X1 += 0.00000001039*cos(1.07426067099 + 1159.0494931866*$t);
$X1 += 0.00000000952*cos(2.30173432343 + 239.8819808975*$t);
$X1 += 0.00000001181*cos(0.98375947358 + 1468.3278158424*$t);
$X1 += 0.00000001137*cos(2.73354004808 + 2.69149803831*$t);
$X1 += 0.00000000941*cos(1.23572643410 + 124.18959773749*$t);
$X1 += 0.00000000942*cos(3.50129097588 + 115.11600514891*$t);
$X1 += 0.00000001020*cos(1.79568687186 + 196.3805033981*$t);
$X1 += 0.00000001065*cos(1.53835988752 + 494.2348732801*$t);
$X1 += 0.00000000945*cos(4.39156950811 + 121.0082039998*$t);
$X1 += 0.00000000941*cos(3.67244160492 + 120.01136625851*$t);
$X1 += 0.00000000996*cos(3.06866654160 + 4863.4417305527*$t);
$X1 += 0.00000001059*cos(4.47767598624 + 25653.94758621389*$t);
$X1 += 0.00000000936*cos(1.21580989528 + 307.07445958451*$t);
$X1 += 0.00000000986*cos(1.95558000476 + 5842.0067476303*$t);
$X1 += 0.00000001061*cos(3.92781056471 + 418.97770183331*$t);
$X1 += 0.00000000941*cos(5.52302459792 + 97.17169833279*$t);
$X1 += 0.00000001049*cos(3.59730911706 + 416.79314583689*$t);
$X1 += 0.00000000956*cos(2.39282306271 + 141.4550731249*$t);
$X1 += 0.00000000922*cos(4.97372856088 + 1364.4842820984*$t);
$X1 += 0.00000001090*cos(1.18314786349 + 1151.93594618579*$t);
$X1 += 0.00000000945*cos(5.48577517665 + 220.8689082434*$t);
$X1 += 0.00000000945*cos(2.54544364353 + 206.2169175996*$t);
$X1 += 0.00000000906*cos(2.01210100437 + 12779.6946129043*$t);
$X1 += 0.00000000913*cos(6.06812377280 + 285.61619850311*$t);
$X1 += 0.00000000993*cos(0.00718300554 + 73.0533083755*$t);
$X1 += 0.00000000923*cos(3.95449289739 + 1048.58004740881*$t);
$X1 += 0.00000000910*cos(2.91944659858 + 1250.83344258291*$t);
$X1 += 0.00000001055*cos(2.96570583025 + 287.6938641699*$t);
$X1 += 0.00000000891*cos(4.95995674723 + 4443.9570866775*$t);
$X1 += 0.00000000890*cos(3.44861046216 + 952.3401877601*$t);
$X1 += 0.00000001011*cos(3.98082100593 + 138.9043267061*$t);
$X1 += 0.00000000943*cos(2.88169222264 + 1368.4164353615*$t);
$X1 += 0.00000001240*cos(2.96642006057 + 105.7842722569*$t);
$X1 += 0.00000001240*cos(2.96642006057 + 105.2966372899*$t);
$X1 += 0.00000000975*cos(1.42837247530 + 700.90805668431*$t);
$X1 += 0.00000000963*cos(2.83983881025 + 5378.90560164571*$t);
$X1 += 0.00000001131*cos(3.49207338910 + 640.0929196877*$t);
$X1 += 0.00000001014*cos(3.84499571511 + 246.68001371321*$t);
$X1 += 0.00000000922*cos(3.37907074746 + 9772.21644384989*$t);
$X1 += 0.00000000896*cos(4.52407069260 + 1571.1574655026*$t);
$X1 += 0.00000001121*cos(5.34360557183 + 6467.68194047809*$t);
$X1 += 0.00000000872*cos(2.88021294314 + 519.63984183961*$t);
$X1 += 0.00000001164*cos(0.08165804323 + 739.0410923221*$t);
$X1 += 0.00000001090*cos(2.12969540273 + 1699.0353990197*$t);
$X1 += 0.00000001180*cos(2.44363933993 + 636.47207509279*$t);
$X1 += 0.00000000912*cos(4.11625838132 + 31.2633061205*$t);
$X1 += 0.00000000892*cos(3.93430854425 + 212.579705075*$t);
$X1 += 0.00000000892*cos(3.93430854425 + 212.092070108*$t);
$X1 += 0.00000000985*cos(5.09403476262 + 988.0255428431*$t);
$X1 += 0.00000000860*cos(4.51926390946 + 1585.38455950421*$t);
$X1 += 0.00000000990*cos(0.10745457981 + 3149.44778508089*$t);
$X1 += 0.00000001177*cos(0.16333880643 + 1328.79643488791*$t);
$X1 += 0.00000000864*cos(1.23920060185 + 12146.42323862409*$t);
$X1 += 0.00000001007*cos(2.26868943041 + 685.2301198692*$t);
$X1 += 0.00000001007*cos(5.41028208400 + 685.7177548362*$t);
$X1 += 0.00000000853*cos(5.50195803246 + 2641.5850959557*$t);
$X1 += 0.00000000993*cos(2.58838169596 + 2111.8941308611*$t);
$X1 += 0.00000000844*cos(4.99931164886 + 1239.78774231901*$t);
$X1 += 0.00000000846*cos(3.17548903050 + 2115.0755245988*$t);
$X1 += 0.00000000964*cos(2.75317670197 + 756.56720014041*$t);
$X1 += 0.00000000981*cos(1.46114906045 + 1471.2460850217*$t);
$X1 += 0.00000001164*cos(6.03626063674 + 3391.68870348911*$t);
$X1 += 0.00000000885*cos(3.21468341749 + 609.1216151605*$t);
$X1 += 0.00000000821*cos(0.43214580939 + 388.2213377547*$t);
$X1 += 0.00000000906*cos(2.38644851609 + 327.19375243699*$t);
$X1 += 0.00000000903*cos(3.04044650688 + 477.2445845386*$t);
$X1 += 0.00000000841*cos(3.88859140273 + 473.31243127551*$t);
$X1 += 0.00000000904*cos(0.75775511775 + 635.4752373515*$t);
$X1 += 0.00000000822*cos(0.09352704461 + 1365.23504162379*$t);
$X1 += 0.00000000997*cos(0.25000097268 + 123.2958258602*$t);
$X1 += 0.00000000879*cos(5.54528283460 + 3362.74688051889*$t);
$X1 += 0.00000000846*cos(1.99050608386 + 227.81819103291*$t);
$X1 += 0.00000000846*cos(6.04071273632 + 199.26763481011*$t);
$X1 += 0.00000000947*cos(4.80416752233 + 222.6165055101*$t);
$X1 += 0.00000000875*cos(3.48686422480 + 9993.1167212557*$t);
$X1 += 0.00000001117*cos(0.69343471577 + 319.0833676949*$t);
$X1 += 0.00000000800*cos(5.83577165546 + 834.7933170038*$t);
$X1 += 0.00000000839*cos(6.01134529585 + 206.64181424181*$t);
$X1 += 0.00000000839*cos(2.01987352433 + 220.44401160121*$t);
$X1 += 0.00000000838*cos(3.26925163574 + 2442.5130945193*$t);
$X1 += 0.00000000830*cos(2.56385471112 + 1891.4814884223*$t);
$X1 += 0.00000000841*cos(1.50960565043 + 60.04756252381*$t);
$X1 += 0.00000000826*cos(3.67482294787 + 220.1351950605*$t);
$X1 += 0.00000000854*cos(1.21615128625 + 540.2297233166*$t);
$X1 += 0.00000000842*cos(5.83341675596 + 2854.3965564267*$t);
$X1 += 0.00000000858*cos(5.69541304884 + 781.8399944059*$t);
$X1 += 0.00000000860*cos(2.63629505046 + 5436.7491977567*$t);
$X1 += 0.00000000785*cos(2.62141651385 + 3494.2938427407*$t);
return $X1*$t;
}
function Saturn_X2($t) // 511 terms of order 2
{
$X2 = 0.00862721930*cos(2.44701762869 + 213.5429129215*$t);
$X2 += 0.00611630287*cos(2.28479450822 + 0.2438174835*$t);
$X2 += 0.00561413805*cos(1.25489421778 + 206.42936592071*$t);
$X2 += 0.00547271370*cos(3.61668298145 + 220.6564599223*$t);
$X2 += 0.00234984093*cos(2.44660941367 + 426.8420083595*$t);
$X2 += 0.00088108317*cos(4.86838582414 + 7.3573644843*$t);
$X2 += 0.00050142527*cos(2.69730354414 + 433.9555553603*$t);
$X2 += 0.00045054746*cos(0.35338915884 + 419.72846135871*$t);
$X2 += 0.00033335009*cos(1.58127217455 + 640.1411037975*$t);
$X2 += 0.00027185514*cos(3.49604874733 + 227.77000692311*$t);
$X2 += 0.00018651786*cos(0.02912884251 + 213.0552779545*$t);
$X2 += 0.00012946617*cos(1.40691297654 + 199.3158189199*$t);
$X2 += 0.00010383025*cos(4.75910342894 + 14.47091148511*$t);
$X2 += 0.00006684574*cos(5.66699712629 + 110.45013870291*$t);
$X2 += 0.00004661903*cos(1.83447973785 + 647.25465079831*$t);
$X2 += 0.00004933834*cos(3.08177201518 + 216.72430665921*$t);
$X2 += 0.00004778577*cos(1.81292692641 + 210.36151918381*$t);
$X2 += 0.00004377928*cos(5.24025788610 + 316.6356871401*$t);
$X2 += 0.00003532396*cos(0.77695513689 + 853.4401992355*$t);
$X2 += 0.00002688895*cos(3.15397291653 + 209.6107596584*$t);
$X2 += 0.00002540548*cos(2.64953783571 + 441.06910236111*$t);
$X2 += 0.00002540549*cos(1.72979147362 + 217.4750661846*$t);
$X2 += 0.00002506252*cos(4.68668320836 + 117.5636857037*$t);
$X2 += 0.00002582753*cos(1.59861873487 + 103.3365917021*$t);
$X2 += 0.00002111683*cos(0.27536451133 + 633.0275567967*$t);
$X2 += 0.00002306046*cos(3.67686226266 + 205.9417309537*$t);
$X2 += 0.00001843706*cos(3.97050945214 + 323.74923414091*$t);
$X2 += 0.00001272298*cos(0.25661618943 + 412.6149143579*$t);
$X2 += 0.00000940336*cos(0.85421668175 + 6.86972951729*$t);
$X2 += 0.00000804980*cos(3.35669822169 + 234.8835539239*$t);
$X2 += 0.00000698973*cos(5.48447806995 + 95.7354097343*$t);
$X2 += 0.00000653010*cos(3.44302214541 + 198.82818395289*$t);
$X2 += 0.00000766827*cos(1.08680299509 + 202.4972126576*$t);
$X2 += 0.00000662176*cos(5.13243854047 + 426.3543733925*$t);
$X2 += 0.00000565841*cos(6.26658788528 + 220.16882495529*$t);
$X2 += 0.00000765788*cos(3.85596138373 + 224.5886131854*$t);
$X2 += 0.00000672412*cos(1.14437192898 + 309.5221401393*$t);
$X2 += 0.00000490992*cos(4.81907666832 + 109.9625037359*$t);
$X2 += 0.00000440264*cos(3.59515263445 + 330.8627811417*$t);
$X2 += 0.00000426768*cos(0.70988535006 + 11.2895177474*$t);
$X2 += 0.00000427613*cos(1.00345444265 + 860.55374623631*$t);
$X2 += 0.00000505832*cos(4.26386101303 + 309.0345051723*$t);
$X2 += 0.00000559499*cos(3.55753813954 + 102.84895673509*$t);
$X2 += 0.00000439569*cos(4.61666678676 + 21.5844584859*$t);
$X2 += 0.00000404335*cos(2.95264099159 + 223.83785366*$t);
$X2 += 0.00000400108*cos(2.21768387014 + 430.02340209721*$t);
$X2 += 0.00000338086*cos(0.01109251698 + 1066.7392946735*$t);
$X2 += 0.00000310691*cos(4.43935743139 + 3.42521122121*$t);
$X2 += 0.00000356340*cos(2.07173270088 + 422.9098550964*$t);
$X2 += 0.00000268315*cos(5.61477011539 + 88.6218627335*$t);
$X2 += 0.00000265067*cos(1.09651380636 + 423.66061462181*$t);
$X2 += 0.00000249792*cos(3.78368875676 + 4.1759707466*$t);
$X2 += 0.00000244377*cos(1.81782248050 + 654.3681977991*$t);
$X2 += 0.00000305650*cos(3.17709889511 + 419.2408263917*$t);
$X2 += 0.00000263490*cos(3.32799413830 + 124.6772327045*$t);
$X2 += 0.00000243362*cos(1.58340419486 + 96.2230447013*$t);
$X2 += 0.00000228016*cos(3.15581836524 + 522.3336006103*$t);
$X2 += 0.00000208205*cos(1.59689210791 + 192.2022719191*$t);
$X2 += 0.00000262941*cos(3.81998984240 + 522.8212355773*$t);
$X2 += 0.00000217559*cos(2.12737362973 + 412.12727939089*$t);
$X2 += 0.00000204218*cos(2.31819875139 + 149.8070146181*$t);
$X2 += 0.00000207097*cos(2.04294057461 + 625.9140097959*$t);
$X2 += 0.00000226266*cos(2.00241821857 + 203.247972183*$t);
$X2 += 0.00000164818*cos(2.78185091937 + 537.0483295789*$t);
$X2 += 0.00000154166*cos(2.09392737387 + 302.40859313851*$t);
$X2 += 0.00000159821*cos(5.14771420694 + 529.9347825781*$t);
$X2 += 0.00000127987*cos(3.10053496626 + 515.2200536095*$t);
$X2 += 0.00000150521*cos(4.33804123124 + 301.9209581715*$t);
$X2 += 0.00000109809*cos(2.44188223375 + 277.2788112249*$t);
$X2 += 0.00000107126*cos(4.17749068544 + 10.538758222*$t);
$X2 += 0.00000125246*cos(3.27781318747 + 437.8877086234*$t);
$X2 += 0.00000119913*cos(4.03198023861 + 625.42637482889*$t);
$X2 += 0.00000095870*cos(0.55536550370 + 13.9832765181*$t);
$X2 += 0.00000093192*cos(1.91525183876 + 430.7741616226*$t);
$X2 += 0.00000082653*cos(2.55387341854 + 448.1826493619*$t);
$X2 += 0.00000080395*cos(4.59254494799 + 231.70216018621*$t);
$X2 += 0.00000086059*cos(4.21228581841 + 742.74624304909*$t);
$X2 += 0.00000078439*cos(3.94622515922 + 415.7963080956*$t);
$X2 += 0.00000095719*cos(0.39732138114 + 846.3266522347*$t);
$X2 += 0.00000069822*cos(2.93302398470 + 838.72547026689*$t);
$X2 += 0.00000088159*cos(4.69429588352 + 743.23387801611*$t);
$X2 += 0.00000062703*cos(1.89462060621 + 728.5191490475*$t);
$X2 += 0.00000061768*cos(5.02462718406 + 3.6883357796*$t);
$X2 += 0.00000059007*cos(0.78786498806 + 316.14805217309*$t);
$X2 += 0.00000057483*cos(5.15275075778 + 18.40306474821*$t);
$X2 += 0.00000068064*cos(2.90200859132 + 736.1203310153*$t);
$X2 += 0.00000073156*cos(3.00215539369 + 735.6326960483*$t);
$X2 += 0.00000066143*cos(5.32689397063 + 529.44714761109*$t);
$X2 += 0.00000046643*cos(2.82828712050 + 831.6119232661*$t);
$X2 += 0.00000046381*cos(2.73650889523 + 544.1618765797*$t);
$X2 += 0.00000049127*cos(3.98526295508 + 515.70768857651*$t);
$X2 += 0.00000045075*cos(3.61480562395 + 195.38366565681*$t);
$X2 += 0.00000045874*cos(0.00322886163 + 408.68276109481*$t);
$X2 += 0.00000039597*cos(0.18910102232 + 1073.85284167431*$t);
$X2 += 0.00000037898*cos(5.19338156968 + 1059.6257476727*$t);
$X2 += 0.00000044466*cos(3.71987438426 + 941.8182444855*$t);
$X2 += 0.00000034788*cos(1.53042898513 + 363.1061100561*$t);
$X2 += 0.00000032598*cos(5.38947358762 + 433.46792039329*$t);
$X2 += 0.00000033292*cos(3.55448256672 + 191.7146369521*$t);
$X2 += 0.00000041206*cos(4.06677518336 + 618.3128278281*$t);
$X2 += 0.00000032714*cos(3.96597866859 + 1059.1381127057*$t);
$X2 += 0.00000041218*cos(1.19485367697 + 636.2089505344*$t);
$X2 += 0.00000036847*cos(0.14902811646 + 223.1041404771*$t);
$X2 += 0.00000028979*cos(4.45566358804 + 113.6315324406*$t);
$X2 += 0.00000030445*cos(5.99732067739 + 56.3785338191*$t);
$X2 += 0.00000038514*cos(2.16683520575 + 86.07111631471*$t);
$X2 += 0.00000033922*cos(2.16638658532 + 437.136949098*$t);
$X2 += 0.00000029740*cos(5.33246443349 + 270.1652642241*$t);
$X2 += 0.00000034418*cos(1.38531328883 + 643.32249753521*$t);
$X2 += 0.00000031920*cos(2.71809642095 + 337.9763281425*$t);
$X2 += 0.00000035309*cos(4.64777361590 + 203.9816853659*$t);
$X2 += 0.00000026923*cos(2.72104940113 + 131.79077970531*$t);
$X2 += 0.00000026272*cos(2.14472258006 + 750.3474250169*$t);
$X2 += 0.00000025940*cos(1.96359688358 + 76.50988875911*$t);
$X2 += 0.00000029423*cos(5.51595511461 + 1280.0383901115*$t);
$X2 += 0.00000026782*cos(2.69721459229 + 1155.1173399235*$t);
$X2 += 0.00000024375*cos(5.77172279789 + 81.50831573269*$t);
$X2 += 0.00000025294*cos(4.58498242616 + 483.4643596621*$t);
$X2 += 0.00000023209*cos(1.00054709783 + 867.6672932371*$t);
$X2 += 0.00000022169*cos(0.86121660984 + 288.32451148881*$t);
$X2 += 0.00000023117*cos(6.14239842522 + 227.2823719561*$t);
$X2 += 0.00000021350*cos(3.80984077151 + 160.852714882*$t);
$X2 += 0.00000022067*cos(1.65390020558 + 1044.9110187041*$t);
$X2 += 0.00000022088*cos(2.09313761105 + 70.6056278207*$t);
$X2 += 0.00000020601*cos(2.14444325102 + 22.3352180113*$t);
$X2 += 0.00000020035*cos(2.56955927602 + 1148.00379292269*$t);
$X2 += 0.00000026634*cos(2.72752998143 + 1052.02456570489*$t);
$X2 += 0.00000020249*cos(1.08828213970 + 416.547067621*$t);
$X2 += 0.00000019318*cos(0.56867565113 + 497.69145366371*$t);
$X2 += 0.00000017591*cos(0.47058042874 + 629.0954035336*$t);
$X2 += 0.00000018938*cos(3.01811688461 + 107.2687449652*$t);
$X2 += 0.00000021595*cos(5.64697422334 + 490.5779066629*$t);
$X2 += 0.00000020105*cos(2.11272613285 + 839.2131052339*$t);
$X2 += 0.00000021565*cos(4.03058232828 + 956.53297345411*$t);
$X2 += 0.00000016938*cos(2.88265146092 + 89.10949770051*$t);
$X2 += 0.00000016497*cos(4.71187682763 + 106.5179854398*$t);
$X2 += 0.00000021360*cos(5.07283473961 + 845.8390172677*$t);
$X2 += 0.00000019384*cos(3.45868972702 + 1258.21011414209*$t);
$X2 += 0.00000015417*cos(3.16624042233 + 241.9971009247*$t);
$X2 += 0.00000016591*cos(4.54165521178 + 639.6534688305*$t);
$X2 += 0.00000016177*cos(6.04286742202 + 344.9468627914*$t);
$X2 += 0.00000014854*cos(1.11858145356 + 266.233110961*$t);
$X2 += 0.00000019063*cos(2.07999478622 + 201.01273994931*$t);
$X2 += 0.00000018723*cos(2.80004753140 + 226.07308589371*$t);
$X2 += 0.00000018567*cos(6.15802064616 + 142.6934676173*$t);
$X2 += 0.00000014166*cos(3.57626351086 + 632.5399218297*$t);
$X2 += 0.00000017119*cos(0.83663196525 + 352.06040979221*$t);
$X2 += 0.00000018888*cos(2.63389139857 + 52.446380556*$t);
$X2 += 0.00000013506*cos(4.03963934050 + 138.76131435421*$t);
$X2 += 0.00000017909*cos(3.76988751681 + 934.70469748469*$t);
$X2 += 0.00000013747*cos(2.11060380479 + 359.173956793*$t);
$X2 += 0.00000014401*cos(0.42335490960 + 405.5013673571*$t);
$X2 += 0.00000016878*cos(2.75966318459 + 341.01470952831*$t);
$X2 += 0.00000013527*cos(6.11265092399 + 284.39235822571*$t);
$X2 += 0.00000013436*cos(4.50317832794 + 6290.4332144757*$t);
$X2 += 0.00000012962*cos(0.85501464894 + 181.2995840071*$t);
$X2 += 0.00000015865*cos(2.58925256281 + 651.1868040614*$t);
$X2 += 0.00000013136*cos(2.14345131759 + 6276.2061204741*$t);
$X2 += 0.00000012088*cos(4.09973262355 + 127.22797912329*$t);
$X2 += 0.00000012658*cos(3.42538380158 + 948.9317914863*$t);
$X2 += 0.00000012303*cos(3.76145799738 + 445.00125562421*$t);
$X2 += 0.00000011905*cos(0.05199682564 + 424.39432780471*$t);
$X2 += 0.00000012624*cos(5.92655665827 + 10220.6429106953*$t);
$X2 += 0.00000012885*cos(3.71011528810 + 1375.52998236229*$t);
$X2 += 0.00000012454*cos(2.37524428293 + 295.2950461377*$t);
$X2 += 0.00000012341*cos(3.56682893682 + 10206.4158166937*$t);
$X2 += 0.00000011182*cos(4.71695359508 + 209.12312469139*$t);
$X2 += 0.00000010860*cos(2.79531710541 + 350.5759370839*$t);
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$X2 += 0.00000010568*cos(4.02434153212 + 245.7862418359*$t);
$X2 += 0.00000011834*cos(5.61242569644 + 191.45151239371*$t);
$X2 += 0.00000013045*cos(2.99603652801 + 323.2615991739*$t);
$X2 += 0.00000012746*cos(3.09998912111 + 729.0067840145*$t);
$X2 += 0.00000011214*cos(2.26091951790 + 618.8004627951*$t);
$X2 += 0.00000011539*cos(0.54965317551 + 75.0254160508*$t);
$X2 += 0.00000012236*cos(4.46231008485 + 294.80741117069*$t);
$X2 += 0.00000009934*cos(4.15810018234 + 209.87388421679*$t);
$X2 += 0.00000010182*cos(5.59563792015 + 235.6343134493*$t);
$X2 += 0.00000009148*cos(2.31017574698 + 1464.3956625793*$t);
$X2 += 0.00000009436*cos(3.25931284572 + 508.10650660869*$t);
$X2 += 0.00000008422*cos(1.74868225923 + 661.4817447999*$t);
$X2 += 0.00000008359*cos(1.43667117664 + 1361.3028883607*$t);
$X2 += 0.00000008253*cos(0.86562358245 + 565.35950523021*$t);
$X2 += 0.00000009478*cos(2.12166784380 + 949.4194264533*$t);
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$X2 += 0.00000004944*cos(2.25390759795 + 1787.9010792367*$t);
$X2 += 0.00000004821*cos(2.05306967383 + 644.0732570606*$t);
$X2 += 0.00000004551*cos(2.00498534256 + 757.4609720177*$t);
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$X2 += 0.00000004026*cos(6.02985977936 + 710.99054910171*$t);
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$X2 += 0.00000001423*cos(0.84203295561 + 201.7634994747*$t);
$X2 += 0.00000001568*cos(0.17276009703 + 685.7177548362*$t);
$X2 += 0.00000001663*cos(2.39240670265 + 3597.8742519263*$t);
$X2 += 0.00000001491*cos(2.09091136066 + 240.36961586451*$t);
$X2 += 0.00000001913*cos(1.64595427075 + 295.4380584896*$t);
$X2 += 0.00000001496*cos(3.10700890764 + 1045.3986536711*$t);
$X2 += 0.00000001477*cos(5.34776911444 + 440.5814673941*$t);
$X2 += 0.00000001410*cos(3.85254018400 + 137.2768416459*$t);
$X2 += 0.00000001748*cos(3.62192812061 + 519.15220687259*$t);
$X2 += 0.00000001325*cos(2.98811767557 + 980.91199584231*$t);
$X2 += 0.00000001352*cos(5.53324653057 + 5429.63565075589*$t);
$X2 += 0.00000001414*cos(6.21378141122 + 1371.59782909919*$t);
$X2 += 0.00000001697*cos(2.96957793002 + 1898.10740045609*$t);
$X2 += 0.00000001424*cos(3.32164076256 + 721.40560204669*$t);
$X2 += 0.00000001424*cos(3.32164076256 + 721.8932370137*$t);
$X2 += 0.00000001295*cos(5.37619224276 + 1905.2209474569*$t);
$X2 += 0.00000001272*cos(5.72341064428 + 127.71561409031*$t);
$X2 += 0.00000001740*cos(2.98134401594 + 1883.8803064545*$t);
$X2 += 0.00000001435*cos(1.83931362023 + 699.94484883781*$t);
$X2 += 0.00000001260*cos(0.96015330455 + 850.25880549781*$t);
$X2 += 0.00000001316*cos(0.48574200131 + 1382.64352936309*$t);
$X2 += 0.00000001303*cos(4.34276081528 + 28.6980054867*$t);
$X2 += 0.00000001701*cos(3.01361282532 + 312.70353387701*$t);
$X2 += 0.00000001245*cos(0.67360153650 + 9359.84534697549*$t);
$X2 += 0.00000001240*cos(1.28978443782 + 1994.08662767389*$t);
$X2 += 0.00000001286*cos(2.12726478428 + 1048.8431719672*$t);
$X2 += 0.00000001240*cos(0.05914920282 + 148.32254190981*$t);
$X2 += 0.00000001365*cos(2.52639842443 + 212.79215339611*$t);
$X2 += 0.00000001362*cos(5.50511551601 + 214.2936724469*$t);
$X2 += 0.00000001206*cos(2.27873859730 + 739.5648493114*$t);
$X2 += 0.00000001503*cos(3.64035751539 + 1243.98302014049*$t);
$X2 += 0.00000001305*cos(3.14322057429 + 259.1195639602*$t);
$X2 += 0.00000001167*cos(3.43763509907 + 233.1866328945*$t);
$X2 += 0.00000001167*cos(4.59358372111 + 193.8991929485*$t);
$X2 += 0.00000001155*cos(2.09477644020 + 153.73916788121*$t);
$X2 += 0.00000001220*cos(4.50978581010 + 283.9047232587*$t);
$X2 += 0.00000001153*cos(1.49807886709 + 525.7419968841*$t);
$X2 += 0.00000001188*cos(1.37272384469 + 258.6319289932*$t);
$X2 += 0.00000001558*cos(6.24300347417 + 4216.4308972379*$t);
$X2 += 0.00000001423*cos(2.20117675779 + 2420.68481854989*$t);
$X2 += 0.00000001138*cos(5.47453297293 + 17.91542978119*$t);
$X2 += 0.00000001133*cos(1.27426244635 + 841.9068640046*$t);
$X2 += 0.00000001109*cos(5.77014938471 + 121.0082039998*$t);
$X2 += 0.00000001109*cos(1.74252937792 + 629.846163059*$t);
$X2 += 0.00000001434*cos(2.33577168517 + 6062.4193900691*$t);
$X2 += 0.00000001122*cos(4.02937359406 + 128.6093859676*$t);
$X2 += 0.00000001123*cos(4.63883211615 + 3178.38960805111*$t);
$X2 += 0.00000001154*cos(5.89138208590 + 67.91186905*$t);
$X2 += 0.00000001130*cos(3.68532102062 + 731.70054278519*$t);
$X2 += 0.00000001305*cos(3.82341882270 + 97.11681657861*$t);
$X2 += 0.00000001248*cos(2.25171827957 + 2523.7775927685*$t);
$X2 += 0.00000001161*cos(3.82920355830 + 81.9959506997*$t);
$X2 += 0.00000001178*cos(2.27177304436 + 1056.444353935*$t);
$X2 += 0.00000001342*cos(0.90865804529 + 355.99256305531*$t);
$X2 += 0.00000001249*cos(3.35095586398 + 526.2657538734*$t);
$X2 += 0.00000001034*cos(6.13425127848 + 777.17412795991*$t);
$X2 += 0.00000001332*cos(3.33641634482 + 835.5440765292*$t);
$X2 += 0.00000001024*cos(4.46551378693 + 5635.8211991931*$t);
$X2 += 0.00000001173*cos(2.59368230210 + 74.53778108379*$t);
$X2 += 0.00000001173*cos(1.88536238484 + 2317.5920443313*$t);
$X2 += 0.00000001012*cos(4.43552013111 + 215.2398339509*$t);
$X2 += 0.00000001186*cos(4.99759781142 + 1272.9248431107*$t);
$X2 += 0.00000001049*cos(2.89184213238 + 6062.9070250361*$t);
$X2 += 0.00000001154*cos(1.74865938292 + 2406.4577245483*$t);
$X2 += 0.00000001062*cos(4.97332239252 + 906.130397275*$t);
$X2 += 0.00000001124*cos(2.19046669320 + 3914.26612158291*$t);
$X2 += 0.00000000993*cos(3.56282013143 + 211.8459918921*$t);
$X2 += 0.00000000986*cos(4.64695151983 + 525.514994348*$t);
$X2 += 0.00000000986*cos(1.18009463616 + 602.00806815971*$t);
$X2 += 0.00000000992*cos(1.73454490947 + 306.34074640161*$t);
$X2 += 0.00000001239*cos(2.83323142368 + 2193.1586291103*$t);
$X2 += 0.00000001134*cos(1.51692947764 + 2729.96314120569*$t);
$X2 += 0.00000001041*cos(0.96856014126 + 945.7503977486*$t);
$X2 += 0.00000001025*cos(4.65212942292 + 32.48714639791*$t);
$X2 += 0.00000001044*cos(3.13333997041 + 472.4186593982*$t);
$X2 += 0.00000001335*cos(3.23250354837 + 2324.70559133209*$t);
$X2 += 0.00000001199*cos(5.97883679965 + 4113.3381230193*$t);
$X2 += 0.00000001174*cos(6.24416585602 + 1176.9456158929*$t);
$X2 += 0.00000001213*cos(1.85427016032 + 252.8997888367*$t);
$X2 += 0.00000000973*cos(3.32855151003 + 245.03548231051*$t);
$X2 += 0.00000000973*cos(1.56107465656 + 182.05034353251*$t);
$X2 += 0.00000001167*cos(4.51079844988 + 635.72131556739*$t);
$X2 += 0.00000000936*cos(4.89205060352 + 220.1351950605*$t);
$X2 += 0.00000001073*cos(2.28404354413 + 1773.6739852351*$t);
$X2 += 0.00000000931*cos(3.12796311727 + 206.9506307825*$t);
$X2 += 0.00000000931*cos(4.22108011413 + 1582.2031657665*$t);
$X2 += 0.00000001237*cos(5.91198768163 + 2964.60287764609*$t);
$X2 += 0.00000001074*cos(3.43802549251 + 738.814089786*$t);
$X2 += 0.00000000976*cos(4.61137219155 + 31.9995114309*$t);
$X2 += 0.00000000907*cos(5.15190704681 + 1802.6158082053*$t);
$X2 += 0.00000000925*cos(4.33653627215 + 3494.7814777077*$t);
$X2 += 0.00000000999*cos(5.63756377401 + 171.8984151459*$t);
$X2 += 0.00000000931*cos(3.19108655615 + 1037.7974717033*$t);
$X2 += 0.00000001094*cos(2.28588137520 + 2516.66404576769*$t);
$X2 += 0.00000000949*cos(5.39859475117 + 1809.72935520611*$t);
$X2 += 0.00000000964*cos(4.14879961487 + 2641.5850959557*$t);
$X2 += 0.00000000947*cos(4.37174355210 + 2111.40649589409*$t);
$X2 += 0.00000000898*cos(5.87505951681 + 9566.03089541269*$t);
$X2 += 0.00000001029*cos(4.83213149276 + 519.63984183961*$t);
$X2 += 0.00000000989*cos(5.52532133338 + 255.1874106971*$t);
$X2 += 0.00000001003*cos(2.89315844222 + 60.52313540329*$t);
$X2 += 0.00000000886*cos(5.44090853481 + 305.10235190919*$t);
$X2 += 0.00000000920*cos(3.26822857927 + 459.0853372739*$t);
$X2 += 0.00000000888*cos(6.08377383987 + 3259.6541063003*$t);
$X2 += 0.00000000888*cos(6.08377383987 + 3260.1417412673*$t);
$X2 += 0.00000000960*cos(4.90164911800 + 84.6897094704*$t);
$X2 += 0.00000000881*cos(5.34840991118 + 397.9001853893*$t);
$X2 += 0.00000000924*cos(0.50062273312 + 731.92754532131*$t);
$X2 += 0.00000000960*cos(4.40263473154 + 5856.7214765989*$t);
$X2 += 0.00000000886*cos(4.84941446555 + 471.9310244312*$t);
$X2 += 0.00000000909*cos(2.87462833456 + 746.15463932291*$t);
return $X2*$t*$t;
}
function Saturn_X3($t) // 250 terms of order 3
{
$X3 = 0.00076886822*cos(2.95726755259 + 206.42936592071*$t);
$X3 += 0.00075865107*cos(1.87343394188 + 220.6564599223*$t);
$X3 += 0.00028377246*cos(3.86557149479 + 0.2438174835*$t);
$X3 += 0.00011451297*cos(0.52950959639 + 426.8420083595*$t);
$X3 += 0.00009043324*cos(0.90644151923 + 433.9555553603*$t);
$X3 += 0.00007419530*cos(1.78113005821 + 227.77000692311*$t);
$X3 += 0.00008292033*cos(3.07262247518 + 7.3573644843*$t);
$X3 += 0.00004421142*cos(2.21157518590 + 419.72846135871*$t);
$X3 += 0.00003519324*cos(3.11036333131 + 199.3158189199*$t);
$X3 += 0.00003064445*cos(5.96466087519 + 640.1411037975*$t);
$X3 += 0.00002363042*cos(3.04029814628 + 14.47091148511*$t);
$X3 += 0.00001027777*cos(0.00466674598 + 647.25465079831*$t);
$X3 += 0.00000789743*cos(0.89493947314 + 441.06910236111*$t);
$X3 += 0.00000810744*cos(1.27206560500 + 216.72430665921*$t);
$X3 += 0.00000766386*cos(3.60274923273 + 210.36151918381*$t);
$X3 += 0.00000673097*cos(3.76715088659 + 213.0552779545*$t);
$X3 += 0.00000506614*cos(3.74427289102 + 213.5429129215*$t);
$X3 += 0.00000384956*cos(3.04387305073 + 117.5636857037*$t);
$X3 += 0.00000463540*cos(5.12353455374 + 853.4401992355*$t);
$X3 += 0.00000411246*cos(3.75278799309 + 110.45013870291*$t);
$X3 += 0.00000324142*cos(1.64931862119 + 234.8835539239*$t);
$X3 += 0.00000285917*cos(1.98200727487 + 412.6149143579*$t);
$X3 += 0.00000238406*cos(3.32280489930 + 103.3365917021*$t);
$X3 += 0.00000192441*cos(0.61468306333 + 316.6356871401*$t);
$X3 += 0.00000189600*cos(5.40892808690 + 6.86972951729*$t);
$X3 += 0.00000189610*cos(2.26186337972 + 633.0275567967*$t);
$X3 += 0.00000213874*cos(5.57078419443 + 205.9417309537*$t);
$X3 += 0.00000153605*cos(2.27746123288 + 323.74923414091*$t);
$X3 += 0.00000154083*cos(2.88123748841 + 21.5844584859*$t);
$X3 += 0.00000130169*cos(1.38079516386 + 209.6107596584*$t);
$X3 += 0.00000121811*cos(5.19039452998 + 198.82818395289*$t);
$X3 += 0.00000112652*cos(4.50657670209 + 220.16882495529*$t);
$X3 += 0.00000109203*cos(3.33018599514 + 217.4750661846*$t);
$X3 += 0.00000111589*cos(5.41300222633 + 860.55374623631*$t);
$X3 += 0.00000097336*cos(0.97161200873 + 95.7354097343*$t);
$X3 += 0.00000114728*cos(1.16141976921 + 223.83785366*$t);
$X3 += 0.00000085497*cos(1.88744465241 + 330.8627811417*$t);
$X3 += 0.00000103793*cos(2.96083959404 + 309.5221401393*$t);
$X3 += 0.00000085243*cos(0.03105121395 + 654.3681977991*$t);
$X3 += 0.00000081972*cos(3.29167838280 + 192.2022719191*$t);
$X3 += 0.00000093735*cos(3.09844453957 + 426.3543733925*$t);
$X3 += 0.00000078232*cos(1.55716671048 + 124.6772327045*$t);
$X3 += 0.00000073732*cos(1.05194572850 + 88.6218627335*$t);
$X3 += 0.00000068659*cos(3.09861369147 + 109.9625037359*$t);
$X3 += 0.00000087657*cos(0.36385164600 + 430.02340209721*$t);
$X3 += 0.00000057790*cos(1.70437193383 + 224.5886131854*$t);
$X3 += 0.00000050888*cos(3.09413498180 + 202.4972126576*$t);
$X3 += 0.00000048029*cos(3.83068266955 + 302.40859313851*$t);
$X3 += 0.00000057606*cos(3.83723480361 + 203.247972183*$t);
$X3 += 0.00000056960*cos(4.32645734701 + 1066.7392946735*$t);
$X3 += 0.00000045308*cos(3.25423824441 + 96.2230447013*$t);
$X3 += 0.00000048067*cos(6.08559382039 + 309.0345051723*$t);
$X3 += 0.00000036732*cos(0.80231221541 + 448.1826493619*$t);
$X3 += 0.00000038865*cos(3.77730274172 + 625.9140097959*$t);
$X3 += 0.00000043853*cos(0.20832317981 + 422.9098550964*$t);
$X3 += 0.00000036680*cos(5.09355802388 + 13.9832765181*$t);
$X3 += 0.00000035412*cos(5.54558308698 + 522.8212355773*$t);
$X3 += 0.00000030232*cos(3.87085631365 + 412.12727939089*$t);
$X3 += 0.00000034292*cos(6.06837760251 + 301.9209581715*$t);
$X3 += 0.00000025919*cos(5.31578501663 + 4.1759707466*$t);
$X3 += 0.00000026527*cos(3.52104928312 + 423.66061462181*$t);
$X3 += 0.00000023623*cos(4.82567426056 + 515.2200536095*$t);
$X3 += 0.00000017831*cos(5.24620312943 + 11.2895177474*$t);
$X3 += 0.00000017289*cos(0.98528821511 + 537.0483295789*$t);
$X3 += 0.00000016881*cos(5.38329398416 + 195.38366565681*$t);
$X3 += 0.00000013511*cos(5.72506783696 + 515.70768857651*$t);
$X3 += 0.00000012893*cos(1.12369483024 + 437.8877086234*$t);
$X3 += 0.00000011197*cos(2.55648325655 + 742.74624304909*$t);
$X3 += 0.00000013451*cos(5.19262853301 + 522.3336006103*$t);
$X3 += 0.00000010292*cos(0.86377999055 + 337.9763281425*$t);
$X3 += 0.00000011481*cos(5.27139699788 + 191.7146369521*$t);
$X3 += 0.00000011394*cos(5.93878680228 + 625.42637482889*$t);
$X3 += 0.00000011380*cos(4.58881936707 + 1073.85284167431*$t);
$X3 += 0.00000009884*cos(0.96968966802 + 131.79077970531*$t);
$X3 += 0.00000009268*cos(1.28597973750 + 81.50831573269*$t);
$X3 += 0.00000010374*cos(0.94317330721 + 544.1618765797*$t);
$X3 += 0.00000011913*cos(0.32742179509 + 437.136949098*$t);
$X3 += 0.00000008626*cos(3.66458258994 + 728.5191490475*$t);
$X3 += 0.00000008671*cos(4.32466808269 + 419.2408263917*$t);
$X3 += 0.00000008821*cos(4.57655314696 + 831.6119232661*$t);
$X3 += 0.00000008112*cos(0.50007270362 + 149.8070146181*$t);
$X3 += 0.00000009768*cos(5.81884437871 + 618.3128278281*$t);
$X3 += 0.00000008329*cos(5.47343196835 + 867.6672932371*$t);
$X3 += 0.00000007645*cos(2.39585916890 + 846.3266522347*$t);
$X3 += 0.00000008659*cos(5.79445660573 + 643.32249753521*$t);
$X3 += 0.00000007205*cos(4.39953882951 + 227.2823719561*$t);
$X3 += 0.00000007157*cos(5.63667649779 + 636.2089505344*$t);
$X3 += 0.00000007036*cos(2.63239333334 + 231.70216018621*$t);
$X3 += 0.00000007083*cos(4.84184174066 + 89.10949770051*$t);
$X3 += 0.00000006556*cos(2.67135559119 + 743.23387801611*$t);
$X3 += 0.00000005903*cos(0.87375775835 + 270.1652642241*$t);
$X3 += 0.00000006615*cos(3.63831273611 + 433.46792039329*$t);
$X3 += 0.00000006469*cos(2.05411382166 + 408.68276109481*$t);
$X3 += 0.00000005426*cos(1.51765079988 + 241.9971009247*$t);
$X3 += 0.00000005648*cos(2.55416366478 + 529.9347825781*$t);
$X3 += 0.00000007105*cos(3.01903914273 + 18.40306474821*$t);
$X3 += 0.00000005052*cos(5.18252086135 + 416.547067621*$t);
$X3 += 0.00000006189*cos(4.68404979693 + 736.1203310153*$t);
$X3 += 0.00000005821*cos(3.50616955116 + 1280.0383901115*$t);
$X3 += 0.00000005043*cos(3.76766161323 + 277.2788112249*$t);
$X3 += 0.00000004744*cos(1.46479508366 + 56.3785338191*$t);
$X3 += 0.00000005705*cos(4.87015493433 + 430.7741616226*$t);
$X3 += 0.00000005226*cos(5.29097572967 + 415.7963080956*$t);
$X3 += 0.00000005511*cos(3.59570699682 + 529.44714761109*$t);
$X3 += 0.00000004520*cos(2.36588968635 + 1059.1381127057*$t);
$X3 += 0.00000004583*cos(0.00787099904 + 294.80741117069*$t);
$X3 += 0.00000004789*cos(4.15071050239 + 295.2950461377*$t);
$X3 += 0.00000004026*cos(0.04020873612 + 483.4643596621*$t);
$X3 += 0.00000003728*cos(0.24380479533 + 185.08872491831*$t);
$X3 += 0.00000003578*cos(2.51284387407 + 405.5013673571*$t);
$X3 += 0.00000003890*cos(0.29060160988 + 750.3474250169*$t);
$X3 += 0.00000004291*cos(5.60521207533 + 941.8182444855*$t);
$X3 += 0.00000003758*cos(6.26818424862 + 661.4817447999*$t);
$X3 += 0.00000003547*cos(0.40358942005 + 70.6056278207*$t);
$X3 += 0.00000003641*cos(3.81013693999 + 839.2131052339*$t);
$X3 += 0.00000004196*cos(3.97690464270 + 618.8004627951*$t);
$X3 += 0.00000003709*cos(4.96509425454 + 508.10650660869*$t);
$X3 += 0.00000004193*cos(5.05036487395 + 838.72547026689*$t);
$X3 += 0.00000003571*cos(4.46056188614 + 1148.00379292269*$t);
$X3 += 0.00000003647*cos(5.59898306379 + 934.70469748469*$t);
$X3 += 0.00000002978*cos(3.43782247022 + 1044.9110187041*$t);
$X3 += 0.00000002876*cos(5.29356968989 + 398.38782035631*$t);
$X3 += 0.00000002643*cos(5.23820067295 + 497.69145366371*$t);
$X3 += 0.00000002725*cos(5.89016060143 + 363.1061100561*$t);
$X3 += 0.00000003246*cos(2.57150474119 + 639.6534688305*$t);
$X3 += 0.00000002721*cos(4.14564904530 + 1464.3956625793*$t);
$X3 += 0.00000002917*cos(2.38362703069 + 113.6315324406*$t);
$X3 += 0.00000002560*cos(4.95049691984 + 729.0067840145*$t);
$X3 += 0.00000002380*cos(6.24323945584 + 86.07111631471*$t);
$X3 += 0.00000002667*cos(0.09012233039 + 10.8018827804*$t);
$X3 += 0.00000002238*cos(2.26341623480 + 10.538758222*$t);
$X3 += 0.00000002305*cos(2.02658716121 + 956.53297345411*$t);
$X3 += 0.00000002316*cos(2.01244422105 + 3.42521122121*$t);
$X3 += 0.00000002282*cos(5.91510901442 + 611.1992808273*$t);
$X3 += 0.00000001988*cos(0.28661492755 + 651.1868040614*$t);
$X3 += 0.00000002365*cos(5.33155242941 + 2111.40649589409*$t);
$X3 += 0.00000002485*cos(4.32833388537 + 316.14805217309*$t);
$X3 += 0.00000002670*cos(0.63080955086 + 196.1344251822*$t);
$X3 += 0.00000002670*cos(1.11722396213 + 230.9514006608*$t);
$X3 += 0.00000001974*cos(3.29767644397 + 1059.6257476727*$t);
$X3 += 0.00000002440*cos(2.29714766763 + 106.0303504728*$t);
$X3 += 0.00000002032*cos(2.08292611476 + 1375.52998236229*$t);
$X3 += 0.00000002151*cos(4.69823758687 + 824.4983762653*$t);
$X3 += 0.00000001875*cos(1.50694339603 + 344.9468627914*$t);
$X3 += 0.00000002440*cos(1.37504875250 + 323.2615991739*$t);
$X3 += 0.00000002034*cos(5.64959382524 + 927.5911504839*$t);
$X3 += 0.00000002310*cos(4.84647061416 + 99.6675629974*$t);
$X3 += 0.00000001764*cos(1.86111058424 + 191.45151239371*$t);
$X3 += 0.00000002032*cos(3.74188450688 + 636.95971005981*$t);
$X3 += 0.00000001993*cos(5.41370582068 + 1258.21011414209*$t);
$X3 += 0.00000001921*cos(4.30051805390 + 2641.0974609887*$t);
$X3 += 0.00000001620*cos(5.90686570991 + 1596.43025976811*$t);
$X3 += 0.00000001903*cos(3.15206555826 + 2634.47154895491*$t);
$X3 += 0.00000001568*cos(3.03962897704 + 235.6343134493*$t);
$X3 += 0.00000001835*cos(0.46838409843 + 536.5606946119*$t);
$X3 += 0.00000001523*cos(4.48022908171 + 956.04533848709*$t);
$X3 += 0.00000002086*cos(1.63830662169 + 445.00125562421*$t);
$X3 += 0.00000001666*cos(1.70124586487 + 1876.76675945369*$t);
$X3 += 0.00000001479*cos(2.77539985198 + 6290.4332144757*$t);
$X3 += 0.00000001479*cos(5.26668359322 + 5849.1202946311*$t);
$X3 += 0.00000001439*cos(3.22610898757 + 2538.4923217371*$t);
$X3 += 0.00000001464*cos(4.18005026025 + 5863.3473886327*$t);
$X3 += 0.00000001464*cos(3.86203316672 + 6276.2061204741*$t);
$X3 += 0.00000001676*cos(5.34747324592 + 1251.0965671413*$t);
$X3 += 0.00000001945*cos(3.48549478580 + 845.8390172677*$t);
$X3 += 0.00000001436*cos(6.23499570787 + 508.5941415757*$t);
$X3 += 0.00000001481*cos(4.49861202018 + 284.39235822571*$t);
$X3 += 0.00000001709*cos(3.35714658968 + 2318.0796792983*$t);
$X3 += 0.00000001305*cos(4.10818846677 + 107.2687449652*$t);
$X3 += 0.00000001548*cos(2.81939196041 + 2943.74987161071*$t);
$X3 += 0.00000001465*cos(2.76905277973 + 2531.3787747363*$t);
$X3 += 0.00000001494*cos(3.94286053931 + 1780.78753223589*$t);
$X3 += 0.00000001243*cos(5.53319819376 + 218.2087793675*$t);
$X3 += 0.00000001234*cos(2.48191739575 + 208.8770464755*$t);
$X3 += 0.00000001359*cos(1.84182551916 + 142.6934676173*$t);
$X3 += 0.00000001217*cos(5.17100163408 + 1052.51220067191*$t);
$X3 += 0.00000001352*cos(0.35400553171 + 209.87388421679*$t);
$X3 += 0.00000001391*cos(5.36503473377 + 1243.98302014049*$t);
$X3 += 0.00000001426*cos(0.53946388105 + 852.9525642685*$t);
$X3 += 0.00000001501*cos(2.10731420473 + 1691.9218520189*$t);
$X3 += 0.00000001326*cos(6.28017468529 + 2751.79141717511*$t);
$X3 += 0.00000001171*cos(1.32902114795 + 67.91186905*$t);
$X3 += 0.00000001462*cos(1.51066849209 + 160.852714882*$t);
$X3 += 0.00000001164*cos(4.63302622392 + 117.0760507367*$t);
$X3 += 0.00000001337*cos(3.11900326329 + 2627.3580019541*$t);
$X3 += 0.00000001509*cos(4.93045095005 + 1574.6019837987*$t);
$X3 += 0.00000001213*cos(4.31502095540 + 1354.6769763269*$t);
$X3 += 0.00000001241*cos(4.40235607417 + 1140.8902459219*$t);
$X3 += 0.00000001288*cos(2.87027499482 + 2950.8634186115*$t);
$X3 += 0.00000001337*cos(3.78093252376 + 2421.1724535169*$t);
$X3 += 0.00000001327*cos(4.98650305262 + 1567.48843679789*$t);
$X3 += 0.00000001118*cos(3.03705756384 + 209.12312469139*$t);
$X3 += 0.00000001043*cos(3.94898504220 + 156.9205616189*$t);
$X3 += 0.00000001069*cos(3.08968284008 + 194.89603068979*$t);
$X3 += 0.00000001088*cos(2.53876092916 + 1272.9248431107*$t);
$X3 += 0.00000001270*cos(4.16462693224 + 2516.66404576769*$t);
$X3 += 0.00000001032*cos(3.44230149136 + 1361.3028883607*$t);
$X3 += 0.00000001009*cos(4.86702032393 + 52.446380556*$t);
$X3 += 0.00000001100*cos(4.02565365863 + 1671.06884598351*$t);
$X3 += 0.00000001071*cos(2.74654865620 + 1354.18934135989*$t);
$X3 += 0.00000001120*cos(2.93643432204 + 1037.7974717033*$t);
$X3 += 0.00000001271*cos(1.45604360323 + 721.40560204669*$t);
$X3 += 0.00000001009*cos(2.57702574321 + 1670.5812110165*$t);
$X3 += 0.00000001145*cos(1.75945733161 + 3157.04896704871*$t);
$X3 += 0.00000001072*cos(0.27481402100 + 2435.3995475185*$t);
$X3 += 0.00000001044*cos(5.08425663596 + 1560.3748897971*$t);
$X3 += 0.00000001195*cos(2.65932688138 + 632.5399218297*$t);
$X3 += 0.00000001043*cos(3.11389723945 + 2729.96314120569*$t);
$X3 += 0.00000000889*cos(0.42212522834 + 359.173956793*$t);
$X3 += 0.00000000881*cos(5.64403825823 + 1148.49142788971*$t);
$X3 += 0.00000001040*cos(3.92524025620 + 1773.6739852351*$t);
$X3 += 0.00000001118*cos(4.70881220655 + 1890.9938534553*$t);
$X3 += 0.00000001047*cos(2.54344637059 + 3260.1417412673*$t);
$X3 += 0.00000001087*cos(3.60856902528 + 2001.2001746747*$t);
$X3 += 0.00000001087*cos(3.60856902527 + 2001.68780964171*$t);
$X3 += 0.00000000974*cos(3.71347864898 + 1987.4607156401*$t);
$X3 += 0.00000000869*cos(1.74331052904 + 621.98185653281*$t);
$X3 += 0.00000001085*cos(2.89917981696 + 2214.98690507971*$t);
$X3 += 0.00000000841*cos(4.92696318078 + 629.0954035336*$t);
$X3 += 0.00000000875*cos(2.65002330643 + 2847.77064439291*$t);
$X3 += 0.00000001063*cos(4.38870058058 + 2200.2721761111*$t);
$X3 += 0.00000000853*cos(5.24982533241 + 288.32451148881*$t);
$X3 += 0.00000001056*cos(1.76497744402 + 2332.3067732999*$t);
$X3 += 0.00000000888*cos(5.03418369313 + 1155.1173399235*$t);
$X3 += 0.00000001045*cos(4.85721663734 + 2.9375762542*$t);
$X3 += 0.00000000793*cos(4.83325249319 + 341.01470952831*$t);
$X3 += 0.00000000817*cos(5.39128218727 + 1802.12817323829*$t);
$X3 += 0.00000000780*cos(5.10185484903 + 1382.64352936309*$t);
$X3 += 0.00000000798*cos(1.50816477183 + 2015.42726867629*$t);
$X3 += 0.00000000798*cos(4.64975742542 + 2015.9149036433*$t);
$X3 += 0.00000000834*cos(3.90981062264 + 1802.6158082053*$t);
$X3 += 0.00000000766*cos(5.01481205403 + 1471.50920958009*$t);
$X3 += 0.00000000875*cos(4.28307795111 + 2523.7775927685*$t);
$X3 += 0.00000000829*cos(2.87306260461 + 1162.23088692429*$t);
$X3 += 0.00000000749*cos(3.65030777836 + 1809.72935520611*$t);
$X3 += 0.00000000942*cos(1.83557306265 + 2008.3137216755*$t);
$X3 += 0.00000000730*cos(5.63130452905 + 138.76131435421*$t);
$X3 += 0.00000000734*cos(5.54620111084 + 749.8597900499*$t);
$X3 += 0.00000000727*cos(2.38685285770 + 181.2995840071*$t);
$X3 += 0.00000000727*cos(2.50277330889 + 245.7862418359*$t);
$X3 += 0.00000000986*cos(2.62709892303 + 1795.0146262375*$t);
$X3 += 0.00000000914*cos(3.38925031218 + 266.233110961*$t);
$X3 += 0.00000000774*cos(0.28234439952 + 2840.1694624251*$t);
$X3 += 0.00000000774*cos(3.42393705311 + 2840.6570973921*$t);
$X3 += 0.00000000806*cos(4.44962138010 + 1912.8221294247*$t);
$X3 += 0.00000000828*cos(1.60210145147 + 100.1551979644*$t);
$X3 += 0.00000000700*cos(0.41140636858 + 9779.32999085069*$t);
$X3 += 0.00000000700*cos(4.19439623716 + 10220.6429106953*$t);
$X3 += 0.00000000687*cos(4.43661173924 + 102.84895673509*$t);
$X3 += 0.00000000801*cos(4.16672540134 + 1457.2821155785*$t);
return $X3*$t*$t*$t;
}
function Saturn_X4($t) // 110 terms of order 4
{
$X4 = 0.00007957923*cos(0.10292939767 + 220.6564599223*$t);
$X4 += 0.00007883034*cos(4.66633773762 + 206.42936592071*$t);
$X4 += 0.00001517028*cos(0.05577219527 + 227.77000692311*$t);
$X4 += 0.00001235695*cos(5.39600292264 + 433.9555553603*$t);
$X4 += 0.00001152216*cos(5.24396587079 + 213.5429129215*$t);
$X4 += 0.00000879616*cos(5.34174983557 + 0.2438174835*$t);
$X4 += 0.00000709628*cos(4.81919971142 + 199.3158189199*$t);
$X4 += 0.00000602013*cos(1.23511363469 + 7.3573644843*$t);
$X4 += 0.00000507367*cos(4.78792568609 + 426.8420083595*$t);
$X4 += 0.00000386382*cos(1.30105603325 + 14.47091148511*$t);
$X4 += 0.00000338827*cos(4.08599989607 + 419.72846135871*$t);
$X4 += 0.00000186029*cos(5.42685623154 + 441.06910236111*$t);
$X4 += 0.00000220262*cos(4.07756916511 + 640.1411037975*$t);
$X4 += 0.00000173210*cos(4.46238384072 + 647.25465079831*$t);
$X4 += 0.00000084974*cos(6.19195566472 + 234.8835539239*$t);
$X4 += 0.00000085340*cos(2.82637979462 + 213.0552779545*$t);
$X4 += 0.00000044264*cos(1.34743358639 + 117.5636857037*$t);
$X4 += 0.00000045849*cos(3.59457316555 + 6.86972951729*$t);
$X4 += 0.00000047835*cos(3.21421968827 + 853.4401992355*$t);
$X4 += 0.00000041104*cos(3.75480601059 + 412.6149143579*$t);
$X4 += 0.00000030735*cos(1.14073508300 + 21.5844584859*$t);
$X4 += 0.00000022639*cos(4.54040624066 + 654.3681977991*$t);
$X4 += 0.00000021067*cos(4.91324359260 + 103.3365917021*$t);
$X4 += 0.00000020230*cos(1.74358717590 + 110.45013870291*$t);
$X4 += 0.00000021389*cos(0.96555928483 + 205.9417309537*$t);
$X4 += 0.00000016854*cos(5.95101073162 + 124.6772327045*$t);
$X4 += 0.00000021739*cos(3.56778546142 + 860.55374623631*$t);
$X4 += 0.00000017501*cos(2.66582523466 + 220.16882495529*$t);
$X4 += 0.00000014506*cos(2.82815343470 + 88.6218627335*$t);
$X4 += 0.00000017401*cos(0.69153050158 + 198.82818395289*$t);
$X4 += 0.00000013517*cos(4.90527630680 + 309.5221401393*$t);
$X4 += 0.00000011814*cos(0.44837969058 + 323.74923414091*$t);
$X4 += 0.00000012071*cos(5.31212364211 + 448.1826493619*$t);
$X4 += 0.00000011725*cos(0.04357660859 + 330.8627811417*$t);
$X4 += 0.00000010174*cos(2.85692484188 + 95.7354097343*$t);
$X4 += 0.00000011491*cos(5.22879894174 + 192.2022719191*$t);
$X4 += 0.00000010611*cos(5.64300353639 + 302.40859313851*$t);
$X4 += 0.00000012147*cos(4.23365602535 + 633.0275567967*$t);
$X4 += 0.00000009067*cos(2.69785298236 + 13.9832765181*$t);
$X4 += 0.00000008918*cos(1.46910827681 + 426.3543733925*$t);
$X4 += 0.00000008311*cos(4.67543017537 + 430.02340209721*$t);
$X4 += 0.00000007296*cos(2.34933784290 + 316.6356871401*$t);
$X4 += 0.00000007890*cos(2.51218274353 + 1066.7392946735*$t);
$X4 += 0.00000006699*cos(1.49841716625 + 109.9625037359*$t);
$X4 += 0.00000006339*cos(5.32790301740 + 216.72430665921*$t);
$X4 += 0.00000006254*cos(2.70033795328 + 210.36151918381*$t);
$X4 += 0.00000006126*cos(1.64892191331 + 301.9209581715*$t);
$X4 += 0.00000006725*cos(5.51198561168 + 625.9140097959*$t);
$X4 += 0.00000006784*cos(5.78945551800 + 223.83785366*$t);
$X4 += 0.00000006868*cos(2.22797475448 + 203.247972183*$t);
$X4 += 0.00000006111*cos(5.16124898313 + 96.2230447013*$t);
$X4 += 0.00000004468*cos(1.72149500008 + 309.0345051723*$t);
$X4 += 0.00000004160*cos(1.03429820392 + 522.8212355773*$t);
$X4 += 0.00000003681*cos(0.94893010872 + 423.66061462181*$t);
$X4 += 0.00000003615*cos(0.40952028826 + 405.5013673571*$t);
$X4 += 0.00000003079*cos(5.63647951312 + 412.12727939089*$t);
$X4 += 0.00000003614*cos(0.37301132942 + 515.2200536095*$t);
$X4 += 0.00000002896*cos(1.28921720639 + 515.70768857651*$t);
$X4 += 0.00000003000*cos(4.72788705186 + 422.9098550964*$t);
$X4 += 0.00000002685*cos(5.00319133132 + 209.6107596584*$t);
$X4 += 0.00000002918*cos(0.73261775434 + 89.10949770051*$t);
$X4 += 0.00000002617*cos(2.98014804776 + 217.4750661846*$t);
$X4 += 0.00000002884*cos(0.63120048927 + 191.7146369521*$t);
$X4 += 0.00000002281*cos(0.61985347120 + 316.14805217309*$t);
$X4 += 0.00000002717*cos(5.35927194820 + 131.79077970531*$t);
$X4 += 0.00000002556*cos(4.65487521363 + 337.9763281425*$t);
$X4 += 0.00000001782*cos(6.08157929050 + 241.9971009247*$t);
$X4 += 0.00000001782*cos(1.94963952968 + 185.08872491831*$t);
$X4 += 0.00000001856*cos(1.22219785032 + 618.3128278281*$t);
$X4 += 0.00000001713*cos(1.39863052168 + 625.42637482889*$t);
$X4 += 0.00000001632*cos(5.57529252306 + 728.5191490475*$t);
$X4 += 0.00000001980*cos(0.12344871269 + 831.6119232661*$t);
$X4 += 0.00000001607*cos(4.53783680441 + 611.1992808273*$t);
$X4 += 0.00000001801*cos(2.70567446780 + 227.2823719561*$t);
$X4 += 0.00000001532*cos(0.60049717130 + 1052.51220067191*$t);
$X4 += 0.00000001510*cos(1.01685015001 + 742.74624304909*$t);
$X4 += 0.00000001531*cos(4.91027438516 + 529.44714761109*$t);
$X4 += 0.00000001394*cos(2.02930508328 + 1361.3028883607*$t);
$X4 += 0.00000001427*cos(0.73295227059 + 1251.0965671413*$t);
$X4 += 0.00000001649*cos(5.83036907174 + 295.2950461377*$t);
$X4 += 0.00000001249*cos(5.31804281913 + 743.23387801611*$t);
$X4 += 0.00000001353*cos(5.64535868524 + 1678.1823929843*$t);
$X4 += 0.00000001674*cos(0.75228934735 + 231.70216018621*$t);
$X4 += 0.00000001646*cos(0.97572157001 + 195.38366565681*$t);
$X4 += 0.00000001305*cos(1.00406093433 + 934.70469748469*$t);
$X4 += 0.00000001160*cos(6.07115885491 + 81.50831573269*$t);
$X4 += 0.00000001537*cos(0.07816179599 + 21.0968235189*$t);
$X4 += 0.00000001096*cos(1.15801707287 + 832.0995582331*$t);
$X4 += 0.00000001156*cos(0.08524385094 + 508.10650660869*$t);
$X4 += 0.00000001062*cos(1.72268908914 + 294.80741117069*$t);
$X4 += 0.00000001285*cos(5.87120310708 + 1464.3956625793*$t);
$X4 += 0.00000001079*cos(6.04015764687 + 1368.9040703285*$t);
$X4 += 0.00000001006*cos(0.12126175121 + 1361.79052332771*$t);
$X4 += 0.00000001290*cos(6.26123764935 + 736.1203310153*$t);
$X4 += 0.00000001051*cos(1.11902862643 + 941.8182444855*$t);
$X4 += 0.00000001027*cos(2.13247533522 + 433.46792039329*$t);
$X4 += 0.00000001021*cos(0.91271229263 + 522.3336006103*$t);
$X4 += 0.00000001137*cos(4.47891183265 + 1891.4814884223*$t);
$X4 += 0.00000000991*cos(5.35089033439 + 1994.5742626409*$t);
$X4 += 0.00000001038*cos(6.06703363765 + 1148.00379292269*$t);
$X4 += 0.00000000865*cos(1.97882029045 + 750.3474250169*$t);
$X4 += 0.00000000859*cos(1.14491409094 + 416.547067621*$t);
$X4 += 0.00000000862*cos(4.75102573016 + 437.136949098*$t);
$X4 += 0.00000000776*cos(6.05032387495 + 102.84895673509*$t);
$X4 += 0.00000000797*cos(0.47611886612 + 1375.52998236229*$t);
$X4 += 0.00000000824*cos(2.96565494557 + 639.6534688305*$t);
$X4 += 0.00000000881*cos(5.02815372820 + 1258.6977491091*$t);
$X4 += 0.00000000686*cos(0.20449337417 + 234.3959189569*$t);
$X4 += 0.00000000684*cos(5.09702256485 + 661.4817447999*$t);
$X4 += 0.00000000859*cos(5.20905469515 + 537.0483295789*$t);
return $X4*$t*$t*$t*$t;
}
function Saturn_X5($t) // 40 terms of order 5
{
$X5 = 0.00000605503*cos(4.59646585232 + 220.6564599223*$t);
$X5 += 0.00000576439*cos(0.06437124594 + 206.42936592071*$t);
$X5 += 0.00000227348*cos(4.59085116990 + 227.77000692311*$t);
$X5 += 0.00000133503*cos(3.58841633128 + 433.9555553603*$t);
$X5 += 0.00000094765*cos(0.27215838233 + 199.3158189199*$t);
$X5 += 0.00000039851*cos(5.86635990391 + 14.47091148511*$t);
$X5 += 0.00000034190*cos(3.64452029703 + 441.06910236111*$t);
$X5 += 0.00000024941*cos(5.41093732098 + 0.2438174835*$t);
$X5 += 0.00000023155*cos(2.64207066157 + 647.25465079831*$t);
$X5 += 0.00000016208*cos(2.39130620524 + 426.8420083595*$t);
$X5 += 0.00000012333*cos(2.18222106376 + 640.1411037975*$t);
$X5 += 0.00000010358*cos(4.50067908167 + 234.8835539239*$t);
$X5 += 0.00000010534*cos(0.41421931470 + 419.72846135871*$t);
$X5 += 0.00000008668*cos(3.51972888423 + 192.2022719191*$t);
$X5 += 0.00000008840*cos(5.55216757332 + 213.5429129215*$t);
$X5 += 0.00000004707*cos(4.57538541908 + 88.6218627335*$t);
$X5 += 0.00000005904*cos(4.73107708292 + 7.3573644843*$t);
$X5 += 0.00000003895*cos(2.30231207024 + 405.5013673571*$t);
$X5 += 0.00000003976*cos(1.96984083585 + 6.86972951729*$t);
$X5 += 0.00000003675*cos(0.47302446664 + 213.0552779545*$t);
$X5 += 0.00000003472*cos(1.35605117518 + 853.4401992355*$t);
$X5 += 0.00000004393*cos(2.75554415948 + 654.3681977991*$t);
$X5 += 0.00000003290*cos(3.89078522206 + 124.6772327045*$t);
$X5 += 0.00000002569*cos(5.91571375440 + 109.9625037359*$t);
$X5 += 0.00000002467*cos(3.15983568463 + 515.70768857651*$t);
$X5 += 0.00000002708*cos(1.73056604662 + 860.55374623631*$t);
$X5 += 0.00000002138*cos(3.58678888073 + 448.1826493619*$t);
$X5 += 0.00000002447*cos(0.90027079514 + 220.16882495529*$t);
$X5 += 0.00000001979*cos(0.98519013325 + 302.40859313851*$t);
$X5 += 0.00000002238*cos(5.57282036056 + 198.82818395289*$t);
$X5 += 0.00000001727*cos(0.08010225619 + 301.9209581715*$t);
$X5 += 0.00000001398*cos(1.62923220404 + 309.5221401393*$t);
$X5 += 0.00000001536*cos(2.37774872925 + 205.9417309537*$t);
$X5 += 0.00000001195*cos(5.50915521926 + 117.5636857037*$t);
$X5 += 0.00000001000*cos(4.01529701865 + 223.83785366*$t);
$X5 += 0.00000000984*cos(3.95579224093 + 203.247972183*$t);
$X5 += 0.00000000791*cos(2.18561862902 + 330.8627811417*$t);
$X5 += 0.00000000979*cos(5.20989352885 + 95.7354097343*$t);
$X5 += 0.00000000784*cos(3.19070192516 + 522.8212355773*$t);
$X5 += 0.00000000910*cos(2.05287501643 + 96.2230447013*$t);
return $X5*$t*$t*$t*$t*$t;
}
function Saturn_Y0($t) // 2047 terms of order 0
{
$Y0 = 9.52312533591*cos(5.58640389526 + 213.5429129215*$t);
$Y0 += 0.79501390398*cos(3.19501080417 + 0.2438174835*$t);
$Y0 += 0.26427074351*cos(4.83578897954 + 426.8420083595*$t);
$Y0 += 0.06836881382*cos(2.57458281509 + 206.42936592071*$t);
$Y0 += 0.06628914946*cos(5.46296215793 + 220.6564599223*$t);
$Y0 += 0.02340967916*cos(0.44899651249 + 7.3573644843*$t);
$Y0 += 0.01250581159*cos(0.60313024847 + 110.45013870291*$t);
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$Y0 += 0.00000000800*cos(3.03519680815 + 279.72649177971*$t);
$Y0 += 0.00000000800*cos(4.99602201203 + 147.3593340633*$t);
$Y0 += 0.00000000868*cos(0.37647106732 + 669.4009330803*$t);
$Y0 += 0.00000000769*cos(5.99489096281 + 3465.8396547375*$t);
$Y0 += 0.00000000745*cos(2.84189249473 + 843.145258497*$t);
$Y0 += 0.00000000848*cos(2.77841948796 + 103.3847758119*$t);
$Y0 += 0.00000000703*cos(4.75219753735 + 4003.1318017999*$t);
$Y0 += 0.00000000719*cos(4.53501064500 + 9988.69693302559*$t);
$Y0 += 0.00000000818*cos(5.15275579739 + 311.48218572709*$t);
$Y0 += 0.00000000901*cos(0.79248369499 + 937.8860912224*$t);
$Y0 += 0.00000000783*cos(5.11638993720 + 199.83708378171*$t);
$Y0 += 0.00000000783*cos(6.05642153657 + 227.24874206131*$t);
$Y0 += 0.00000000909*cos(0.64248903432 + 4009.7577138337*$t);
$Y0 += 0.00000000711*cos(1.76892643060 + 457.3738620295*$t);
$Y0 += 0.00000000705*cos(3.12679135200 + 5653.98044645779*$t);
$Y0 += 0.00000000712*cos(6.07513529815 + 354.2810878109*$t);
$Y0 += 0.00000000733*cos(0.21809967139 + 37.6285857234*$t);
$Y0 += 0.00000000708*cos(1.27557908922 + 840.6975779422*$t);
$Y0 += 0.00000000708*cos(1.27557908922 + 840.2099429752*$t);
$Y0 += 0.00000000695*cos(6.08215837207 + 812.70191647599*$t);
$Y0 += 0.00000000695*cos(2.94056571848 + 813.189551443*$t);
$Y0 += 0.00000000736*cos(5.91292146424 + 403.9474586796*$t);
$Y0 += 0.00000000733*cos(2.29907033586 + 182.0357893175*$t);
$Y0 += 0.00000000836*cos(5.01712963721 + 2331.8191383329*$t);
$Y0 += 0.00000000928*cos(0.59357203459 + 842.13386654071*$t);
$Y0 += 0.00000000768*cos(3.70421774103 + 1460.2003847578*$t);
$Y0 += 0.00000000685*cos(4.29010164874 + 455.29619636271*$t);
$Y0 += 0.00000000792*cos(3.19395503975 + 5422.5221037551*$t);
$Y0 += 0.00000000837*cos(3.85260493508 + 570.7761312016*$t);
$Y0 += 0.00000000682*cos(3.31484357591 + 3693.8534791441*$t);
$Y0 += 0.00000000752*cos(0.56556241430 + 413.34862754081*$t);
$Y0 += 0.00000000817*cos(3.10337024087 + 391.73279989249*$t);
$Y0 += 0.00000000681*cos(0.83323807589 + 458.33457774851*$t);
$Y0 += 0.00000000803*cos(0.28965764669 + 418.49006686629*$t);
$Y0 += 0.00000000681*cos(1.95625262651 + 414.5749599457*$t);
return $Y0;
}
function Saturn_Y1($t) // 1023 terms of order 1
{
$Y1 = 0.09285877988*cos(5.32917891541 + 0.2438174835*$t);
$Y1 += 0.03086501680*cos(2.70413999679 + 426.8420083595*$t);
$Y1 += 0.02728479923*cos(4.27396756341 + 206.42936592071*$t);
$Y1 += 0.02644990371*cos(3.76176749725 + 220.6564599223*$t);
$Y1 += 0.00629201988*cos(5.03696656027 + 7.3573644843*$t);
$Y1 += 0.00256626023*cos(1.95374338915 + 640.1411037975*$t);
$Y1 += 0.00312353889*cos(3.25876676291 + 419.72846135871*$t);
$Y1 += 0.00189297041*cos(2.91534956216 + 433.9555553603*$t);
$Y1 += 0.00204465020*cos(5.78983620425 + 213.5429129215*$t);
$Y1 += 0.00118113185*cos(5.87589622232 + 110.45013870291*$t);
$Y1 += 0.00067024295*cos(2.16159727865 + 316.6356871401*$t);
$Y1 += 0.00066948413*cos(3.63141659236 + 227.77000692311*$t);
$Y1 += 0.00031931062*cos(4.42042826334 + 199.3158189199*$t);
$Y1 += 0.00024548187*cos(3.29398145587 + 205.9417309537*$t);
$Y1 += 0.00030521021*cos(4.89424590805 + 14.47091148511*$t);
$Y1 += 0.00022265017*cos(4.62323431127 + 103.3365917021*$t);
$Y1 += 0.00018939520*cos(1.20474851114 + 853.4401992355*$t);
$Y1 += 0.00018082904*cos(3.51824365057 + 209.6107596584*$t);
$Y1 += 0.00017786477*cos(4.53241903621 + 217.4750661846*$t);
$Y1 += 0.00016307253*cos(3.29827125771 + 216.72430665921*$t);
$Y1 += 0.00016919177*cos(3.01391698262 + 633.0275567967*$t);
$Y1 += 0.00015920273*cos(4.74692264945 + 210.36151918381*$t);
$Y1 += 0.00016167186*cos(4.03963160527 + 323.74923414091*$t);
$Y1 += 0.00014472589*cos(2.10335699916 + 647.25465079831*$t);
$Y1 += 0.00011071575*cos(4.74242577082 + 117.5636857037*$t);
$Y1 += 0.00009887534*cos(3.61558352957 + 202.4972126576*$t);
$Y1 += 0.00008713930*cos(4.46375520442 + 224.5886131854*$t);
$Y1 += 0.00006197025*cos(2.93543981790 + 213.0552779545*$t);
$Y1 += 0.00005502258*cos(2.83240853648 + 441.06910236111*$t);
$Y1 += 0.00005466098*cos(1.03278600709 + 11.2895177474*$t);
$Y1 += 0.00003484091*cos(4.11221224874 + 6.86972951729*$t);
$Y1 += 0.00003596198*cos(4.07360530172 + 309.0345051723*$t);
$Y1 += 0.00003029001*cos(2.81952991155 + 522.3336006103*$t);
$Y1 += 0.00003353859*cos(5.31984150246 + 95.7354097343*$t);
$Y1 += 0.00002987715*cos(4.07245500326 + 309.5221401393*$t);
$Y1 += 0.00002732424*cos(2.53884637625 + 149.8070146181*$t);
$Y1 += 0.00003741808*cos(3.25277228789 + 412.6149143579*$t);
$Y1 += 0.00002374342*cos(3.28677124286 + 198.82818395289*$t);
$Y1 += 0.00002875345*cos(1.68013950973 + 426.3543733925*$t);
$Y1 += 0.00002121841*cos(3.27302778600 + 220.16882495529*$t);
$Y1 += 0.00002386687*cos(1.79649482549 + 109.9625037359*$t);
$Y1 += 0.00001755551*cos(5.48701989649 + 277.2788112249*$t);
$Y1 += 0.00001690652*cos(2.40558615589 + 422.9098550964*$t);
$Y1 += 0.00001545396*cos(3.73180599039 + 330.8627811417*$t);
$Y1 += 0.00001447492*cos(0.46419209839 + 4.1759707466*$t);
$Y1 += 0.00001392451*cos(0.46330792664 + 1066.7392946735*$t);
$Y1 += 0.00001331483*cos(3.49216178249 + 234.8835539239*$t);
$Y1 += 0.00001452348*cos(4.64285489428 + 3.42521122121*$t);
$Y1 += 0.00001285559*cos(0.83411182275 + 415.7963080956*$t);
$Y1 += 0.00001159539*cos(3.03310034622 + 537.0483295789*$t);
$Y1 += 0.00001128476*cos(3.88012638153 + 423.66061462181*$t);
$Y1 += 0.00001131769*cos(4.43729716045 + 529.9347825781*$t);
$Y1 += 0.00001127023*cos(1.31091242342 + 860.55374623631*$t);
$Y1 += 0.00001101803*cos(2.50576870008 + 430.02340209721*$t);
$Y1 += 0.00001061927*cos(2.81261932039 + 846.3266522347*$t);
$Y1 += 0.00001343360*cos(1.41831229286 + 211.09523236671*$t);
$Y1 += 0.00001331640*cos(0.33818120038 + 215.99059347631*$t);
$Y1 += 0.00001287848*cos(0.51354213126 + 522.8212355773*$t);
$Y1 += 0.00001050973*cos(1.98569718820 + 412.12727939089*$t);
$Y1 += 0.00000900723*cos(2.55020173482 + 838.72547026689*$t);
$Y1 += 0.00000882663*cos(3.84497584849 + 437.8877086234*$t);
$Y1 += 0.00000924505*cos(5.02323714134 + 743.23387801611*$t);
$Y1 += 0.00000876882*cos(4.58871940602 + 96.2230447013*$t);
$Y1 += 0.00000905253*cos(4.94395759972 + 3.6883357796*$t);
$Y1 += 0.00000820808*cos(3.17476222193 + 223.83785366*$t);
$Y1 += 0.00000844907*cos(3.81271524339 + 625.42637482889*$t);
$Y1 += 0.00000760731*cos(5.03884679059 + 625.9140097959*$t);
$Y1 += 0.00000657423*cos(3.32272595203 + 316.14805217309*$t);
$Y1 += 0.00000813631*cos(4.73875446278 + 21.5844584859*$t);
$Y1 += 0.00000642768*cos(4.79907912774 + 1059.6257476727*$t);
$Y1 += 0.00000657845*cos(5.47081914900 + 88.6218627335*$t);
$Y1 += 0.00000715042*cos(4.55303572982 + 430.7741616226*$t);
$Y1 += 0.00000596876*cos(3.52791235957 + 124.6772327045*$t);
$Y1 += 0.00000472020*cos(2.03831166729 + 654.3681977991*$t);
$Y1 += 0.00000467656*cos(2.94972694776 + 515.2200536095*$t);
$Y1 += 0.00000472526*cos(4.89215133877 + 203.247972183*$t);
$Y1 += 0.00000487417*cos(5.85503954683 + 736.1203310153*$t);
$Y1 += 0.00000402114*cos(2.85533132593 + 86.07111631471*$t);
$Y1 += 0.00000376954*cos(2.14121779282 + 76.50988875911*$t);
$Y1 += 0.00000419410*cos(1.17666971099 + 742.74624304909*$t);
$Y1 += 0.00000439384*cos(4.19607195732 + 301.9209581715*$t);
$Y1 += 0.00000458871*cos(2.23384913618 + 529.44714761109*$t);
$Y1 += 0.00000345395*cos(4.60405141742 + 192.2022719191*$t);
$Y1 += 0.00000334209*cos(2.28268923760 + 1155.1173399235*$t);
$Y1 += 0.00000330276*cos(5.07000098007 + 302.40859313851*$t);
$Y1 += 0.00000339713*cos(1.16737882478 + 218.2087793675*$t);
$Y1 += 0.00000304950*cos(4.89660174852 + 231.70216018621*$t);
$Y1 += 0.00000312395*cos(0.79548009041 + 629.0954035336*$t);
$Y1 += 0.00000311746*cos(3.50532316923 + 941.8182444855*$t);
$Y1 += 0.00000299095*cos(0.58884669599 + 208.8770464755*$t);
$Y1 += 0.00000299955*cos(1.74484418656 + 728.5191490475*$t);
$Y1 += 0.00000271105*cos(1.13283461800 + 288.32451148881*$t);
$Y1 += 0.00000260779*cos(5.58254809430 + 18.40306474821*$t);
$Y1 += 0.00000278736*cos(0.64654515892 + 632.5399218297*$t);
$Y1 += 0.00000335527*cos(1.50873501393 + 203.9816853659*$t);
$Y1 += 0.00000259607*cos(4.43314622304 + 10.538758222*$t);
$Y1 += 0.00000263983*cos(1.98364017133 + 363.1061100561*$t);
$Y1 += 0.00000291544*cos(0.24051609787 + 223.1041404771*$t);
$Y1 += 0.00000214376*cos(4.46071700955 + 208.1262869501*$t);
$Y1 += 0.00000208551*cos(3.59347779220 + 218.9595388929*$t);
$Y1 += 0.00000208257*cos(2.81646625431 + 408.68276109481*$t);
$Y1 += 0.00000211653*cos(0.53562740874 + 138.76131435421*$t);
$Y1 += 0.00000199845*cos(3.86657932388 + 13.9832765181*$t);
$Y1 += 0.00000195781*cos(1.92507988390 + 52.446380556*$t);
$Y1 += 0.00000192346*cos(4.64457398897 + 201.01273994931*$t);
$Y1 += 0.00000191573*cos(5.16049975639 + 341.01470952831*$t);
$Y1 += 0.00000185995*cos(0.07444798265 + 948.9317914863*$t);
$Y1 += 0.00000168803*cos(2.67981533571 + 831.6119232661*$t);
$Y1 += 0.00000170172*cos(5.89341892618 + 350.5759370839*$t);
$Y1 += 0.00000167553*cos(3.43189093041 + 226.07308589371*$t);
$Y1 += 0.00000177510*cos(3.37006198906 + 210.6221516147*$t);
$Y1 += 0.00000177755*cos(4.64994019967 + 216.4636742283*$t);
$Y1 += 0.00000157494*cos(0.14772881381 + 195.38366565681*$t);
$Y1 += 0.00000162215*cos(4.44587835630 + 956.53297345411*$t);
$Y1 += 0.00000160622*cos(3.78223230286 + 127.22797912329*$t);
$Y1 += 0.00000147298*cos(5.02251206802 + 9.8050450391*$t);
$Y1 += 0.00000177635*cos(4.69945913164 + 160.852714882*$t);
$Y1 += 0.00000170308*cos(1.06394430192 + 207.913838629*$t);
$Y1 += 0.00000158062*cos(0.92038060554 + 1059.1381127057*$t);
$Y1 += 0.00000138665*cos(2.01815199316 + 1471.50920958009*$t);
$Y1 += 0.00000150976*cos(1.56848256275 + 636.2089505344*$t);
$Y1 += 0.00000136839*cos(2.94611079491 + 544.1618765797*$t);
$Y1 += 0.00000163932*cos(0.66823863663 + 219.171987214*$t);
$Y1 += 0.00000164921*cos(3.04782245643 + 22.3352180113*$t);
$Y1 += 0.00000134204*cos(5.97046820042 + 703.8770021009*$t);
$Y1 += 0.00000141934*cos(2.16098044416 + 202.0095776906*$t);
$Y1 += 0.00000153018*cos(5.84706089618 + 56.3785338191*$t);
$Y1 += 0.00000132722*cos(2.40576881332 + 750.3474250169*$t);
$Y1 += 0.00000136617*cos(3.21579900111 + 1258.21011414209*$t);
$Y1 += 0.00000124984*cos(2.71780492845 + 448.1826493619*$t);
$Y1 += 0.00000138310*cos(2.83136566148 + 142.6934676173*$t);
$Y1 += 0.00000121140*cos(4.87825139023 + 949.4194264533*$t);
$Y1 += 0.00000146873*cos(2.04601008330 + 845.8390172677*$t);
$Y1 += 0.00000135623*cos(5.56318477713 + 490.5779066629*$t);
$Y1 += 0.00000114737*cos(2.40589233064 + 433.46792039329*$t);
$Y1 += 0.00000107506*cos(1.17561460871 + 565.35950523021*$t);
$Y1 += 0.00000105407*cos(2.01232380969 + 209.35012722751*$t);
$Y1 += 0.00000123012*cos(1.28213994555 + 483.4643596621*$t);
$Y1 += 0.00000104647*cos(6.01500032787 + 217.73569861551*$t);
$Y1 += 0.00000123445*cos(3.28644134532 + 266.233110961*$t);
$Y1 += 0.00000121327*cos(3.91515678280 + 618.3128278281*$t);
$Y1 += 0.00000121539*cos(0.70927003130 + 515.70768857651*$t);
$Y1 += 0.00000098330*cos(5.98392277878 + 1280.0383901115*$t);
$Y1 += 0.00000123139*cos(0.15397612176 + 12.77399045571*$t);
$Y1 += 0.00000106461*cos(1.50068457652 + 1044.9110187041*$t);
$Y1 += 0.00000134338*cos(1.70318102108 + 419.2408263917*$t);
$Y1 += 0.00000107530*cos(0.47701797778 + 424.39432780471*$t);
$Y1 += 0.00000114356*cos(1.93414468084 + 270.1652642241*$t);
$Y1 += 0.00000094347*cos(6.05574583632 + 1265.32366114289*$t);
$Y1 += 0.00000104237*cos(5.37674274043 + 70.6056278207*$t);
$Y1 += 0.00000088410*cos(0.52764897299 + 1073.85284167431*$t);
$Y1 += 0.00000091547*cos(4.90814232105 + 106.5179854398*$t);
$Y1 += 0.00000084219*cos(4.60141274305 + 113.6315324406*$t);
$Y1 += 0.00000091641*cos(0.73842419997 + 497.69145366371*$t);
$Y1 += 0.00000080939*cos(3.13738230860 + 651.1868040614*$t);
$Y1 += 0.00000082304*cos(1.71469250601 + 643.32249753521*$t);
$Y1 += 0.00000099237*cos(1.11729387995 + 639.6534688305*$t);
$Y1 += 0.00000073063*cos(2.41573369601 + 1148.00379292269*$t);
$Y1 += 0.00000079913*cos(1.43967739894 + 191.45151239371*$t);
$Y1 += 0.00000070813*cos(0.83698988794 + 251.6759485593*$t);
$Y1 += 0.00000072632*cos(6.03093469770 + 107.2687449652*$t);
$Y1 += 0.00000075817*cos(6.15403374919 + 284.39235822571*$t);
$Y1 += 0.00000072415*cos(3.44390490336 + 191.7146369521*$t);
$Y1 += 0.00000084109*cos(0.20089617421 + 219.6932520758*$t);
$Y1 += 0.00000066814*cos(3.27992928467 + 636.95971005981*$t);
$Y1 += 0.00000064253*cos(3.30962112459 + 71.09326278771*$t);
$Y1 += 0.00000073347*cos(2.74891631991 + 344.9468627914*$t);
$Y1 += 0.00000061578*cos(3.56151396455 + 479.532206399*$t);
$Y1 += 0.00000060447*cos(1.75736763354 + 1787.9010792367*$t);
$Y1 += 0.00000063039*cos(2.40833995336 + 437.136949098*$t);
$Y1 += 0.00000064265*cos(2.93065048354 + 1574.6019837987*$t);
$Y1 += 0.00000058169*cos(1.49924118883 + 75.0254160508*$t);
$Y1 += 0.00000065491*cos(0.66720972356 + 1375.52998236229*$t);
$Y1 += 0.00000057055*cos(2.86226169724 + 98.6561710411*$t);
$Y1 += 0.00000063072*cos(2.25676507609 + 359.173956793*$t);
$Y1 += 0.00000076825*cos(4.97299930649 + 839.2131052339*$t);
$Y1 += 0.00000065944*cos(1.58727129595 + 207.3925737672*$t);
$Y1 += 0.00000065704*cos(1.95606870146 + 2.9375762542*$t);
$Y1 += 0.00000059449*cos(2.68338567532 + 417.2807808039*$t);
$Y1 += 0.00000066539*cos(1.76632812482 + 1162.23088692429*$t);
$Y1 += 0.00000053194*cos(3.14361310813 + 227.2823719561*$t);
$Y1 += 0.00000063890*cos(0.41831388362 + 235.6343134493*$t);
$Y1 += 0.00000052968*cos(0.91696357138 + 175.40987728371*$t);
$Y1 += 0.00000051480*cos(3.83078819944 + 416.547067621*$t);
$Y1 += 0.00000053788*cos(5.42039296703 + 114.38229196601*$t);
$Y1 += 0.00000052017*cos(0.44065832790 + 220.7046440321*$t);
$Y1 += 0.00000048475*cos(1.74014879125 + 209.12312469139*$t);
$Y1 += 0.00000048625*cos(5.04094706317 + 63.9797157869*$t);
$Y1 += 0.00000047377*cos(5.76160390420 + 1581.7155307995*$t);
$Y1 += 0.00000066468*cos(2.96069437842 + 337.9763281425*$t);
$Y1 += 0.00000047697*cos(0.34705221570 + 352.06040979221*$t);
$Y1 += 0.00000050400*cos(6.23334184252 + 429.28968891431*$t);
$Y1 += 0.00000051302*cos(6.27400713228 + 121.4958389668*$t);
$Y1 += 0.00000048534*cos(1.51516380602 + 151.2914873264*$t);
$Y1 += 0.00000050418*cos(1.08978230509 + 181.2995840071*$t);
$Y1 += 0.00000052765*cos(2.41157347334 + 4.9096839295*$t);
$Y1 += 0.00000056130*cos(5.04459002050 + 404.7506078317*$t);
$Y1 += 0.00000053587*cos(5.28731972971 + 554.31380496631*$t);
$Y1 += 0.00000050974*cos(3.62783678854 + 934.70469748469*$t);
$Y1 += 0.00000044236*cos(1.36935810506 + 63.49208081989*$t);
$Y1 += 0.00000046842*cos(0.67542380780 + 245.7862418359*$t);
$Y1 += 0.00000041530*cos(4.46708578473 + 99.40443843901*$t);
$Y1 += 0.00000044045*cos(0.68746998587 + 205.46615807421*$t);
$Y1 += 0.00000040580*cos(1.25223032785 + 867.6672932371*$t);
$Y1 += 0.00000041030*cos(5.60558897869 + 81.50831573269*$t);
$Y1 += 0.00000040882*cos(2.19047548175 + 621.98185653281*$t);
$Y1 += 0.00000038986*cos(2.89088740116 + 131.79077970531*$t);
$Y1 += 0.00000045904*cos(5.16474077315 + 1589.3167127673*$t);
$Y1 += 0.00000053423*cos(5.90391742845 + 1052.51220067191*$t);
$Y1 += 0.00000041233*cos(1.27392005885 + 1361.3028883607*$t);
$Y1 += 0.00000046867*cos(4.41668443242 + 10.8018827804*$t);
$Y1 += 0.00000046594*cos(6.19397089476 + 323.2615991739*$t);
$Y1 += 0.00000037309*cos(1.75965892305 + 194.89603068979*$t);
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$Y1 += 0.00000001240*cos(1.39562373377 + 105.7842722569*$t);
$Y1 += 0.00000001240*cos(4.53721638736 + 105.2966372899*$t);
$Y1 += 0.00000000975*cos(6.14076145568 + 700.90805668431*$t);
$Y1 += 0.00000000963*cos(1.26904248346 + 5378.90560164571*$t);
$Y1 += 0.00000001131*cos(1.92127706230 + 640.0929196877*$t);
$Y1 += 0.00000001014*cos(2.27419938832 + 246.68001371321*$t);
$Y1 += 0.00000000922*cos(4.94986707425 + 9772.21644384989*$t);
$Y1 += 0.00000000896*cos(2.95327436580 + 1571.1574655026*$t);
$Y1 += 0.00000001121*cos(0.63121659144 + 6467.68194047809*$t);
$Y1 += 0.00000000872*cos(1.30941661635 + 519.63984183961*$t);
$Y1 += 0.00000001164*cos(4.79404702362 + 739.0410923221*$t);
$Y1 += 0.00000001090*cos(3.70049172953 + 1699.0353990197*$t);
$Y1 += 0.00000001180*cos(4.01443566672 + 636.47207509279*$t);
$Y1 += 0.00000000912*cos(2.54546205453 + 31.2633061205*$t);
$Y1 += 0.00000000892*cos(2.36351221746 + 212.579705075*$t);
$Y1 += 0.00000000892*cos(5.50510487105 + 212.092070108*$t);
$Y1 += 0.00000000985*cos(3.52323843583 + 988.0255428431*$t);
$Y1 += 0.00000000860*cos(2.94846758267 + 1585.38455950421*$t);
$Y1 += 0.00000000990*cos(1.67825090661 + 3149.44778508089*$t);
$Y1 += 0.00000001177*cos(4.87572778682 + 1328.79643488791*$t);
$Y1 += 0.00000000864*cos(2.80999692865 + 12146.42323862409*$t);
$Y1 += 0.00000001007*cos(3.83948575721 + 685.2301198692*$t);
$Y1 += 0.00000001007*cos(3.83948575721 + 685.7177548362*$t);
$Y1 += 0.00000000853*cos(3.93116170567 + 2641.5850959557*$t);
$Y1 += 0.00000000993*cos(1.01758536916 + 2111.8941308611*$t);
$Y1 += 0.00000000844*cos(3.42851532207 + 1239.78774231901*$t);
$Y1 += 0.00000000846*cos(1.60469270371 + 2115.0755245988*$t);
$Y1 += 0.00000000964*cos(1.18238037517 + 756.56720014041*$t);
$Y1 += 0.00000000981*cos(6.17353804084 + 1471.2460850217*$t);
$Y1 += 0.00000001164*cos(4.46546430995 + 3391.68870348911*$t);
$Y1 += 0.00000000885*cos(1.64388709070 + 609.1216151605*$t);
$Y1 += 0.00000000821*cos(2.00294213618 + 388.2213377547*$t);
$Y1 += 0.00000000906*cos(3.95724484289 + 327.19375243699*$t);
$Y1 += 0.00000000903*cos(1.46965018009 + 477.2445845386*$t);
$Y1 += 0.00000000841*cos(2.31779507594 + 473.31243127551*$t);
$Y1 += 0.00000000904*cos(5.47014409814 + 635.4752373515*$t);
$Y1 += 0.00000000822*cos(1.66432337141 + 1365.23504162379*$t);
$Y1 += 0.00000000997*cos(1.82079729948 + 123.2958258602*$t);
$Y1 += 0.00000000879*cos(0.83289385422 + 3362.74688051889*$t);
$Y1 += 0.00000000846*cos(0.41970975707 + 227.81819103291*$t);
$Y1 += 0.00000000846*cos(4.46991640952 + 199.26763481011*$t);
$Y1 += 0.00000000947*cos(0.09177854194 + 222.6165055101*$t);
$Y1 += 0.00000000875*cos(1.91606789801 + 9993.1167212557*$t);
$Y1 += 0.00000001117*cos(5.40582369615 + 319.0833676949*$t);
$Y1 += 0.00000000800*cos(1.12338267507 + 834.7933170038*$t);
$Y1 += 0.00000000839*cos(4.44054896906 + 206.64181424181*$t);
$Y1 += 0.00000000839*cos(0.44907719753 + 220.44401160121*$t);
$Y1 += 0.00000000838*cos(1.69845530894 + 2442.5130945193*$t);
$Y1 += 0.00000000830*cos(0.99305838433 + 1891.4814884223*$t);
$Y1 += 0.00000000841*cos(6.22199463081 + 60.04756252381*$t);
$Y1 += 0.00000000826*cos(2.10402662108 + 220.1351950605*$t);
$Y1 += 0.00000000854*cos(5.92854026664 + 540.2297233166*$t);
$Y1 += 0.00000000842*cos(1.12102777557 + 2854.3965564267*$t);
$Y1 += 0.00000000858*cos(4.12461672205 + 781.8399944059*$t);
$Y1 += 0.00000000860*cos(4.20709137726 + 5436.7491977567*$t);
$Y1 += 0.00000000785*cos(4.19221284065 + 3494.2938427407*$t);
return $Y1*$t;
}
function Saturn_Y2($t) // 511 terms of order 2
{
$Y2 = 0.00862721930*cos(0.87622130189 + 213.5429129215*$t);
$Y2 += 0.00611630287*cos(0.71399818143 + 0.2438174835*$t);
$Y2 += 0.00561413805*cos(5.96728319816 + 206.42936592071*$t);
$Y2 += 0.00547271370*cos(2.04588665465 + 220.6564599223*$t);
$Y2 += 0.00234984093*cos(0.87581308687 + 426.8420083595*$t);
$Y2 += 0.00088108317*cos(3.29758949735 + 7.3573644843*$t);
$Y2 += 0.00050142527*cos(1.12650721735 + 433.9555553603*$t);
$Y2 += 0.00045054746*cos(5.06577813923 + 419.72846135871*$t);
$Y2 += 0.00033335009*cos(0.01047584776 + 640.1411037975*$t);
$Y2 += 0.00027185514*cos(1.92525242054 + 227.77000692311*$t);
$Y2 += 0.00018651786*cos(1.59992516931 + 213.0552779545*$t);
$Y2 += 0.00012946617*cos(6.11930195692 + 199.3158189199*$t);
$Y2 += 0.00010383025*cos(3.18830710215 + 14.47091148511*$t);
$Y2 += 0.00006684574*cos(4.09620079950 + 110.45013870291*$t);
$Y2 += 0.00004661903*cos(0.26368341105 + 647.25465079831*$t);
$Y2 += 0.00004933834*cos(1.51097568839 + 216.72430665921*$t);
$Y2 += 0.00004778577*cos(0.24213059962 + 210.36151918381*$t);
$Y2 += 0.00004377928*cos(3.66946155930 + 316.6356871401*$t);
$Y2 += 0.00003532396*cos(5.48934411728 + 853.4401992355*$t);
$Y2 += 0.00002688895*cos(1.58317658973 + 209.6107596584*$t);
$Y2 += 0.00002540548*cos(1.07874150891 + 441.06910236111*$t);
$Y2 += 0.00002540549*cos(0.15899514683 + 217.4750661846*$t);
$Y2 += 0.00002506252*cos(3.11588688157 + 117.5636857037*$t);
$Y2 += 0.00002582753*cos(0.02782240807 + 103.3365917021*$t);
$Y2 += 0.00002111683*cos(4.98775349171 + 633.0275567967*$t);
$Y2 += 0.00002306046*cos(5.24765858946 + 205.9417309537*$t);
$Y2 += 0.00001843706*cos(2.39971312535 + 323.74923414091*$t);
$Y2 += 0.00001272298*cos(4.96900516981 + 412.6149143579*$t);
$Y2 += 0.00000940336*cos(2.42501300855 + 6.86972951729*$t);
$Y2 += 0.00000804980*cos(1.78590189490 + 234.8835539239*$t);
$Y2 += 0.00000698973*cos(0.77208908956 + 95.7354097343*$t);
$Y2 += 0.00000653010*cos(5.01381847221 + 198.82818395289*$t);
$Y2 += 0.00000766827*cos(5.79919197548 + 202.4972126576*$t);
$Y2 += 0.00000662176*cos(0.42004956009 + 426.3543733925*$t);
$Y2 += 0.00000565841*cos(1.55419890490 + 220.16882495529*$t);
$Y2 += 0.00000765788*cos(2.28516505694 + 224.5886131854*$t);
$Y2 += 0.00000672412*cos(5.85676090936 + 309.5221401393*$t);
$Y2 += 0.00000490992*cos(0.10668768793 + 109.9625037359*$t);
$Y2 += 0.00000440264*cos(2.02435630765 + 330.8627811417*$t);
$Y2 += 0.00000426768*cos(5.42227433044 + 11.2895177474*$t);
$Y2 += 0.00000427613*cos(5.71584342304 + 860.55374623631*$t);
$Y2 += 0.00000505832*cos(5.83465733982 + 309.0345051723*$t);
$Y2 += 0.00000559499*cos(5.12833446634 + 102.84895673509*$t);
$Y2 += 0.00000439569*cos(3.04587045996 + 21.5844584859*$t);
$Y2 += 0.00000404335*cos(1.38184466479 + 223.83785366*$t);
$Y2 += 0.00000400108*cos(0.64688754335 + 430.02340209721*$t);
$Y2 += 0.00000338086*cos(4.72348149737 + 1066.7392946735*$t);
$Y2 += 0.00000310691*cos(2.86856110459 + 3.42521122121*$t);
$Y2 += 0.00000356340*cos(0.50093637409 + 422.9098550964*$t);
$Y2 += 0.00000268315*cos(0.90238113501 + 88.6218627335*$t);
$Y2 += 0.00000265067*cos(5.80890278675 + 423.66061462181*$t);
$Y2 += 0.00000249792*cos(2.21289242997 + 4.1759707466*$t);
$Y2 += 0.00000244377*cos(0.24702615370 + 654.3681977991*$t);
$Y2 += 0.00000305650*cos(4.74789522190 + 419.2408263917*$t);
$Y2 += 0.00000263490*cos(1.75719781150 + 124.6772327045*$t);
$Y2 += 0.00000243362*cos(0.01260786807 + 96.2230447013*$t);
$Y2 += 0.00000228016*cos(4.72661469203 + 522.3336006103*$t);
$Y2 += 0.00000208205*cos(0.02609578112 + 192.2022719191*$t);
$Y2 += 0.00000262941*cos(2.24919351561 + 522.8212355773*$t);
$Y2 += 0.00000217559*cos(3.69816995653 + 412.12727939089*$t);
$Y2 += 0.00000204218*cos(0.74740242459 + 149.8070146181*$t);
$Y2 += 0.00000207097*cos(0.47214424781 + 625.9140097959*$t);
$Y2 += 0.00000226266*cos(0.43162189178 + 203.247972183*$t);
$Y2 += 0.00000164818*cos(1.21105459258 + 537.0483295789*$t);
$Y2 += 0.00000154166*cos(0.52313104707 + 302.40859313851*$t);
$Y2 += 0.00000159821*cos(3.57691788014 + 529.9347825781*$t);
$Y2 += 0.00000127987*cos(4.67133129306 + 515.2200536095*$t);
$Y2 += 0.00000150521*cos(5.90883755804 + 301.9209581715*$t);
$Y2 += 0.00000109809*cos(0.87108590696 + 277.2788112249*$t);
$Y2 += 0.00000107126*cos(2.60669435864 + 10.538758222*$t);
$Y2 += 0.00000125246*cos(1.70701686068 + 437.8877086234*$t);
$Y2 += 0.00000119913*cos(5.60277656541 + 625.42637482889*$t);
$Y2 += 0.00000095870*cos(2.12616183050 + 13.9832765181*$t);
$Y2 += 0.00000093192*cos(0.34445551196 + 430.7741616226*$t);
$Y2 += 0.00000082653*cos(0.98307709174 + 448.1826493619*$t);
$Y2 += 0.00000080395*cos(3.02174862119 + 231.70216018621*$t);
$Y2 += 0.00000086059*cos(5.78308214520 + 742.74624304909*$t);
$Y2 += 0.00000078439*cos(2.37542883243 + 415.7963080956*$t);
$Y2 += 0.00000095719*cos(5.10971036152 + 846.3266522347*$t);
$Y2 += 0.00000069822*cos(4.50382031149 + 838.72547026689*$t);
$Y2 += 0.00000088159*cos(3.12349955672 + 743.23387801611*$t);
$Y2 += 0.00000062703*cos(3.46541693301 + 728.5191490475*$t);
$Y2 += 0.00000061768*cos(0.31223820367 + 3.6883357796*$t);
$Y2 += 0.00000059007*cos(2.35866131486 + 316.14805217309*$t);
$Y2 += 0.00000057483*cos(3.58195443098 + 18.40306474821*$t);
$Y2 += 0.00000068064*cos(1.33121226452 + 736.1203310153*$t);
$Y2 += 0.00000073156*cos(4.57295172048 + 735.6326960483*$t);
$Y2 += 0.00000066143*cos(0.61450499024 + 529.44714761109*$t);
$Y2 += 0.00000046643*cos(4.39908344730 + 831.6119232661*$t);
$Y2 += 0.00000046381*cos(1.16571256843 + 544.1618765797*$t);
$Y2 += 0.00000049127*cos(2.41446662828 + 515.70768857651*$t);
$Y2 += 0.00000045075*cos(2.04400929715 + 195.38366565681*$t);
$Y2 += 0.00000045874*cos(4.71561784201 + 408.68276109481*$t);
$Y2 += 0.00000039597*cos(4.90149000270 + 1073.85284167431*$t);
$Y2 += 0.00000037898*cos(3.62258524288 + 1059.6257476727*$t);
$Y2 += 0.00000044466*cos(5.29067071105 + 941.8182444855*$t);
$Y2 += 0.00000034788*cos(6.24281796552 + 363.1061100561*$t);
$Y2 += 0.00000032598*cos(0.67708460723 + 433.46792039329*$t);
$Y2 += 0.00000033292*cos(5.12527889351 + 191.7146369521*$t);
$Y2 += 0.00000041206*cos(5.63757151016 + 618.3128278281*$t);
$Y2 += 0.00000032714*cos(5.53677499538 + 1059.1381127057*$t);
$Y2 += 0.00000041218*cos(5.90724265736 + 636.2089505344*$t);
$Y2 += 0.00000036847*cos(4.86141709685 + 223.1041404771*$t);
$Y2 += 0.00000028979*cos(2.88486726124 + 113.6315324406*$t);
$Y2 += 0.00000030445*cos(1.28493169701 + 56.3785338191*$t);
$Y2 += 0.00000038514*cos(0.59603887895 + 86.07111631471*$t);
$Y2 += 0.00000033922*cos(0.59559025853 + 437.136949098*$t);
$Y2 += 0.00000029740*cos(3.76166810670 + 270.1652642241*$t);
$Y2 += 0.00000034418*cos(6.09770226922 + 643.32249753521*$t);
$Y2 += 0.00000031920*cos(1.14730009415 + 337.9763281425*$t);
$Y2 += 0.00000035309*cos(3.07697728911 + 203.9816853659*$t);
$Y2 += 0.00000026923*cos(1.15025307434 + 131.79077970531*$t);
$Y2 += 0.00000026272*cos(0.57392625326 + 750.3474250169*$t);
$Y2 += 0.00000025940*cos(0.39280055678 + 76.50988875911*$t);
$Y2 += 0.00000029423*cos(3.94515878782 + 1280.0383901115*$t);
$Y2 += 0.00000026782*cos(4.26801091908 + 1155.1173399235*$t);
$Y2 += 0.00000024375*cos(1.05933381750 + 81.50831573269*$t);
$Y2 += 0.00000025294*cos(3.01418609936 + 483.4643596621*$t);
$Y2 += 0.00000023209*cos(5.71293607821 + 867.6672932371*$t);
$Y2 += 0.00000022169*cos(5.57360559022 + 288.32451148881*$t);
$Y2 += 0.00000023117*cos(1.43000944484 + 227.2823719561*$t);
$Y2 += 0.00000021350*cos(2.23904444472 + 160.852714882*$t);
$Y2 += 0.00000022067*cos(3.22469653238 + 1044.9110187041*$t);
$Y2 += 0.00000022088*cos(3.66393393785 + 70.6056278207*$t);
$Y2 += 0.00000020601*cos(0.57364692423 + 22.3352180113*$t);
$Y2 += 0.00000020035*cos(4.14035560282 + 1148.00379292269*$t);
$Y2 += 0.00000026634*cos(4.29832630822 + 1052.02456570489*$t);
$Y2 += 0.00000020249*cos(5.80067112008 + 416.547067621*$t);
$Y2 += 0.00000019318*cos(5.28106463151 + 497.69145366371*$t);
$Y2 += 0.00000017591*cos(5.18296940913 + 629.0954035336*$t);
$Y2 += 0.00000018938*cos(1.44732055781 + 107.2687449652*$t);
$Y2 += 0.00000021595*cos(4.07617789654 + 490.5779066629*$t);
$Y2 += 0.00000020105*cos(0.54192980606 + 839.2131052339*$t);
$Y2 += 0.00000021565*cos(2.45978600148 + 956.53297345411*$t);
$Y2 += 0.00000016938*cos(1.31185513413 + 89.10949770051*$t);
$Y2 += 0.00000016497*cos(3.14108050084 + 106.5179854398*$t);
$Y2 += 0.00000021360*cos(0.36044575923 + 845.8390172677*$t);
$Y2 += 0.00000019384*cos(5.02948605381 + 1258.21011414209*$t);
$Y2 += 0.00000015417*cos(1.59544409554 + 241.9971009247*$t);
$Y2 += 0.00000016591*cos(6.11245153858 + 639.6534688305*$t);
$Y2 += 0.00000016177*cos(4.47207109523 + 344.9468627914*$t);
$Y2 += 0.00000014854*cos(5.83097043394 + 266.233110961*$t);
$Y2 += 0.00000019063*cos(0.50919845943 + 201.01273994931*$t);
$Y2 += 0.00000018723*cos(1.22925120460 + 226.07308589371*$t);
$Y2 += 0.00000018567*cos(4.58722431937 + 142.6934676173*$t);
$Y2 += 0.00000014166*cos(5.14705983766 + 632.5399218297*$t);
$Y2 += 0.00000017119*cos(5.54902094563 + 352.06040979221*$t);
$Y2 += 0.00000018888*cos(4.20468772536 + 52.446380556*$t);
$Y2 += 0.00000013506*cos(2.46884301371 + 138.76131435421*$t);
$Y2 += 0.00000017909*cos(5.34068384361 + 934.70469748469*$t);
$Y2 += 0.00000013747*cos(0.53980747800 + 359.173956793*$t);
$Y2 += 0.00000014401*cos(5.13574388998 + 405.5013673571*$t);
$Y2 += 0.00000016878*cos(1.18886685780 + 341.01470952831*$t);
$Y2 += 0.00000013527*cos(4.54185459719 + 284.39235822571*$t);
$Y2 += 0.00000013436*cos(2.93238200114 + 6290.4332144757*$t);
$Y2 += 0.00000012962*cos(5.56740362933 + 181.2995840071*$t);
$Y2 += 0.00000015865*cos(1.01845623601 + 651.1868040614*$t);
$Y2 += 0.00000013136*cos(0.57265499079 + 6276.2061204741*$t);
$Y2 += 0.00000012088*cos(5.67052895035 + 127.22797912329*$t);
$Y2 += 0.00000012658*cos(4.99618012837 + 948.9317914863*$t);
$Y2 += 0.00000012303*cos(2.19066167059 + 445.00125562421*$t);
$Y2 += 0.00000011905*cos(4.76438580603 + 424.39432780471*$t);
$Y2 += 0.00000012624*cos(4.35576033147 + 10220.6429106953*$t);
$Y2 += 0.00000012885*cos(5.28091161489 + 1375.52998236229*$t);
$Y2 += 0.00000012454*cos(0.80444795613 + 295.2950461377*$t);
$Y2 += 0.00000012341*cos(1.99603261002 + 10206.4158166937*$t);
$Y2 += 0.00000011182*cos(0.00456461469 + 209.12312469139*$t);
$Y2 += 0.00000010860*cos(1.22452077861 + 350.5759370839*$t);
$Y2 += 0.00000010568*cos(4.31488618104 + 12.77399045571*$t);
$Y2 += 0.00000010726*cos(4.07799467328 + 703.8770021009*$t);
$Y2 += 0.00000013731*cos(5.49770812826 + 636.95971005981*$t);
$Y2 += 0.00000011066*cos(4.06922769849 + 1471.50920958009*$t);
$Y2 += 0.00000010568*cos(2.45354520533 + 245.7862418359*$t);
$Y2 += 0.00000011834*cos(4.04162936965 + 191.45151239371*$t);
$Y2 += 0.00000013045*cos(4.56683285480 + 323.2615991739*$t);
$Y2 += 0.00000012746*cos(1.52919279431 + 729.0067840145*$t);
$Y2 += 0.00000011214*cos(0.69012319111 + 618.8004627951*$t);
$Y2 += 0.00000011539*cos(5.26204215590 + 75.0254160508*$t);
$Y2 += 0.00000012236*cos(6.03310641164 + 294.80741117069*$t);
$Y2 += 0.00000009934*cos(5.72889650913 + 209.87388421679*$t);
$Y2 += 0.00000010182*cos(4.02484159335 + 235.6343134493*$t);
$Y2 += 0.00000009148*cos(3.88097207377 + 1464.3956625793*$t);
$Y2 += 0.00000009436*cos(4.83010917251 + 508.10650660869*$t);
$Y2 += 0.00000008422*cos(0.17788593244 + 661.4817447999*$t);
$Y2 += 0.00000008359*cos(3.00746750344 + 1361.3028883607*$t);
$Y2 += 0.00000008253*cos(5.57801256284 + 565.35950523021*$t);
$Y2 += 0.00000009478*cos(0.55087151701 + 949.4194264533*$t);
$Y2 += 0.00000010785*cos(4.05427228564 + 1368.4164353615*$t);
$Y2 += 0.00000008229*cos(5.11025535831 + 5849.1202946311*$t);
$Y2 += 0.00000007715*cos(2.36462770264 + 10.8018827804*$t);
$Y2 += 0.00000008470*cos(1.44876764278 + 1052.51220067191*$t);
$Y2 += 0.00000007922*cos(1.18690846899 + 5863.3473886327*$t);
$Y2 += 0.00000007332*cos(1.23083436431 + 404.7506078317*$t);
$Y2 += 0.00000007694*cos(0.25064967436 + 9779.32999085069*$t);
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$Y2 += 0.00000001434*cos(3.90656801196 + 6062.4193900691*$t);
$Y2 += 0.00000001122*cos(2.45857726727 + 128.6093859676*$t);
$Y2 += 0.00000001123*cos(3.06803578936 + 3178.38960805111*$t);
$Y2 += 0.00000001154*cos(4.32058575911 + 67.91186905*$t);
$Y2 += 0.00000001130*cos(5.25611734741 + 731.70054278519*$t);
$Y2 += 0.00000001305*cos(2.25262249590 + 97.11681657861*$t);
$Y2 += 0.00000001248*cos(3.82251460637 + 2523.7775927685*$t);
$Y2 += 0.00000001161*cos(2.25840723150 + 81.9959506997*$t);
$Y2 += 0.00000001178*cos(0.70097671757 + 1056.444353935*$t);
$Y2 += 0.00000001342*cos(5.62104702567 + 355.99256305531*$t);
$Y2 += 0.00000001249*cos(4.92175219077 + 526.2657538734*$t);
$Y2 += 0.00000001034*cos(4.56345495168 + 777.17412795991*$t);
$Y2 += 0.00000001332*cos(4.90721267162 + 835.5440765292*$t);
$Y2 += 0.00000001024*cos(6.03631011372 + 5635.8211991931*$t);
$Y2 += 0.00000001173*cos(4.16447862889 + 74.53778108379*$t);
$Y2 += 0.00000001173*cos(3.45615871164 + 2317.5920443313*$t);
$Y2 += 0.00000001012*cos(2.86472380431 + 215.2398339509*$t);
$Y2 += 0.00000001186*cos(3.42680148463 + 1272.9248431107*$t);
$Y2 += 0.00000001049*cos(1.32104580559 + 6062.9070250361*$t);
$Y2 += 0.00000001154*cos(3.31945570971 + 2406.4577245483*$t);
$Y2 += 0.00000001062*cos(3.40252606572 + 906.130397275*$t);
$Y2 += 0.00000001124*cos(0.61967036641 + 3914.26612158291*$t);
$Y2 += 0.00000000993*cos(1.99202380463 + 211.8459918921*$t);
$Y2 += 0.00000000986*cos(6.21774784663 + 525.514994348*$t);
$Y2 += 0.00000000986*cos(5.89248361654 + 602.00806815971*$t);
$Y2 += 0.00000000992*cos(0.16374858268 + 306.34074640161*$t);
$Y2 += 0.00000001239*cos(4.40402775047 + 2193.1586291103*$t);
$Y2 += 0.00000001134*cos(3.08772580443 + 2729.96314120569*$t);
$Y2 += 0.00000001041*cos(2.53935646805 + 945.7503977486*$t);
$Y2 += 0.00000001025*cos(3.08133309612 + 32.48714639791*$t);
$Y2 += 0.00000001044*cos(1.56254364362 + 472.4186593982*$t);
$Y2 += 0.00000001335*cos(4.80329987516 + 2324.70559133209*$t);
$Y2 += 0.00000001199*cos(4.40804047285 + 4113.3381230193*$t);
$Y2 += 0.00000001174*cos(4.67336952922 + 1176.9456158929*$t);
$Y2 += 0.00000001213*cos(0.28347383353 + 252.8997888367*$t);
$Y2 += 0.00000000973*cos(1.75775518324 + 245.03548231051*$t);
$Y2 += 0.00000000973*cos(6.27346363694 + 182.05034353251*$t);
$Y2 += 0.00000001167*cos(6.08159477667 + 635.72131556739*$t);
$Y2 += 0.00000000936*cos(3.32125427673 + 220.1351950605*$t);
$Y2 += 0.00000001073*cos(3.85483987093 + 1773.6739852351*$t);
$Y2 += 0.00000000931*cos(1.55716679047 + 206.9506307825*$t);
$Y2 += 0.00000000931*cos(2.65028378733 + 1582.2031657665*$t);
$Y2 += 0.00000001237*cos(1.19959870124 + 2964.60287764609*$t);
$Y2 += 0.00000001074*cos(5.00882181931 + 738.814089786*$t);
$Y2 += 0.00000000976*cos(6.18216851835 + 31.9995114309*$t);
$Y2 += 0.00000000907*cos(3.58111072001 + 1802.6158082053*$t);
$Y2 += 0.00000000925*cos(2.76573994536 + 3494.7814777077*$t);
$Y2 += 0.00000000999*cos(4.06676744721 + 171.8984151459*$t);
$Y2 += 0.00000000931*cos(4.76188288294 + 1037.7974717033*$t);
$Y2 += 0.00000001094*cos(3.85667770199 + 2516.66404576769*$t);
$Y2 += 0.00000000949*cos(3.82779842438 + 1809.72935520611*$t);
$Y2 += 0.00000000964*cos(2.57800328808 + 2641.5850959557*$t);
$Y2 += 0.00000000947*cos(5.94253987889 + 2111.40649589409*$t);
$Y2 += 0.00000000898*cos(1.16267053643 + 9566.03089541269*$t);
$Y2 += 0.00000001029*cos(3.26133516597 + 519.63984183961*$t);
$Y2 += 0.00000000989*cos(3.95452500658 + 255.1874106971*$t);
$Y2 += 0.00000001003*cos(4.46395476902 + 60.52313540329*$t);
$Y2 += 0.00000000886*cos(0.72851955442 + 305.10235190919*$t);
$Y2 += 0.00000000920*cos(1.69743225247 + 459.0853372739*$t);
$Y2 += 0.00000000888*cos(1.37138485948 + 3259.6541063003*$t);
$Y2 += 0.00000000888*cos(4.51297751307 + 3260.1417412673*$t);
$Y2 += 0.00000000960*cos(0.18926013762 + 84.6897094704*$t);
$Y2 += 0.00000000881*cos(0.63602093080 + 397.9001853893*$t);
$Y2 += 0.00000000924*cos(5.21301171350 + 731.92754532131*$t);
$Y2 += 0.00000000960*cos(2.83183840474 + 5856.7214765989*$t);
$Y2 += 0.00000000886*cos(0.13702548516 + 471.9310244312*$t);
$Y2 += 0.00000000909*cos(1.30383200776 + 746.15463932291*$t);
return $Y2*$t*$t;
}
function Saturn_Y3($t) // 250 terms of order 3
{
$Y3 = 0.00076886822*cos(1.38647122579 + 206.42936592071*$t);
$Y3 += 0.00075865107*cos(0.30263761509 + 220.6564599223*$t);
$Y3 += 0.00028377246*cos(2.29477516800 + 0.2438174835*$t);
$Y3 += 0.00011451297*cos(5.24189857677 + 426.8420083595*$t);
$Y3 += 0.00009043324*cos(5.61883049962 + 433.9555553603*$t);
$Y3 += 0.00007419530*cos(0.21033373142 + 227.77000692311*$t);
$Y3 += 0.00008292033*cos(1.50182614839 + 7.3573644843*$t);
$Y3 += 0.00004421142*cos(0.64077885911 + 419.72846135871*$t);
$Y3 += 0.00003519324*cos(1.53956700451 + 199.3158189199*$t);
$Y3 += 0.00003064445*cos(4.39386454839 + 640.1411037975*$t);
$Y3 += 0.00002363042*cos(1.46950181949 + 14.47091148511*$t);
$Y3 += 0.00001027777*cos(4.71705572637 + 647.25465079831*$t);
$Y3 += 0.00000789743*cos(5.60732845352 + 441.06910236111*$t);
$Y3 += 0.00000810744*cos(5.98445458539 + 216.72430665921*$t);
$Y3 += 0.00000766386*cos(2.03195290594 + 210.36151918381*$t);
$Y3 += 0.00000673097*cos(5.33794721338 + 213.0552779545*$t);
$Y3 += 0.00000506614*cos(2.17347656423 + 213.5429129215*$t);
$Y3 += 0.00000384956*cos(1.47307672393 + 117.5636857037*$t);
$Y3 += 0.00000463540*cos(3.55273822694 + 853.4401992355*$t);
$Y3 += 0.00000411246*cos(2.18199166630 + 110.45013870291*$t);
$Y3 += 0.00000324142*cos(0.07852229440 + 234.8835539239*$t);
$Y3 += 0.00000285917*cos(0.41121094808 + 412.6149143579*$t);
$Y3 += 0.00000238406*cos(1.75200857251 + 103.3365917021*$t);
$Y3 += 0.00000192441*cos(5.32707204371 + 316.6356871401*$t);
$Y3 += 0.00000189600*cos(0.69653910652 + 6.86972951729*$t);
$Y3 += 0.00000189610*cos(0.69106705292 + 633.0275567967*$t);
$Y3 += 0.00000213874*cos(0.85839521405 + 205.9417309537*$t);
$Y3 += 0.00000153605*cos(0.70666490608 + 323.74923414091*$t);
$Y3 += 0.00000154083*cos(1.31044116162 + 21.5844584859*$t);
$Y3 += 0.00000130169*cos(6.09318414425 + 209.6107596584*$t);
$Y3 += 0.00000121811*cos(0.47800554959 + 198.82818395289*$t);
$Y3 += 0.00000112652*cos(6.07737302889 + 220.16882495529*$t);
$Y3 += 0.00000109203*cos(1.75938966834 + 217.4750661846*$t);
$Y3 += 0.00000111589*cos(3.84220589954 + 860.55374623631*$t);
$Y3 += 0.00000097336*cos(2.54240833553 + 95.7354097343*$t);
$Y3 += 0.00000114728*cos(5.87380874959 + 223.83785366*$t);
$Y3 += 0.00000085497*cos(0.31664832561 + 330.8627811417*$t);
$Y3 += 0.00000103793*cos(1.39004326725 + 309.5221401393*$t);
$Y3 += 0.00000085243*cos(4.74344019433 + 654.3681977991*$t);
$Y3 += 0.00000081972*cos(1.72088205600 + 192.2022719191*$t);
$Y3 += 0.00000093735*cos(4.66924086636 + 426.3543733925*$t);
$Y3 += 0.00000078232*cos(6.26955569087 + 124.6772327045*$t);
$Y3 += 0.00000073732*cos(2.62274205530 + 88.6218627335*$t);
$Y3 += 0.00000068659*cos(4.66941001827 + 109.9625037359*$t);
$Y3 += 0.00000087657*cos(5.07624062638 + 430.02340209721*$t);
$Y3 += 0.00000057790*cos(0.13357560704 + 224.5886131854*$t);
$Y3 += 0.00000050888*cos(1.52333865500 + 202.4972126576*$t);
$Y3 += 0.00000048029*cos(2.25988634275 + 302.40859313851*$t);
$Y3 += 0.00000057606*cos(2.26643847681 + 203.247972183*$t);
$Y3 += 0.00000056960*cos(2.75566102022 + 1066.7392946735*$t);
$Y3 += 0.00000045308*cos(1.68344191762 + 96.2230447013*$t);
$Y3 += 0.00000048067*cos(1.37320484001 + 309.0345051723*$t);
$Y3 += 0.00000036732*cos(5.51470119579 + 448.1826493619*$t);
$Y3 += 0.00000038865*cos(2.20650641493 + 625.9140097959*$t);
$Y3 += 0.00000043853*cos(4.92071216020 + 422.9098550964*$t);
$Y3 += 0.00000036680*cos(0.38116904350 + 13.9832765181*$t);
$Y3 += 0.00000035412*cos(3.97478676019 + 522.8212355773*$t);
$Y3 += 0.00000030232*cos(5.44165264045 + 412.12727939089*$t);
$Y3 += 0.00000034292*cos(1.35598862213 + 301.9209581715*$t);
$Y3 += 0.00000025919*cos(3.74498868983 + 4.1759707466*$t);
$Y3 += 0.00000026527*cos(1.95025295633 + 423.66061462181*$t);
$Y3 += 0.00000023623*cos(0.11328528018 + 515.2200536095*$t);
$Y3 += 0.00000017831*cos(3.67540680263 + 11.2895177474*$t);
$Y3 += 0.00000017289*cos(5.69767719550 + 537.0483295789*$t);
$Y3 += 0.00000016881*cos(3.81249765736 + 195.38366565681*$t);
$Y3 += 0.00000013511*cos(4.15427151016 + 515.70768857651*$t);
$Y3 += 0.00000012893*cos(5.83608381063 + 437.8877086234*$t);
$Y3 += 0.00000011197*cos(4.12727958334 + 742.74624304909*$t);
$Y3 += 0.00000013451*cos(0.48023955262 + 522.3336006103*$t);
$Y3 += 0.00000010292*cos(5.57616897093 + 337.9763281425*$t);
$Y3 += 0.00000011481*cos(0.55900801750 + 191.7146369521*$t);
$Y3 += 0.00000011394*cos(1.22639782189 + 625.42637482889*$t);
$Y3 += 0.00000011380*cos(3.01802304028 + 1073.85284167431*$t);
$Y3 += 0.00000009884*cos(5.68207864841 + 131.79077970531*$t);
$Y3 += 0.00000009268*cos(2.85677606430 + 81.50831573269*$t);
$Y3 += 0.00000010374*cos(5.65556228759 + 544.1618765797*$t);
$Y3 += 0.00000011913*cos(5.03981077547 + 437.136949098*$t);
$Y3 += 0.00000008626*cos(5.23537891674 + 728.5191490475*$t);
$Y3 += 0.00000008671*cos(5.89546440948 + 419.2408263917*$t);
$Y3 += 0.00000008821*cos(6.14734947376 + 831.6119232661*$t);
$Y3 += 0.00000008112*cos(5.21246168400 + 149.8070146181*$t);
$Y3 += 0.00000009768*cos(1.10645539833 + 618.3128278281*$t);
$Y3 += 0.00000008329*cos(3.90263564155 + 867.6672932371*$t);
$Y3 += 0.00000007645*cos(0.82506284210 + 846.3266522347*$t);
$Y3 += 0.00000008659*cos(4.22366027894 + 643.32249753521*$t);
$Y3 += 0.00000007205*cos(5.97033515631 + 227.2823719561*$t);
$Y3 += 0.00000007157*cos(4.06588017100 + 636.2089505344*$t);
$Y3 += 0.00000007036*cos(1.06159700654 + 231.70216018621*$t);
$Y3 += 0.00000007083*cos(3.27104541387 + 89.10949770051*$t);
$Y3 += 0.00000006556*cos(1.10055926440 + 743.23387801611*$t);
$Y3 += 0.00000005903*cos(5.58614673874 + 270.1652642241*$t);
$Y3 += 0.00000006615*cos(5.20910906290 + 433.46792039329*$t);
$Y3 += 0.00000006469*cos(0.48331749487 + 408.68276109481*$t);
$Y3 += 0.00000005426*cos(6.23003978027 + 241.9971009247*$t);
$Y3 += 0.00000005648*cos(0.98336733799 + 529.9347825781*$t);
$Y3 += 0.00000007105*cos(1.44824281594 + 18.40306474821*$t);
$Y3 += 0.00000005052*cos(3.61172453455 + 416.547067621*$t);
$Y3 += 0.00000006189*cos(3.11325347013 + 736.1203310153*$t);
$Y3 += 0.00000005821*cos(1.93537322437 + 1280.0383901115*$t);
$Y3 += 0.00000005043*cos(2.19686528643 + 277.2788112249*$t);
$Y3 += 0.00000004744*cos(3.03559141046 + 56.3785338191*$t);
$Y3 += 0.00000005705*cos(3.29935860753 + 430.7741616226*$t);
$Y3 += 0.00000005226*cos(3.72017940288 + 415.7963080956*$t);
$Y3 += 0.00000005511*cos(5.16650332361 + 529.44714761109*$t);
$Y3 += 0.00000004520*cos(3.93668601315 + 1059.1381127057*$t);
$Y3 += 0.00000004583*cos(1.57866732584 + 294.80741117069*$t);
$Y3 += 0.00000004789*cos(2.57991417560 + 295.2950461377*$t);
$Y3 += 0.00000004026*cos(4.75259771651 + 483.4643596621*$t);
$Y3 += 0.00000003728*cos(4.95619377571 + 185.08872491831*$t);
$Y3 += 0.00000003578*cos(0.94204754728 + 405.5013673571*$t);
$Y3 += 0.00000003890*cos(5.00299059027 + 750.3474250169*$t);
$Y3 += 0.00000004291*cos(0.89282309495 + 941.8182444855*$t);
$Y3 += 0.00000003758*cos(4.69738792182 + 661.4817447999*$t);
$Y3 += 0.00000003547*cos(1.97438574685 + 70.6056278207*$t);
$Y3 += 0.00000003641*cos(2.23934061320 + 839.2131052339*$t);
$Y3 += 0.00000004196*cos(2.40610831590 + 618.8004627951*$t);
$Y3 += 0.00000003709*cos(0.25270527416 + 508.10650660869*$t);
$Y3 += 0.00000004193*cos(0.33797589356 + 838.72547026689*$t);
$Y3 += 0.00000003571*cos(6.03135821293 + 1148.00379292269*$t);
$Y3 += 0.00000003647*cos(0.88659408340 + 934.70469748469*$t);
$Y3 += 0.00000002978*cos(5.00861879701 + 1044.9110187041*$t);
$Y3 += 0.00000002876*cos(3.72277336310 + 398.38782035631*$t);
$Y3 += 0.00000002643*cos(3.66740434616 + 497.69145366371*$t);
$Y3 += 0.00000002725*cos(4.31936427464 + 363.1061100561*$t);
$Y3 += 0.00000003246*cos(4.14230106799 + 639.6534688305*$t);
$Y3 += 0.00000002721*cos(5.71644537210 + 1464.3956625793*$t);
$Y3 += 0.00000002917*cos(0.81283070390 + 113.6315324406*$t);
$Y3 += 0.00000002560*cos(3.37970059304 + 729.0067840145*$t);
$Y3 += 0.00000002380*cos(4.67244312905 + 86.07111631471*$t);
$Y3 += 0.00000002667*cos(1.66091865719 + 10.8018827804*$t);
$Y3 += 0.00000002238*cos(0.69261990800 + 10.538758222*$t);
$Y3 += 0.00000002305*cos(0.45579083441 + 956.53297345411*$t);
$Y3 += 0.00000002316*cos(0.44164789425 + 3.42521122121*$t);
$Y3 += 0.00000002282*cos(1.20272003403 + 611.1992808273*$t);
$Y3 += 0.00000001988*cos(4.99900390794 + 651.1868040614*$t);
$Y3 += 0.00000002365*cos(0.61916344902 + 2111.40649589409*$t);
$Y3 += 0.00000002485*cos(5.89913021216 + 316.14805217309*$t);
$Y3 += 0.00000002670*cos(5.34319853125 + 196.1344251822*$t);
$Y3 += 0.00000002670*cos(5.82961294252 + 230.9514006608*$t);
$Y3 += 0.00000001974*cos(1.72688011717 + 1059.6257476727*$t);
$Y3 += 0.00000002440*cos(3.86794399442 + 106.0303504728*$t);
$Y3 += 0.00000002032*cos(3.65372244155 + 1375.52998236229*$t);
$Y3 += 0.00000002151*cos(6.26903391366 + 824.4983762653*$t);
$Y3 += 0.00000001875*cos(6.21933237642 + 344.9468627914*$t);
$Y3 += 0.00000002440*cos(2.94584507929 + 323.2615991739*$t);
$Y3 += 0.00000002034*cos(0.93720484486 + 927.5911504839*$t);
$Y3 += 0.00000002310*cos(0.13408163378 + 99.6675629974*$t);
$Y3 += 0.00000001764*cos(0.29031425745 + 191.45151239371*$t);
$Y3 += 0.00000002032*cos(2.17108818008 + 636.95971005981*$t);
$Y3 += 0.00000001993*cos(0.70131684029 + 1258.21011414209*$t);
$Y3 += 0.00000001921*cos(5.87131438069 + 2641.0974609887*$t);
$Y3 += 0.00000001620*cos(4.33606938312 + 1596.43025976811*$t);
$Y3 += 0.00000001903*cos(1.58126923147 + 2634.47154895491*$t);
$Y3 += 0.00000001568*cos(1.46883265025 + 235.6343134493*$t);
$Y3 += 0.00000001835*cos(2.03918042522 + 536.5606946119*$t);
$Y3 += 0.00000001523*cos(6.05102540851 + 956.04533848709*$t);
$Y3 += 0.00000002086*cos(0.06751029490 + 445.00125562421*$t);
$Y3 += 0.00000001666*cos(3.27204219166 + 1876.76675945369*$t);
$Y3 += 0.00000001479*cos(1.20460352519 + 6290.4332144757*$t);
$Y3 += 0.00000001479*cos(0.55429461283 + 5849.1202946311*$t);
$Y3 += 0.00000001439*cos(1.65531266077 + 2538.4923217371*$t);
$Y3 += 0.00000001464*cos(5.75084658705 + 5863.3473886327*$t);
$Y3 += 0.00000001464*cos(2.29123683992 + 6276.2061204741*$t);
$Y3 += 0.00000001676*cos(0.63508426553 + 1251.0965671413*$t);
$Y3 += 0.00000001945*cos(5.05629111259 + 845.8390172677*$t);
$Y3 += 0.00000001436*cos(4.66419938107 + 508.5941415757*$t);
$Y3 += 0.00000001481*cos(2.92781569338 + 284.39235822571*$t);
$Y3 += 0.00000001709*cos(1.78635026289 + 2318.0796792983*$t);
$Y3 += 0.00000001305*cos(2.53739213998 + 107.2687449652*$t);
$Y3 += 0.00000001548*cos(1.24859563362 + 2943.74987161071*$t);
$Y3 += 0.00000001465*cos(1.19825645294 + 2531.3787747363*$t);
$Y3 += 0.00000001494*cos(5.51365686610 + 1780.78753223589*$t);
$Y3 += 0.00000001243*cos(3.96240186696 + 218.2087793675*$t);
$Y3 += 0.00000001234*cos(0.91112106896 + 208.8770464755*$t);
$Y3 += 0.00000001359*cos(0.27102919236 + 142.6934676173*$t);
$Y3 += 0.00000001217*cos(3.60020530728 + 1052.51220067191*$t);
$Y3 += 0.00000001352*cos(1.92480185850 + 209.87388421679*$t);
$Y3 += 0.00000001391*cos(0.65264575339 + 1243.98302014049*$t);
$Y3 += 0.00000001426*cos(2.11026020785 + 852.9525642685*$t);
$Y3 += 0.00000001501*cos(3.67811053153 + 1691.9218520189*$t);
$Y3 += 0.00000001326*cos(4.70937835849 + 2751.79141717511*$t);
$Y3 += 0.00000001171*cos(6.04141012834 + 67.91186905*$t);
$Y3 += 0.00000001462*cos(6.22305747248 + 160.852714882*$t);
$Y3 += 0.00000001164*cos(6.20382255072 + 117.0760507367*$t);
$Y3 += 0.00000001337*cos(1.54820693649 + 2627.3580019541*$t);
$Y3 += 0.00000001509*cos(0.21806196966 + 1574.6019837987*$t);
$Y3 += 0.00000001213*cos(2.74422462860 + 1354.6769763269*$t);
$Y3 += 0.00000001241*cos(5.97315240097 + 1140.8902459219*$t);
$Y3 += 0.00000001288*cos(1.29947866802 + 2950.8634186115*$t);
$Y3 += 0.00000001337*cos(2.21013619697 + 2421.1724535169*$t);
$Y3 += 0.00000001327*cos(0.27411407224 + 1567.48843679789*$t);
$Y3 += 0.00000001118*cos(4.60785389063 + 209.12312469139*$t);
$Y3 += 0.00000001043*cos(2.37818871541 + 156.9205616189*$t);
$Y3 += 0.00000001069*cos(4.66047916687 + 194.89603068979*$t);
$Y3 += 0.00000001088*cos(0.96796460237 + 1272.9248431107*$t);
$Y3 += 0.00000001270*cos(5.73542325903 + 2516.66404576769*$t);
$Y3 += 0.00000001032*cos(5.01309781815 + 1361.3028883607*$t);
$Y3 += 0.00000001009*cos(0.15463134354 + 52.446380556*$t);
$Y3 += 0.00000001100*cos(2.45485733183 + 1671.06884598351*$t);
$Y3 += 0.00000001071*cos(4.31734498299 + 1354.18934135989*$t);
$Y3 += 0.00000001120*cos(4.50723064884 + 1037.7974717033*$t);
$Y3 += 0.00000001271*cos(3.02683993003 + 721.40560204669*$t);
$Y3 += 0.00000001009*cos(4.14782207001 + 1670.5812110165*$t);
$Y3 += 0.00000001145*cos(0.18866100481 + 3157.04896704871*$t);
$Y3 += 0.00000001072*cos(4.98720300139 + 2435.3995475185*$t);
$Y3 += 0.00000001044*cos(0.37186765557 + 1560.3748897971*$t);
$Y3 += 0.00000001195*cos(4.23012320818 + 632.5399218297*$t);
$Y3 += 0.00000001043*cos(4.68469356625 + 2729.96314120569*$t);
$Y3 += 0.00000000889*cos(5.13451420872 + 359.173956793*$t);
$Y3 += 0.00000000881*cos(4.07324193143 + 1148.49142788971*$t);
$Y3 += 0.00000001040*cos(5.49603658299 + 1773.6739852351*$t);
$Y3 += 0.00000001118*cos(6.27960853334 + 1890.9938534553*$t);
$Y3 += 0.00000001047*cos(0.97265004380 + 3260.1417412673*$t);
$Y3 += 0.00000001087*cos(5.17936535207 + 2001.2001746747*$t);
$Y3 += 0.00000001087*cos(2.03777269848 + 2001.68780964171*$t);
$Y3 += 0.00000000974*cos(2.14268232218 + 1987.4607156401*$t);
$Y3 += 0.00000000869*cos(0.17251420225 + 621.98185653281*$t);
$Y3 += 0.00000001085*cos(1.32838349016 + 2214.98690507971*$t);
$Y3 += 0.00000000841*cos(3.35616685398 + 629.0954035336*$t);
$Y3 += 0.00000000875*cos(1.07922697964 + 2847.77064439291*$t);
$Y3 += 0.00000001063*cos(5.95949690738 + 2200.2721761111*$t);
$Y3 += 0.00000000853*cos(3.67902900562 + 288.32451148881*$t);
$Y3 += 0.00000001056*cos(0.19418111722 + 2332.3067732999*$t);
$Y3 += 0.00000000888*cos(0.32179471274 + 1155.1173399235*$t);
$Y3 += 0.00000001045*cos(0.14482765695 + 2.9375762542*$t);
$Y3 += 0.00000000793*cos(3.26245616640 + 341.01470952831*$t);
$Y3 += 0.00000000817*cos(0.67889320689 + 1802.12817323829*$t);
$Y3 += 0.00000000780*cos(0.38946586865 + 1382.64352936309*$t);
$Y3 += 0.00000000798*cos(3.07896109863 + 2015.42726867629*$t);
$Y3 += 0.00000000798*cos(3.07896109863 + 2015.9149036433*$t);
$Y3 += 0.00000000834*cos(2.33901429584 + 1802.6158082053*$t);
$Y3 += 0.00000000766*cos(0.30242307365 + 1471.50920958009*$t);
$Y3 += 0.00000000875*cos(5.85387427791 + 2523.7775927685*$t);
$Y3 += 0.00000000829*cos(4.44385893140 + 1162.23088692429*$t);
$Y3 += 0.00000000749*cos(2.07951145157 + 1809.72935520611*$t);
$Y3 += 0.00000000942*cos(3.40636938944 + 2008.3137216755*$t);
$Y3 += 0.00000000730*cos(4.06050820225 + 138.76131435421*$t);
$Y3 += 0.00000000734*cos(0.83381213045 + 749.8597900499*$t);
$Y3 += 0.00000000727*cos(0.81605653091 + 181.2995840071*$t);
$Y3 += 0.00000000727*cos(0.93197698209 + 245.7862418359*$t);
$Y3 += 0.00000000986*cos(4.19789524983 + 1795.0146262375*$t);
$Y3 += 0.00000000914*cos(1.81845398539 + 266.233110961*$t);
$Y3 += 0.00000000774*cos(1.85314072632 + 2840.1694624251*$t);
$Y3 += 0.00000000774*cos(1.85314072632 + 2840.6570973921*$t);
$Y3 += 0.00000000806*cos(2.87882505331 + 1912.8221294247*$t);
$Y3 += 0.00000000828*cos(0.03130512468 + 100.1551979644*$t);
$Y3 += 0.00000000700*cos(1.98220269537 + 9779.32999085069*$t);
$Y3 += 0.00000000700*cos(2.62359991037 + 10220.6429106953*$t);
$Y3 += 0.00000000687*cos(6.00740806604 + 102.84895673509*$t);
$Y3 += 0.00000000801*cos(5.73752172813 + 1457.2821155785*$t);
return $Y3*$t*$t*$t;
}
function Saturn_Y4($t) // 110 terms of order 4
{
$Y4 = 0.00007957923*cos(4.81531837805 + 220.6564599223*$t);
$Y4 += 0.00007883034*cos(3.09554141083 + 206.42936592071*$t);
$Y4 += 0.00001517028*cos(4.76816117565 + 227.77000692311*$t);
$Y4 += 0.00001235695*cos(3.82520659584 + 433.9555553603*$t);
$Y4 += 0.00001152216*cos(3.67316954399 + 213.5429129215*$t);
$Y4 += 0.00000879616*cos(3.77095350877 + 0.2438174835*$t);
$Y4 += 0.00000709628*cos(3.24840338462 + 199.3158189199*$t);
$Y4 += 0.00000602013*cos(5.94750261507 + 7.3573644843*$t);
$Y4 += 0.00000507367*cos(3.21712935929 + 426.8420083595*$t);
$Y4 += 0.00000386382*cos(6.01344501364 + 14.47091148511*$t);
$Y4 += 0.00000338827*cos(2.51520356928 + 419.72846135871*$t);
$Y4 += 0.00000186029*cos(3.85605990474 + 441.06910236111*$t);
$Y4 += 0.00000220262*cos(2.50677283832 + 640.1411037975*$t);
$Y4 += 0.00000173210*cos(2.89158751393 + 647.25465079831*$t);
$Y4 += 0.00000084974*cos(4.62115933793 + 234.8835539239*$t);
$Y4 += 0.00000085340*cos(4.39717612141 + 213.0552779545*$t);
$Y4 += 0.00000044264*cos(6.05982256678 + 117.5636857037*$t);
$Y4 += 0.00000045849*cos(5.16536949235 + 6.86972951729*$t);
$Y4 += 0.00000047835*cos(1.64342336148 + 853.4401992355*$t);
$Y4 += 0.00000041104*cos(2.18400968380 + 412.6149143579*$t);
$Y4 += 0.00000030735*cos(5.85312406338 + 21.5844584859*$t);
$Y4 += 0.00000022639*cos(2.96960991387 + 654.3681977991*$t);
$Y4 += 0.00000021067*cos(3.34244726581 + 103.3365917021*$t);
$Y4 += 0.00000020230*cos(0.17279084911 + 110.45013870291*$t);
$Y4 += 0.00000021389*cos(2.53635561163 + 205.9417309537*$t);
$Y4 += 0.00000016854*cos(4.38021440482 + 124.6772327045*$t);
$Y4 += 0.00000021739*cos(1.99698913462 + 860.55374623631*$t);
$Y4 += 0.00000017501*cos(4.23662156145 + 220.16882495529*$t);
$Y4 += 0.00000014506*cos(4.39894976150 + 88.6218627335*$t);
$Y4 += 0.00000017401*cos(2.26232682838 + 198.82818395289*$t);
$Y4 += 0.00000013517*cos(3.33447998001 + 309.5221401393*$t);
$Y4 += 0.00000011814*cos(5.16076867097 + 323.74923414091*$t);
$Y4 += 0.00000012071*cos(3.74132731532 + 448.1826493619*$t);
$Y4 += 0.00000011725*cos(4.75596558897 + 330.8627811417*$t);
$Y4 += 0.00000010174*cos(4.42772116867 + 95.7354097343*$t);
$Y4 += 0.00000011491*cos(3.65800261495 + 192.2022719191*$t);
$Y4 += 0.00000010611*cos(4.07220720960 + 302.40859313851*$t);
$Y4 += 0.00000012147*cos(2.66285969856 + 633.0275567967*$t);
$Y4 += 0.00000009067*cos(4.26864930915 + 13.9832765181*$t);
$Y4 += 0.00000008918*cos(3.03990460360 + 426.3543733925*$t);
$Y4 += 0.00000008311*cos(3.10463384858 + 430.02340209721*$t);
$Y4 += 0.00000007296*cos(0.77854151610 + 316.6356871401*$t);
$Y4 += 0.00000007890*cos(0.94138641674 + 1066.7392946735*$t);
$Y4 += 0.00000006699*cos(3.06921349305 + 109.9625037359*$t);
$Y4 += 0.00000006339*cos(3.75710669061 + 216.72430665921*$t);
$Y4 += 0.00000006254*cos(1.12954162648 + 210.36151918381*$t);
$Y4 += 0.00000006126*cos(3.21971824010 + 301.9209581715*$t);
$Y4 += 0.00000006725*cos(3.94118928489 + 625.9140097959*$t);
$Y4 += 0.00000006784*cos(4.21865919120 + 223.83785366*$t);
$Y4 += 0.00000006868*cos(0.65717842769 + 203.247972183*$t);
$Y4 += 0.00000006111*cos(3.59045265634 + 96.2230447013*$t);
$Y4 += 0.00000004468*cos(3.29229132687 + 309.0345051723*$t);
$Y4 += 0.00000004160*cos(5.74668718431 + 522.8212355773*$t);
$Y4 += 0.00000003681*cos(5.66131908910 + 423.66061462181*$t);
$Y4 += 0.00000003615*cos(5.12190926865 + 405.5013673571*$t);
$Y4 += 0.00000003079*cos(0.92409053273 + 412.12727939089*$t);
$Y4 += 0.00000003614*cos(1.94380765622 + 515.2200536095*$t);
$Y4 += 0.00000002896*cos(6.00160618678 + 515.70768857651*$t);
$Y4 += 0.00000003000*cos(3.15709072507 + 422.9098550964*$t);
$Y4 += 0.00000002685*cos(3.43239500452 + 209.6107596584*$t);
$Y4 += 0.00000002918*cos(5.44500673473 + 89.10949770051*$t);
$Y4 += 0.00000002617*cos(1.40935172097 + 217.4750661846*$t);
$Y4 += 0.00000002884*cos(2.20199681607 + 191.7146369521*$t);
$Y4 += 0.00000002281*cos(2.19064979800 + 316.14805217309*$t);
$Y4 += 0.00000002717*cos(3.78847562141 + 131.79077970531*$t);
$Y4 += 0.00000002556*cos(3.08407888684 + 337.9763281425*$t);
$Y4 += 0.00000001782*cos(4.51078296370 + 241.9971009247*$t);
$Y4 += 0.00000001782*cos(0.37884320289 + 185.08872491831*$t);
$Y4 += 0.00000001856*cos(2.79299417712 + 618.3128278281*$t);
$Y4 += 0.00000001713*cos(2.96942684848 + 625.42637482889*$t);
$Y4 += 0.00000001632*cos(0.86290354268 + 728.5191490475*$t);
$Y4 += 0.00000001980*cos(1.69424503948 + 831.6119232661*$t);
$Y4 += 0.00000001607*cos(6.10863313121 + 611.1992808273*$t);
$Y4 += 0.00000001801*cos(4.27647079459 + 227.2823719561*$t);
$Y4 += 0.00000001532*cos(5.31288615169 + 1052.51220067191*$t);
$Y4 += 0.00000001510*cos(2.58764647681 + 742.74624304909*$t);
$Y4 += 0.00000001531*cos(0.19788540477 + 529.44714761109*$t);
$Y4 += 0.00000001394*cos(3.60010141007 + 1361.3028883607*$t);
$Y4 += 0.00000001427*cos(2.30374859738 + 1251.0965671413*$t);
$Y4 += 0.00000001649*cos(4.25957274495 + 295.2950461377*$t);
$Y4 += 0.00000001249*cos(3.74724649234 + 743.23387801611*$t);
$Y4 += 0.00000001353*cos(4.07456235845 + 1678.1823929843*$t);
$Y4 += 0.00000001674*cos(5.46467832773 + 231.70216018621*$t);
$Y4 += 0.00000001646*cos(5.68811055040 + 195.38366565681*$t);
$Y4 += 0.00000001305*cos(2.57485726113 + 934.70469748469*$t);
$Y4 += 0.00000001160*cos(1.35876987453 + 81.50831573269*$t);
$Y4 += 0.00000001537*cos(1.64895812279 + 21.0968235189*$t);
$Y4 += 0.00000001096*cos(5.87040605326 + 832.0995582331*$t);
$Y4 += 0.00000001156*cos(1.65604017773 + 508.10650660869*$t);
$Y4 += 0.00000001062*cos(3.29348541593 + 294.80741117069*$t);
$Y4 += 0.00000001285*cos(1.15881412669 + 1464.3956625793*$t);
$Y4 += 0.00000001079*cos(4.46936132008 + 1368.9040703285*$t);
$Y4 += 0.00000001006*cos(4.83365073160 + 1361.79052332771*$t);
$Y4 += 0.00000001290*cos(4.69044132255 + 736.1203310153*$t);
$Y4 += 0.00000001051*cos(2.68982495323 + 941.8182444855*$t);
$Y4 += 0.00000001027*cos(3.70327166201 + 433.46792039329*$t);
$Y4 += 0.00000001021*cos(2.48350861942 + 522.3336006103*$t);
$Y4 += 0.00000001137*cos(2.90811550586 + 1891.4814884223*$t);
$Y4 += 0.00000000991*cos(3.78009400759 + 1994.5742626409*$t);
$Y4 += 0.00000001038*cos(1.35464465726 + 1148.00379292269*$t);
$Y4 += 0.00000000865*cos(0.40802396366 + 750.3474250169*$t);
$Y4 += 0.00000000859*cos(5.85730307132 + 416.547067621*$t);
$Y4 += 0.00000000862*cos(3.18022940336 + 437.136949098*$t);
$Y4 += 0.00000000776*cos(1.33793489456 + 102.84895673509*$t);
$Y4 += 0.00000000797*cos(2.04691519292 + 1375.52998236229*$t);
$Y4 += 0.00000000824*cos(4.53645127236 + 639.6534688305*$t);
$Y4 += 0.00000000881*cos(3.45735740140 + 1258.6977491091*$t);
$Y4 += 0.00000000686*cos(1.77528970097 + 234.3959189569*$t);
$Y4 += 0.00000000684*cos(3.52622623805 + 661.4817447999*$t);
$Y4 += 0.00000000859*cos(3.63825836835 + 537.0483295789*$t);
return $Y4*$t*$t*$t*$t;
}
function Saturn_Y5($t) // 40 terms of order 5
{
$Y5 = 0.00000605503*cos(3.02566952553 + 220.6564599223*$t);
$Y5 += 0.00000576439*cos(4.77676022633 + 206.42936592071*$t);
$Y5 += 0.00000227348*cos(3.02005484310 + 227.77000692311*$t);
$Y5 += 0.00000133503*cos(2.01762000448 + 433.9555553603*$t);
$Y5 += 0.00000094765*cos(4.98454736271 + 199.3158189199*$t);
$Y5 += 0.00000039851*cos(4.29556357711 + 14.47091148511*$t);
$Y5 += 0.00000034190*cos(2.07372397023 + 441.06910236111*$t);
$Y5 += 0.00000024941*cos(3.84014099419 + 0.2438174835*$t);
$Y5 += 0.00000023155*cos(1.07127433478 + 647.25465079831*$t);
$Y5 += 0.00000016208*cos(0.82050987845 + 426.8420083595*$t);
$Y5 += 0.00000012333*cos(0.61142473697 + 640.1411037975*$t);
$Y5 += 0.00000010358*cos(2.92988275487 + 234.8835539239*$t);
$Y5 += 0.00000010534*cos(5.12660829509 + 419.72846135871*$t);
$Y5 += 0.00000008668*cos(1.94893255744 + 192.2022719191*$t);
$Y5 += 0.00000008840*cos(3.98137124653 + 213.5429129215*$t);
$Y5 += 0.00000004707*cos(6.14618174587 + 88.6218627335*$t);
$Y5 += 0.00000005904*cos(3.16028075613 + 7.3573644843*$t);
$Y5 += 0.00000003895*cos(0.73151574345 + 405.5013673571*$t);
$Y5 += 0.00000003976*cos(3.54063716264 + 6.86972951729*$t);
$Y5 += 0.00000003675*cos(2.04382079343 + 213.0552779545*$t);
$Y5 += 0.00000003472*cos(6.06844015557 + 853.4401992355*$t);
$Y5 += 0.00000004393*cos(1.18474783269 + 654.3681977991*$t);
$Y5 += 0.00000003290*cos(2.31998889526 + 124.6772327045*$t);
$Y5 += 0.00000002569*cos(1.20332477401 + 109.9625037359*$t);
$Y5 += 0.00000002467*cos(1.58903935784 + 515.70768857651*$t);
$Y5 += 0.00000002708*cos(0.15976971982 + 860.55374623631*$t);
$Y5 += 0.00000002138*cos(2.01599255393 + 448.1826493619*$t);
$Y5 += 0.00000002447*cos(2.47106712193 + 220.16882495529*$t);
$Y5 += 0.00000001979*cos(5.69757911363 + 302.40859313851*$t);
$Y5 += 0.00000002238*cos(0.86043138018 + 198.82818395289*$t);
$Y5 += 0.00000001727*cos(1.65089858299 + 301.9209581715*$t);
$Y5 += 0.00000001398*cos(0.05843587724 + 309.5221401393*$t);
$Y5 += 0.00000001536*cos(3.94854505604 + 205.9417309537*$t);
$Y5 += 0.00000001195*cos(3.93835889247 + 117.5636857037*$t);
$Y5 += 0.00000001000*cos(2.44450069185 + 223.83785366*$t);
$Y5 += 0.00000000984*cos(2.38499591413 + 203.247972183*$t);
$Y5 += 0.00000000791*cos(0.61482230222 + 330.8627811417*$t);
$Y5 += 0.00000000979*cos(0.49750454847 + 95.7354097343*$t);
$Y5 += 0.00000000784*cos(1.61990559836 + 522.8212355773*$t);
$Y5 += 0.00000000910*cos(0.48207868964 + 96.2230447013*$t);
return $Y5*$t*$t*$t*$t*$t;
}
function Saturn_Z0($t) // 420 terms of order 0
{
$Z0 = 0.41356950940*cos(3.60234142982 + 213.299095438*$t);
$Z0 += 0.01148283576*cos(2.85128367469 + 426.598190876*$t);
$Z0 += 0.01214249867;
$Z0 += 0.00329280791*cos(0.57121407104 + 206.1855484372*$t);
$Z0 += 0.00286934048*cos(3.48073526693 + 220.4126424388*$t);
$Z0 += 0.00099076584*cos(4.73369511264 + 7.1135470008*$t);
$Z0 += 0.00057361820*cos(4.92611225093 + 110.2063212194*$t);
$Z0 += 0.00047738127*cos(2.10039779728 + 639.897286314*$t);
$Z0 += 0.00043458803*cos(5.84904978051 + 419.4846438752*$t);
$Z0 += 0.00034565673*cos(5.42614229590 + 316.3918696566*$t);
$Z0 += 0.00016185391*cos(2.72987173675 + 433.7117378768*$t);
$Z0 += 0.00009001270*cos(1.38140102737 + 103.0927742186*$t);
$Z0 += 0.00011433574*cos(3.71662021072 + 529.6909650946*$t);
$Z0 += 0.00005398708*cos(5.13204892363 + 202.2533951741*$t);
$Z0 += 0.00003902467*cos(3.71499738796 + 323.5054166574*$t);
$Z0 += 0.00003709212*cos(5.05549348785 + 632.7837393132*$t);
$Z0 += 0.00003614100*cos(3.35210451276 + 227.5261894396*$t);
$Z0 += 0.00003379953*cos(2.13868919206 + 11.0457002639*$t);
$Z0 += 0.00003089874*cos(3.62572857085 + 209.3669421749*$t);
$Z0 += 0.00002683064*cos(4.87689555581 + 224.3447957019*$t);
$Z0 += 0.00002963493*cos(0.46490184985 + 217.2312487011*$t);
$Z0 += 0.00002343367*cos(1.34558278340 + 853.196381752*$t);
$Z0 += 0.00002423663*cos(2.92907094760 + 63.7358983034*$t);
$Z0 += 0.00001701916*cos(1.89892525654 + 735.8765135318*$t);
$Z0 += 0.00001941205*cos(4.59421314662 + 14.2270940016*$t);
$Z0 += 0.00001990145*cos(0.73166053611 + 199.0720014364*$t);
$Z0 += 0.00001460265*cos(3.12851339724 + 522.5774180938*$t);
$Z0 += 0.00001148341*cos(4.41139213915 + 117.3198682202*$t);
$Z0 += 0.00001092809*cos(3.10679381209 + 216.4804891757*$t);
$Z0 += 0.00001015179*cos(1.97897195994 + 647.0108333148*$t);
$Z0 += 0.00001098254*cos(0.96097709156 + 210.1177017003*$t);
$Z0 += 0.00000991030*cos(2.99610026682 + 846.0828347512*$t);
$Z0 += 0.00001028743*cos(2.11933059243 + 415.5524906121*$t);
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$Z0 += 0.00000004020*cos(4.88073386744 + 54.1746707478*$t);
$Z0 += 0.00000004185*cos(3.32405342181 + 245.5424243524*$t);
$Z0 += 0.00000004583*cos(1.85097979187 + 114.3991069134*$t);
$Z0 += 0.00000004596*cos(4.18504944347 + 219.891377577*$t);
$Z0 += 0.00000003552*cos(5.98005739127 + 20.6069278195*$t);
$Z0 += 0.00000003975*cos(5.80157206371 + 14.977853527*$t);
$Z0 += 0.00000003475*cos(2.47178960968 + 1464.6394800628*$t);
$Z0 += 0.00000004395*cos(0.85418906454 + 525.4981794006*$t);
$Z0 += 0.00000003187*cos(2.61148353061 + 2324.9494088156*$t);
$Z0 += 0.00000003966*cos(4.66662911986 + 427.1194557378*$t);
$Z0 += 0.00000003124*cos(0.10655817305 + 14.0146456805*$t);
$Z0 += 0.00000003104*cos(0.38849805992 + 2634.2277314714*$t);
$Z0 += 0.00000003508*cos(2.85265213502 + 87.3117715395*$t);
$Z0 += 0.00000002979*cos(3.04084830124 + 420.9691165835*$t);
$Z0 += 0.00000003143*cos(1.71420147928 + 0.9632078465*$t);
$Z0 += 0.00000003169*cos(1.34499488466 + 159.1244246902*$t);
$Z0 += 0.00000003871*cos(2.71348462732 + 2207.6295405954*$t);
$Z0 += 0.00000002814*cos(0.52649713800 + 778.4147831847*$t);
$Z0 += 0.00000002890*cos(1.29415320006 + 2737.32050569*$t);
$Z0 += 0.00000002831*cos(4.45595764630 + 518.6452648307*$t);
$Z0 += 0.00000002757*cos(2.05371431350 + 214.5229357154*$t);
$Z0 += 0.00000002757*cos(2.83591185309 + 212.0752551606*$t);
$Z0 += 0.00000003187*cos(2.00772012188 + 2847.5268269094*$t);
$Z0 += 0.00000002712*cos(5.27492060596 + 305.3461693927*$t);
$Z0 += 0.00000002771*cos(2.54360038772 + 319.5732633943*$t);
$Z0 += 0.00000002630*cos(5.50124179878 + 423.6774295692*$t);
$Z0 += 0.00000002626*cos(0.49212317679 + 153.4953503977*$t);
$Z0 += 0.00000002828*cos(3.04457317761 + 211.6021744086*$t);
$Z0 += 0.00000002650*cos(2.71849987794 + 145.6310438715*$t);
$Z0 += 0.00000002589*cos(5.18248239650 + 1802.3719907218*$t);
$Z0 += 0.00000002579*cos(1.68789924795 + 6.1503391543*$t);
$Z0 += 0.00000003452*cos(0.69033243447 + 776.9303104764*$t);
$Z0 += 0.00000002527*cos(3.47384786002 + 184.9879197867*$t);
$Z0 += 0.00000002496*cos(5.96218386110 + 2.9207613068*$t);
$Z0 += 0.00000003222*cos(3.60809233593 + 1251.3403846248*$t);
$Z0 += 0.00000002684*cos(5.48972047825 + 391.1734682239*$t);
$Z0 += 0.00000002370*cos(1.54660575926 + 51.2057253312*$t);
$Z0 += 0.00000002310*cos(0.63846192912 + 416.3032501375*$t);
$Z0 += 0.00000002444*cos(3.87972666346 + 182.279606801*$t);
$Z0 += 0.00000002435*cos(2.71829697900 + 627.3671133418*$t);
$Z0 += 0.00000002236*cos(1.31003501645 + 241.6102710893*$t);
$Z0 += 0.00000002653*cos(5.70255270090 + 220.9339073006*$t);
$Z0 += 0.00000002646*cos(3.30185009916 + 696.5196376166*$t);
$Z0 += 0.00000002211*cos(4.72699183302 + 387.2413149608*$t);
$Z0 += 0.00000002313*cos(2.81517281649 + 738.7972748386*$t);
$Z0 += 0.00000002197*cos(2.63929129920 + 436.8931316145*$t);
$Z0 += 0.00000002348*cos(1.83689902078 + 214.9960164674*$t);
$Z0 += 0.00000002842*cos(2.88171478117 + 337.732510659*$t);
$Z0 += 0.00000002195*cos(1.58125142363 + 1677.9385755008*$t);
$Z0 += 0.00000002609*cos(1.41922918177 + 329.7251917809*$t);
$Z0 += 0.00000002207*cos(5.67197607780 + 905.8865797915*$t);
$Z0 += 0.00000002182*cos(3.15263816837 + 439.1283638482*$t);
$Z0 += 0.00000002060*cos(5.78919528834 + 120.358249606*$t);
$Z0 += 0.00000002079*cos(5.08007114480 + 7.065362891*$t);
$Z0 += 0.00000002351*cos(0.26849523535 + 140.001969579*$t);
$Z0 += 0.00000002770*cos(4.57559729641 + 24.3790223882*$t);
$Z0 += 0.00000002705*cos(4.32491993913 + 46.470422916*$t);
$Z0 += 0.00000002052*cos(1.22649156182 + 92.0470739547*$t);
$Z0 += 0.00000002046*cos(5.19173373776 + 347.8844390456*$t);
$Z0 += 0.00000002036*cos(2.88971262431 + 980.6681783588*$t);
$Z0 += 0.00000002481*cos(1.55318712059 + 576.1613880106*$t);
$Z0 += 0.00000002024*cos(4.32935289944 + 31.019488637*$t);
$Z0 += 0.00000002006*cos(2.01138855049 + 211.8628068395*$t);
$Z0 += 0.00000002006*cos(2.87823761610 + 214.7353840365*$t);
$Z0 += 0.00000002026*cos(2.42235724251 + 2641.3412784722*$t);
$Z0 += 0.00000001938*cos(2.48016602910 + 487.3651437628*$t);
$Z0 += 0.00000002065*cos(1.16081214330 + 192.6921676185*$t);
$Z0 += 0.00000002254*cos(5.99623174740 + 1905.4647649404*$t);
$Z0 += 0.00000001922*cos(5.98223148262 + 96.8729990951*$t);
$Z0 += 0.00000002534*cos(2.62272549680 + 421.93232443*$t);
$Z0 += 0.00000002106*cos(1.84883841490 + 299.1263942692*$t);
$Z0 += 0.00000002211*cos(1.86083014117 + 221.1634019642*$t);
$Z0 += 0.00000002083*cos(6.14443432076 + 59.8037450403*$t);
$Z0 += 0.00000001909*cos(1.13231253998 + 282.4516197128*$t);
$Z0 += 0.00000001898*cos(3.53454927143 + 219.6618829134*$t);
$Z0 += 0.00000002007*cos(4.35167828920 + 444.7574381407*$t);
$Z0 += 0.00000001974*cos(5.78637079670 + 430.79097657*$t);
$Z0 += 0.00000001937*cos(4.03561100629 + 429.5189521828*$t);
$Z0 += 0.00000001838*cos(2.97004270413 + 425.8474313506*$t);
$Z0 += 0.00000001880*cos(3.59058053053 + 3340.6124266998*$t);
$Z0 += 0.00000001858*cos(5.83605607376 + 280.9671470045*$t);
$Z0 += 0.00000001768*cos(4.86059839675 + 2118.7638603784*$t);
$Z0 += 0.00000002128*cos(3.95375781114 + 831.1049812242*$t);
$Z0 += 0.00000002111*cos(5.51034879271 + 428.0826635843*$t);
$Z0 += 0.00000002359*cos(3.95534711749 + 2.9689454166*$t);
$Z0 += 0.00000002084*cos(4.99656154667 + 254.9435932136*$t);
$Z0 += 0.00000002189*cos(5.75843317256 + 418.5214360287*$t);
$Z0 += 0.00000002225*cos(5.22774546552 + 638.4128136057*$t);
$Z0 += 0.00000002362*cos(0.10821349524 + 131.4039498699*$t);
$Z0 += 0.00000001938*cos(3.62212314488 + 267.4737661858*$t);
$Z0 += 0.00000002349*cos(2.45602769901 + 2524.021410252*$t);
$Z0 += 0.00000001752*cos(0.17721513623 + 969.6224780949*$t);
$Z0 += 0.00000002216*cos(4.46378373321 + 353.301065017*$t);
$Z0 += 0.00000001697*cos(3.74680430424 + 421.1815649046*$t);
$Z0 += 0.00000001692*cos(1.29673821700 + 2840.4132799086*$t);
$Z0 += 0.00000001698*cos(2.09387250037 + 292.0128472684*$t);
$Z0 += 0.00000002118*cos(2.90133577623 + 205.4347889118*$t);
$Z0 += 0.00000002049*cos(1.88559014939 + 199.2844497575*$t);
$Z0 += 0.00000001712*cos(2.97477489664 + 273.1028404783*$t);
$Z0 += 0.00000001828*cos(2.23147050409 + 1781.0313497194*$t);
$Z0 += 0.00000001933*cos(3.33016281296 + 533.6231183577*$t);
$Z0 += 0.00000001737*cos(2.59432238776 + 264.5048207692*$t);
$Z0 += 0.00000001676*cos(2.73737546375 + 3480.3105662226*$t);
$Z0 += 0.00000001935*cos(2.01080991907 + 7.1617311106*$t);
$Z0 += 0.00000001602*cos(4.81017819939 + 1382.8873468466*$t);
$Z0 += 0.00000001894*cos(4.74702697079 + 558.0021407459*$t);
$Z0 += 0.00000001589*cos(0.85622467383 + 1044.4040766622*$t);
$Z0 += 0.00000001565*cos(5.03064453644 + 458.8415197904*$t);
$Z0 += 0.00000001648*cos(5.00766073214 + 2648.454825473*$t);
$Z0 += 0.00000001562*cos(4.62304098893 + 543.0242872189*$t);
$Z0 += 0.00000001794*cos(2.92299868481 + 227.3137411185*$t);
$Z0 += 0.00000001844*cos(6.25012647811 + 432.2272651685*$t);
$Z0 += 0.00000001821*cos(5.47892889469 + 205.6642835754*$t);
$Z0 += 0.00000001605*cos(2.57251520836 + 3127.3133312618*$t);
$Z0 += 0.00000001477*cos(1.36669731999 + 206.9363079626*$t);
$Z0 += 0.00000001468*cos(4.67912895132 + 339.2864193365*$t);
$Z0 += 0.00000001481*cos(0.92457754588 + 1994.3304451574*$t);
$Z0 += 0.00000001547*cos(0.13419340100 + 465.9550667912*$t);
$Z0 += 0.00000001457*cos(0.52628058703 + 427.3489504014*$t);
$Z0 += 0.00000001902*cos(1.24600006636 + 166.828672522*$t);
$Z0 += 0.00000001529*cos(2.85370771355 + 209.1544938538*$t);
$Z0 += 0.00000001494*cos(3.66845408834 + 1182.9215735329*$t);
$Z0 += 0.00000001588*cos(1.63988438811 + 3163.918696566*$t);
$Z0 += 0.00000001502*cos(4.96348459770 + 373.9079928365*$t);
$Z0 += 0.00000001608*cos(3.59138122093 + 233.9060232575*$t);
$Z0 += 0.00000001460*cos(1.17818401345 + 92.940845832*$t);
$Z0 += 0.00000001462*cos(5.05747764334 + 33.9402499438*$t);
$Z0 += 0.00000001490*cos(2.03601440129 + 217.4436970222*$t);
$Z0 += 0.00000001688*cos(1.50928274793 + 815.0633461142*$t);
$Z0 += 0.00000001778*cos(0.24563726151 + 6.592282139*$t);
$Z0 += 0.00000001834*cos(3.98017256784 + 212.4053235607*$t);
$Z0 += 0.00000001834*cos(0.90945359875 + 214.1928673153*$t);
$Z0 += 0.00000001451*cos(3.59438611623 + 494.2662424425*$t);
$Z0 += 0.00000001474*cos(4.97772142978 + 1699.2792165032*$t);
$Z0 += 0.00000001388*cos(4.77847833406 + 2854.6403739102*$t);
$Z0 += 0.00000001589*cos(5.43527416407 + 2538.2485042536*$t);
$Z0 += 0.00000001390*cos(4.08155384651 + 894.8408795276*$t);
$Z0 += 0.00000001435*cos(1.51395699369 + 867.4234757536*$t);
$Z0 += 0.00000001404*cos(4.02343833901 + 300.6108669775*$t);
return $Z0;
}
function Saturn_Z1($t) // 234 terms of order 1
{
$Z1 = 0.03810308320*cos(5.33520316778 + 213.299095438*$t);
$Z1 -= 0.00707598508;
$Z1 += 0.00144960439*cos(2.30149367100 + 206.1855484372*$t);
$Z1 += 0.00089591263*cos(1.69286730496 + 220.4126424388*$t);
$Z1 += 0.00088982080*cos(6.09698706089 + 426.598190876*$t);
$Z1 += 0.00018761941*cos(1.23200112053 + 419.4846438752*$t);
$Z1 += 0.00018103257*cos(2.90933498453 + 7.1135470008*$t);
$Z1 += 0.00006860076*cos(0.84862244997 + 433.7117378768*$t);
$Z1 += 0.00008398809*cos(5.89715948074 + 639.897286314*$t);
$Z1 += 0.00005939993*cos(0.42396560640 + 316.3918696566*$t);
$Z1 += 0.00002571420*cos(1.61235344206 + 227.5261894396*$t);
$Z1 += 0.00002030372*cos(5.19792292680 + 110.2063212194*$t);
$Z1 += 0.00001632449*cos(2.43938017095 + 199.0720014364*$t);
$Z1 += 0.00001126250*cos(2.85739547477 + 14.2270940016*$t);
$Z1 += 0.00001025703*cos(0.77676708535 + 632.7837393132*$t);
$Z1 += 0.00001035641*cos(2.45710665385 + 217.2312487011*$t);
$Z1 += 0.00000919338*cos(5.69490380320 + 529.6909650946*$t);
$Z1 += 0.00001025261*cos(3.40455226241 + 103.0927742186*$t);
$Z1 += 0.00000788013*cos(2.75643752556 + 210.1177017003*$t);
$Z1 += 0.00000652471*cos(1.66305264153 + 202.2533951741*$t);
$Z1 += 0.00000678403*cos(5.28303371104 + 853.196381752*$t);
$Z1 += 0.00000546618*cos(0.04231005132 + 647.0108333148*$t);
$Z1 += 0.00000616068*cos(1.25272437511 + 216.4804891757*$t);
$Z1 += 0.00000589338*cos(1.25138980225 + 209.3669421749*$t);
$Z1 += 0.00000398211*cos(2.75660806272 + 117.3198682202*$t);
$Z1 += 0.00000342895*cos(1.80589354512 + 224.3447957019*$t);
$Z1 += 0.00000383087*cos(4.43945576495 + 11.0457002639*$t);
$Z1 += 0.00000315596*cos(1.62252525888 + 323.5054166574*$t);
$Z1 += 0.00000215621*cos(0.81176116742 + 440.8252848776*$t);
$Z1 += 0.00000208871*cos(1.21651777785 + 63.7358983034*$t);
$Z1 += 0.00000180311*cos(0.93555501458 + 309.2783226558*$t);
$Z1 += 0.00000172362*cos(0.22156069668 + 735.8765135318*$t);
$Z1 += 0.00000132928*cos(1.49015865779 + 95.9792272178*$t);
$Z1 += 0.00000141627*cos(1.38605092643 + 412.3710968744*$t);
$Z1 += 0.00000114025*cos(4.13401798874 + 415.5524906121*$t);
$Z1 += 0.00000107829*cos(4.67440616464 + 846.0828347512*$t);
$Z1 += 0.00000113250*cos(3.23797737561 + 277.0349937414*$t);
$Z1 += 0.00000096663*cos(5.13321545536 + 522.5774180938*$t);
$Z1 += 0.00000080905*cos(5.97207598010 + 149.5631971346*$t);
$Z1 += 0.00000078248*cos(4.68235800719 + 215.7467759928*$t);
$Z1 += 0.00000073767*cos(3.76912541093 + 74.7815985673*$t);
$Z1 += 0.00000058294*cos(4.12074427198 + 1162.4747044078*$t);
$Z1 += 0.00000059154*cos(0.00909087388 + 1052.2683831884*$t);
$Z1 += 0.00000054000*cos(2.63292711570 + 3.1813937377*$t);
$Z1 += 0.00000053374*cos(1.48573267831 + 234.6397364404*$t);
$Z1 += 0.00000057043*cos(1.87312646111 + 423.4167971383*$t);
$Z1 += 0.00000052955*cos(1.65323274690 + 330.6189636582*$t);
$Z1 += 0.00000050894*cos(2.68041943186 + 742.9900605326*$t);
$Z1 += 0.00000049329*cos(4.95750749572 + 3.9321532631*$t);
$Z1 += 0.00000061047*cos(0.29238361571 + 422.6660376129*$t);
$Z1 += 0.00000053719*cos(2.46146211746 + 490.3340891794*$t);
$Z1 += 0.00000051705*cos(4.60792983851 + 1066.49547719*$t);
$Z1 += 0.00000043576*cos(5.53983423151 + 860.3099287528*$t);
$Z1 += 0.00000038478*cos(2.42479516896 + 430.5303441391*$t);
$Z1 += 0.00000037913*cos(5.63475884335 + 210.8514148832*$t);
$Z1 += 0.00000042636*cos(0.46334621133 + 429.7795846137*$t);
$Z1 += 0.00000038288*cos(3.94527342286 + 351.8165923087*$t);
$Z1 += 0.00000032052*cos(2.73490028872 + 21.3406410024*$t);
$Z1 += 0.00000037226*cos(0.77640416852 + 536.8045120954*$t);
$Z1 += 0.00000034303*cos(5.53964443183 + 949.1756089698*$t);
$Z1 += 0.00000032486*cos(1.51592537935 + 437.6438911399*$t);
$Z1 += 0.00000025209*cos(5.61832461480 + 203.7378678824*$t);
$Z1 += 0.00000032600*cos(1.15985496536 + 223.5940361765*$t);
$Z1 += 0.00000028157*cos(5.03992835097 + 515.463871093*$t);
$Z1 += 0.00000025365*cos(1.63357066215 + 137.0330241624*$t);
$Z1 += 0.00000022772*cos(3.87097220542 + 1478.8665740644*$t);
$Z1 += 0.00000022874*cos(1.52589628823 + 124.433415221*$t);
$Z1 += 0.00000021781*cos(1.25479228248 + 88.865680217*$t);
$Z1 += 0.00000021071*cos(2.91498706203 + 203.0041546995*$t);
$Z1 += 0.00000022077*cos(6.03637528612 + 1368.660252845*$t);
$Z1 += 0.00000021851*cos(3.47826348846 + 38.1330356378*$t);
$Z1 += 0.00000022636*cos(0.42502415739 + 127.4717966068*$t);
$Z1 += 0.00000018793*cos(0.02824698856 + 654.1243803156*$t);
$Z1 += 0.00000018132*cos(0.35264011886 + 85.8272988312*$t);
$Z1 += 0.00000019127*cos(4.85094487248 + 838.9692877504*$t);
$Z1 += 0.00000015811*cos(0.06549781548 + 302.164775655*$t);
$Z1 += 0.00000014993*cos(5.63243246457 + 214.2623032845*$t);
$Z1 += 0.00000016073*cos(5.40920567275 + 1265.5674786264*$t);
$Z1 += 0.00000014177*cos(2.06003944064 + 138.5174968707*$t);
$Z1 += 0.00000014570*cos(5.68093007156 + 942.062061969*$t);
$Z1 += 0.00000012460*cos(2.22381807104 + 213.3472795478*$t);
$Z1 += 0.00000012340*cos(5.42069314117 + 217.964961884*$t);
$Z1 += 0.00000011994*cos(3.89295080099 + 728.762966531*$t);
$Z1 += 0.00000015172*cos(4.88775469732 + 208.633228992*$t);
$Z1 += 0.00000014560*cos(4.02541618429 + 195.1398481733*$t);
$Z1 += 0.00000012463*cos(5.30921040178 + 213.2509113282*$t);
$Z1 += 0.00000011186*cos(1.39522203481 + 210.3783341312*$t);
$Z1 += 0.00000011627*cos(2.81135897939 + 231.4583427027*$t);
$Z1 += 0.00000015326*cos(4.31191275758 + 628.8515860501*$t);
$Z1 += 0.00000012272*cos(2.46356221718 + 200.7689224658*$t);
$Z1 += 0.00000015060*cos(1.90080442413 + 212.3358875915*$t);
$Z1 += 0.00000011799*cos(1.46416357606 + 218.7157214094*$t);
$Z1 += 0.00000010790*cos(0.87460319256 + 408.4389436113*$t);
$Z1 += 0.00000010282*cos(5.35193913607 + 207.6700211455*$t);
$Z1 += 0.00000013027*cos(3.77267768832 + 350.3321196004*$t);
$Z1 += 0.00000010032*cos(2.41897316373 + 10.2949407385*$t);
$Z1 += 0.00000012485*cos(2.56988226727 + 340.7708920448*$t);
$Z1 += 0.00000011155*cos(4.46475107308 + 52.6901980395*$t);
$Z1 += 0.00000011678*cos(5.99973973452 + 191.2076949102*$t);
$Z1 += 0.00000009985*cos(5.55354944984 + 76.2660712756*$t);
$Z1 += 0.00000009222*cos(3.47198476691 + 18.1592472647*$t);
$Z1 += 0.00000008684*cos(3.59341160996 + 1795.258443721*$t);
$Z1 += 0.00000008772*cos(2.84157598451 + 191.9584544356*$t);
$Z1 += 0.00000008792*cos(5.77952076653 + 1685.0521225016*$t);
$Z1 += 0.00000010212*cos(4.67919299694 + 1155.361157407*$t);
$Z1 += 0.00000007416*cos(2.34743956282 + 160.6088973985*$t);
$Z1 += 0.00000008681*cos(3.66196489035 + 222.8603229936*$t);
$Z1 += 0.00000008204*cos(4.00167578990 + 388.4651552382*$t);
$Z1 += 0.00000007229*cos(0.85694899722 + 142.4496501338*$t);
$Z1 += 0.00000007962*cos(6.12384852532 + 209.106309744*$t);
$Z1 += 0.00000008152*cos(0.17850883770 + 1.4844727083*$t);
$Z1 += 0.00000007462*cos(4.54643529511 + 625.6701923124*$t);
$Z1 += 0.00000008149*cos(4.75191185936 + 831.8557407496*$t);
$Z1 += 0.00000007464*cos(5.87758421420 + 362.8622925726*$t);
$Z1 += 0.00000006550*cos(0.37942895236 + 212.7778305762*$t);
$Z1 += 0.00000007220*cos(5.21944812420 + 1581.959348283*$t);
$Z1 += 0.00000006436*cos(0.63886589467 + 22.0914005278*$t);
$Z1 += 0.00000007311*cos(0.07712493176 + 265.9892934775*$t);
$Z1 += 0.00000007040*cos(5.39023352132 + 1258.4539316256*$t);
$Z1 += 0.00000006246*cos(6.10782448635 + 618.5566453116*$t);
$Z1 += 0.00000005540*cos(1.63194253275 + 56.6223513026*$t);
$Z1 += 0.00000007460*cos(2.16123164874 + 207.8824694666*$t);
$Z1 += 0.00000006689*cos(5.61849505042 + 483.2205421786*$t);
$Z1 += 0.00000005366*cos(2.54918207389 + 554.0699874828*$t);
$Z1 += 0.00000007245*cos(3.44291004853 + 12.5301729722*$t);
$Z1 += 0.00000005769*cos(0.85039589871 + 225.8292684102*$t);
$Z1 += 0.00000006530*cos(0.87136105335 + 213.8203602998*$t);
$Z1 += 0.00000005249*cos(0.71690429208 + 447.9388318784*$t);
$Z1 += 0.00000004793*cos(4.97423814367 + 212.5483359126*$t);
$Z1 += 0.00000005801*cos(0.02624779337 + 269.9214467406*$t);
$Z1 += 0.00000004710*cos(3.07134751984 + 1375.7737998458*$t);
$Z1 += 0.00000005649*cos(5.76570118321 + 635.9651330509*$t);
$Z1 += 0.00000004366*cos(4.43717368507 + 235.3904959658*$t);
$Z1 += 0.00000005595*cos(1.00573470142 + 70.8494453042*$t);
$Z1 += 0.00000005094*cos(0.10066001708 + 750.1036075334*$t);
$Z1 += 0.00000004487*cos(4.79200734443 + 218.9281697305*$t);
$Z1 += 0.00000004220*cos(3.11074964024 + 703.6331846174*$t);
$Z1 += 0.00000004530*cos(2.43215667228 + 216.2198567448*$t);
$Z1 += 0.00000004076*cos(1.21943503644 + 417.0369633204*$t);
$Z1 += 0.00000004075*cos(5.52140305637 + 2001.4439921582*$t);
$Z1 += 0.00000004489*cos(5.12835463313 + 1574.8458012822*$t);
$Z1 += 0.00000003835*cos(4.59484102776 + 424.1505103212*$t);
$Z1 += 0.00000004075*cos(4.07912904262 + 1279.794572628*$t);
$Z1 += 0.00000004918*cos(4.36928157904 + 1471.7530270636*$t);
$Z1 += 0.00000003719*cos(3.42064399733 + 1045.1548361876*$t);
$Z1 += 0.00000004734*cos(5.61204474661 + 9.5612275556*$t);
$Z1 += 0.00000004537*cos(0.79869612235 + 543.9180590962*$t);
$Z1 += 0.00000003610*cos(5.94058751363 + 934.9485149682*$t);
$Z1 += 0.00000004230*cos(5.90345986772 + 173.9422195228*$t);
$Z1 += 0.00000003444*cos(2.86327846707 + 106.2741679563*$t);
$Z1 += 0.00000003432*cos(4.89216582171 + 497.4476361802*$t);
$Z1 += 0.00000003553*cos(4.80761740206 + 1073.6090241908*$t);
$Z1 += 0.00000004601*cos(4.77897976995 + 288.0806940053*$t);
$Z1 += 0.00000003314*cos(3.41625676576 + 2111.6503133776*$t);
$Z1 += 0.00000003264*cos(4.45520175360 + 107.0249274817*$t);
$Z1 += 0.00000003442*cos(2.57824148394 + 113.3877149571*$t);
$Z1 += 0.00000003664*cos(4.49847588517 + 1148.2476104062*$t);
$Z1 += 0.00000003349*cos(1.27990783834 + 344.7030453079*$t);
$Z1 += 0.00000002971*cos(4.31371705105 + 219.4494345923*$t);
$Z1 += 0.00000002920*cos(1.64503980864 + 636.7158925763*$t);
$Z1 += 0.00000002971*cos(2.61742682364 + 404.5067903482*$t);
$Z1 += 0.00000003051*cos(5.10422803245 + 1898.3512179396*$t);
$Z1 += 0.00000002774*cos(3.14101665470 + 217.491881132*$t);
$Z1 += 0.00000002950*cos(5.37168308363 + 175.1660598002*$t);
$Z1 += 0.00000002822*cos(1.33413781392 + 650.9429865779*$t);
$Z1 += 0.00000003174*cos(1.19063213567 + 337.732510659*$t);
$Z1 += 0.00000003041*cos(6.26099119193 + 207.1487562837*$t);
$Z1 += 0.00000002591*cos(4.52751512849 + 565.1156877467*$t);
$Z1 += 0.00000003416*cos(5.97202994093 + 643.0786800517*$t);
$Z1 += 0.00000002507*cos(0.83753919585 + 436.8931316145*$t);
$Z1 += 0.00000002350*cos(2.16713733034 + 177.8743727859*$t);
$Z1 += 0.00000002755*cos(3.61967991567 + 114.1384744825*$t);
$Z1 += 0.00000002495*cos(4.64668211731 + 429.0458714308*$t);
$Z1 += 0.00000002768*cos(4.77439427919 + 1891.2376709388*$t);
$Z1 += 0.00000002238*cos(4.00121267561 + 284.1485407422*$t);
$Z1 += 0.00000002251*cos(4.90436209991 + 2214.7430875962*$t);
$Z1 += 0.00000002409*cos(3.56267761888 + 1169.5882514086*$t);
$Z1 += 0.00000002157*cos(3.02442510484 + 1692.1656695024*$t);
$Z1 += 0.00000002003*cos(2.47564274875 + 416.3032501375*$t);
$Z1 += 0.00000002085*cos(4.09277149039 + 1272.6810256272*$t);
$Z1 += 0.00000001945*cos(0.97841451672 + 114.3991069134*$t);
$Z1 += 0.00000001907*cos(3.36673783584 + 1059.3819301892*$t);
$Z1 += 0.00000001861*cos(4.45402970588 + 508.3503240922*$t);
$Z1 += 0.00000001874*cos(2.73629728926 + 214.0498549634*$t);
$Z1 += 0.00000001905*cos(2.99492664264 + 1361.5467058442*$t);
$Z1 += 0.00000002064*cos(5.39674851006 + 245.5424243524*$t);
$Z1 += 0.00000001878*cos(0.56676085326 + 621.7380390493*$t);
$Z1 += 0.00000002525*cos(1.19036969669 + 479.2883889155*$t);
$Z1 += 0.00000001966*cos(2.58393370207 + 99.1606209555*$t);
$Z1 += 0.00000001908*cos(2.85404393589 + 355.7487455718*$t);
$Z1 += 0.00000002056*cos(2.39618093351 + 2435.155730035*$t);
$Z1 += 0.00000002158*cos(4.97710925643 + 2317.8358618148*$t);
$Z1 += 0.00000002202*cos(0.84567094644 + 358.9301393095*$t);
$Z1 += 0.00000001881*cos(1.13062277248 + 757.2171545342*$t);
$Z1 += 0.00000001707*cos(1.57935987501 + 6069.7767545534*$t);
$Z1 += 0.00000002151*cos(4.06616159617 + 1788.1448967202*$t);
$Z1 += 0.00000001746*cos(3.06455575770 + 2008.557539159*$t);
$Z1 += 0.00000001746*cos(5.09056895026 + 220.4608265486*$t);
$Z1 += 0.00000001795*cos(2.95316519456 + 1781.0313497194*$t);
$Z1 += 0.00000001700*cos(6.05669760153 + 206.1373643274*$t);
$Z1 += 0.00000001614*cos(5.96461527769 + 867.4234757536*$t);
$Z1 += 0.00000001956*cos(2.13214810643 + 252.6559713532*$t);
$Z1 += 0.00000001739*cos(5.77930712282 + 181.0557665236*$t);
$Z1 += 0.00000001553*cos(1.32350368373 + 131.5469622218*$t);
$Z1 += 0.00000001599*cos(0.86145918975 + 81.7521332162*$t);
$Z1 += 0.00000001792*cos(0.86879017108 + 4.665866446*$t);
$Z1 += 0.00000001548*cos(4.47085375766 + 121.2520214833*$t);
$Z1 += 0.00000001619*cos(4.79891754382 + 842.1506814881*$t);
$Z1 += 0.00000001513*cos(3.01415732754 + 2428.0421830342*$t);
$Z1 += 0.00000001822*cos(2.62978911169 + 643.8294395771*$t);
$Z1 += 0.00000002085*cos(3.00604517701 + 563.6312150384*$t);
$Z1 += 0.00000001939*cos(2.25124681713 + 1677.9385755008*$t);
$Z1 += 0.00000001472*cos(3.39986301851 + 956.2891559706*$t);
$Z1 += 0.00000001467*cos(4.24274724035 + 98.8999885246*$t);
$Z1 += 0.00000001384*cos(2.33959628851 + 444.7574381407*$t);
$Z1 += 0.00000001810*cos(2.02611183018 + 2420.9286360334*$t);
$Z1 += 0.00000001628*cos(4.47984535594 + 251.4321310758*$t);
$Z1 += 0.00000001593*cos(1.97508934614 + 62.2514255951*$t);
$Z1 += 0.00000001516*cos(1.25225067905 + 425.1137181677*$t);
$Z1 += 0.00000001181*cos(5.09622518839 + 414.0680179038*$t);
$Z1 += 0.00000001211*cos(0.96174816662 + 214.7835681463*$t);
$Z1 += 0.00000001429*cos(2.95386700663 + 65.2203710117*$t);
$Z1 += 0.00000001042*cos(5.99222596459 + 151.0476698429*$t);
$Z1 += 0.00000001200*cos(0.65918491217 + 211.8146227297*$t);
$Z1 += 0.00000000967*cos(6.01089625149 + 1589.0728952838*$t);
$Z1 += 0.00000000904*cos(0.07909774752 + 213.4109700226*$t);
$Z1 += 0.00000000904*cos(1.66925524906 + 213.1872208534*$t);
$Z1 += 0.00000001071*cos(3.60798747502 + 248.7238180901*$t);
$Z1 += 0.00000000815*cos(4.93878023673 + 2.4476805548*$t);
$Z1 += 0.00000000775*cos(3.45264409045 + 198.321241911*$t);
$Z1 += 0.00000000983*cos(3.20558404998 + 312.1990839626*$t);
$Z1 += 0.00000000760*cos(2.28889729136 + 213.0866471169*$t);
$Z1 += 0.00000000760*cos(5.74264101239 + 213.5115437591*$t);
$Z1 += 0.00000000724*cos(4.57593199965 + 228.276948965*$t);
return $Z1*$t;
}
function Saturn_Z2($t) // 91 terms of order 2
{
$Z2 = 0.00195192259*cos(0.50946874402 + 213.299095438*$t);
$Z2 += 0.00036491216*cos(3.99604491617 + 206.1855484372*$t);
$Z2 += 0.00015091412*cos(6.17687148383 + 220.4126424388*$t);
$Z2 += 0.00019236496;
$Z2 += 0.00003420562*cos(3.04256365132 + 419.4846438752*$t);
$Z2 += 0.00001903731*cos(1.01852901874 + 7.1135470008*$t);
$Z2 += 0.00001553807*cos(5.27527652115 + 433.7117378768*$t);
$Z2 += 0.00001658586*cos(5.05753354015 + 426.598190876*$t);
$Z2 += 0.00000939968*cos(6.15093957163 + 227.5261894396*$t);
$Z2 += 0.00000665875*cos(1.95823182523 + 316.3918696566*$t);
$Z2 += 0.00000727405*cos(3.86689219213 + 639.897286314*$t);
$Z2 += 0.00000708634*cos(4.14159824503 + 199.0720014364*$t);
$Z2 += 0.00000332785*cos(1.11013701815 + 14.2270940016*$t);
$Z2 += 0.00000276129*cos(4.52772200630 + 210.1177017003*$t);
$Z2 += 0.00000246881*cos(4.50860976295 + 103.0927742186*$t);
$Z2 += 0.00000236419*cos(1.02568314619 + 110.2063212194*$t);
$Z2 += 0.00000193411*cos(4.35154385844 + 217.2312487011*$t);
$Z2 += 0.00000170756*cos(2.72871130039 + 632.7837393132*$t);
$Z2 += 0.00000154811*cos(4.42812217496 + 647.0108333148*$t);
$Z2 += 0.00000159221*cos(5.67806982371 + 216.4804891757*$t);
$Z2 += 0.00000100473*cos(3.17382026227 + 853.196381752*$t);
$Z2 += 0.00000090850*cos(5.30427538537 + 440.8252848776*$t);
$Z2 += 0.00000077600*cos(3.28475417716 + 202.2533951741*$t);
$Z2 += 0.00000072917*cos(1.06686891373 + 117.3198682202*$t);
$Z2 += 0.00000061331*cos(1.61343080245 + 529.6909650946*$t);
$Z2 += 0.00000064246*cos(3.02694204128 + 412.3710968744*$t);
$Z2 += 0.00000063778*cos(5.55207588103 + 209.3669421749*$t);
$Z2 += 0.00000041451*cos(3.33188411884 + 309.2783226558*$t);
$Z2 += 0.00000033437*cos(0.11560358087 + 323.5054166574*$t);
$Z2 += 0.00000029893*cos(6.03701243746 + 234.6397364404*$t);
$Z2 += 0.00000025877*cos(3.50813571651 + 95.9792272178*$t);
$Z2 += 0.00000017574*cos(0.22180355628 + 3.9321532631*$t);
$Z2 += 0.00000016154*cos(3.77501334464 + 423.4167971383*$t);
$Z2 += 0.00000015793*cos(1.02173188447 + 21.3406410024*$t);
$Z2 += 0.00000014438*cos(5.60523358660 + 223.5940361765*$t);
$Z2 += 0.00000013542*cos(4.81528922933 + 429.7795846137*$t);
$Z2 += 0.00000015398*cos(5.52110630605 + 224.3447957019*$t);
$Z2 += 0.00000011511*cos(4.71374175861 + 203.0041546995*$t);
$Z2 += 0.00000014090*cos(5.07886462834 + 277.0349937414*$t);
$Z2 += 0.00000014469*cos(3.60157016903 + 860.3099287528*$t);
$Z2 += 0.00000012120*cos(0.05423484257 + 415.5524906121*$t);
$Z2 += 0.00000013400*cos(0.51901182147 + 522.5774180938*$t);
$Z2 += 0.00000010074*cos(4.55389948936 + 422.6660376129*$t);
$Z2 += 0.00000012614*cos(6.15368985726 + 330.6189636582*$t);
$Z2 += 0.00000010793*cos(2.51124542537 + 1066.49547719*$t);
$Z2 += 0.00000008990*cos(6.00345025989 + 124.433415221*$t);
$Z2 += 0.00000010308*cos(6.00841164198 + 11.0457002639*$t);
$Z2 += 0.00000008308*cos(0.68581626528 + 3.1813937377*$t);
$Z2 += 0.00000009597*cos(5.80785895962 + 63.7358983034*$t);
$Z2 += 0.00000007930*cos(5.51468008833 + 735.8765135318*$t);
$Z2 += 0.00000008053*cos(3.03363150224 + 88.865680217*$t);
$Z2 += 0.00000008834*cos(4.47705749563 + 654.1243803156*$t);
$Z2 += 0.00000007356*cos(4.43315310489 + 191.9584544356*$t);
$Z2 += 0.00000006543*cos(4.88541538755 + 625.6701923124*$t);
$Z2 += 0.00000008411*cos(1.49318798287 + 742.9900605326*$t);
$Z2 += 0.00000006909*cos(4.48978383769 + 430.5303441391*$t);
$Z2 += 0.00000006388*cos(0.08457977809 + 215.7467759928*$t);
$Z2 += 0.00000007107*cos(0.70220678131 + 949.1756089698*$t);
$Z2 += 0.00000005669*cos(0.46049062500 + 515.463871093*$t);
$Z2 += 0.00000005034*cos(5.23865643179 + 74.7815985673*$t);
$Z2 += 0.00000004315*cos(1.63053592014 + 1059.3819301892*$t);
$Z2 += 0.00000004299*cos(1.18161521312 + 210.8514148832*$t);
$Z2 += 0.00000003314*cos(5.42600783265 + 437.6438911399*$t);
$Z2 += 0.00000003489*cos(0.53174386810 + 10.2949407385*$t);
$Z2 += 0.00000003355*cos(5.23729212209 + 447.9388318784*$t);
$Z2 += 0.00000003056*cos(1.18250311873 + 942.062061969*$t);
$Z2 += 0.00000002996*cos(5.62814654221 + 728.762966531*$t);
$Z2 += 0.00000003361*cos(5.11461252953 + 536.8045120954*$t);
$Z2 += 0.00000002396*cos(1.84582366198 + 1471.7530270636*$t);
$Z2 += 0.00000002280*cos(0.09630660324 + 195.1398481733*$t);
$Z2 += 0.00000002351*cos(1.27223026559 + 231.4583427027*$t);
$Z2 += 0.00000002515*cos(0.03375128717 + 838.9692877504*$t);
$Z2 += 0.00000002748*cos(1.32449995239 + 203.7378678824*$t);
$Z2 += 0.00000002290*cos(3.07698270979 + 408.4389436113*$t);
$Z2 += 0.00000002040*cos(5.80760536835 + 1162.4747044078*$t);
$Z2 += 0.00000002084*cos(0.74674443126 + 1265.5674786264*$t);
$Z2 += 0.00000002283*cos(1.77539793334 + 846.0828347512*$t);
$Z2 += 0.00000001868*cos(0.23989474559 + 1898.3512179396*$t);
$Z2 += 0.00000001720*cos(1.98614962644 + 18.1592472647*$t);
$Z2 += 0.00000001849*cos(0.68415972849 + 1258.4539316256*$t);
$Z2 += 0.00000001575*cos(2.31138086283 + 302.164775655*$t);
$Z2 += 0.00000001874*cos(0.84722174143 + 1375.7737998458*$t);
$Z2 += 0.00000001401*cos(3.28871251562 + 1073.6090241908*$t);
$Z2 += 0.00000001369*cos(4.66184064286 + 490.3340891794*$t);
$Z2 += 0.00000001319*cos(0.58131415395 + 618.5566453116*$t);
$Z2 += 0.00000001430*cos(2.32626814584 + 1368.660252845*$t);
$Z2 += 0.00000001519*cos(0.21611173188 + 831.8557407496*$t);
$Z2 += 0.00000001250*cos(5.97999895371 + 351.8165923087*$t);
$Z2 += 0.00000000966*cos(2.64913416683 + 85.8272988312*$t);
$Z2 += 0.00000000771*cos(1.16732337173 + 217.964961884*$t);
$Z2 += 0.00000000697*cos(0.53637719953 + 628.8515860501*$t);
return $Z2*$t*$t;
}
function Saturn_Z3($t) // 45 terms of order 3
{
$Z3 = 0.00006552316*cos(1.98918006303 + 213.299095438*$t);
$Z3 += 0.00006205120*cos(5.69682939522 + 206.1855484372*$t);
$Z3 += 0.00005692884;
$Z3 += 0.00001736879*cos(4.32959476351 + 220.4126424388*$t);
$Z3 += 0.00000450555*cos(4.83582005306 + 419.4846438752*$t);
$Z3 += 0.00000231881*cos(4.39490786964 + 227.5261894396*$t);
$Z3 += 0.00000199865*cos(2.33322152046 + 426.598190876*$t);
$Z3 += 0.00000205985*cos(5.84743845970 + 199.0720014364*$t);
$Z3 += 0.00000242710*cos(3.41690207168 + 433.7117378768*$t);
$Z3 += 0.00000139339*cos(5.28736351227 + 7.1135470008*$t);
$Z3 += 0.00000067206*cos(5.62860360986 + 14.2270940016*$t);
$Z3 += 0.00000056299*cos(1.93019307649 + 639.897286314*$t);
$Z3 += 0.00000055780*cos(0.01778616215 + 210.1177017003*$t);
$Z3 += 0.00000050857*cos(3.44381337767 + 316.3918696566*$t);
$Z3 += 0.00000029135*cos(0.23714193891 + 103.0927742186*$t);
$Z3 += 0.00000030392*cos(2.54675335277 + 647.0108333148*$t);
$Z3 += 0.00000025847*cos(3.51464713160 + 440.8252848776*$t);
$Z3 += 0.00000020480*cos(3.72108337650 + 216.4804891757*$t);
$Z3 += 0.00000018853*cos(6.10978933980 + 217.2312487011*$t);
$Z3 += 0.00000018881*cos(4.62069633304 + 632.7837393132*$t);
$Z3 += 0.00000017464*cos(4.72219191592 + 412.3710968744*$t);
$Z3 += 0.00000010821*cos(1.21499195673 + 853.196381752*$t);
$Z3 += 0.00000010927*cos(4.30569213091 + 234.6397364404*$t);
$Z3 += 0.00000009297*cos(5.60250826661 + 117.3198682202*$t);
$Z3 += 0.00000007656*cos(5.66078016942 + 309.2783226558*$t);
$Z3 += 0.00000007303*cos(5.47485612817 + 202.2533951741*$t);
$Z3 += 0.00000005000*cos(5.51413752856 + 21.3406410024*$t);
$Z3 += 0.00000004259*cos(5.49035642189 + 95.9792272178*$t);
$Z3 += 0.00000004838*cos(0.29619340824 + 110.2063212194*$t);
$Z3 += 0.00000003957*cos(6.09695713906 + 191.9584544356*$t);
$Z3 += 0.00000003467*cos(3.73810181850 + 223.5940361765*$t);
$Z3 += 0.00000003322*cos(1.65077341966 + 860.3099287528*$t);
$Z3 += 0.00000002905*cos(4.28100382746 + 323.5054166574*$t);
$Z3 += 0.00000002380*cos(2.83328075768 + 429.7795846137*$t);
$Z3 += 0.00000002398*cos(4.14927979178 + 124.433415221*$t);
$Z3 += 0.00000002780*cos(2.64718847967 + 654.1243803156*$t);
$Z3 += 0.00000002787*cos(0.65101567800 + 203.0041546995*$t);
$Z3 += 0.00000001947*cos(1.53880195116 + 209.3669421749*$t);
$Z3 += 0.00000001856*cos(5.62026724615 + 302.164775655*$t);
$Z3 += 0.00000001819*cos(4.80294039631 + 88.865680217*$t);
$Z3 += 0.00000001959*cos(4.38771818896 + 330.6189636582*$t);
$Z3 += 0.00000001487*cos(3.12393556594 + 529.6909650946*$t);
$Z3 += 0.00000001276*cos(3.91936027558 + 447.9388318784*$t);
$Z3 += 0.00000001374*cos(1.28276260217 + 1066.49547719*$t);
$Z3 += 0.00000000804*cos(4.10158366806 + 224.3447957019*$t);
return $Z3*$t*$t*$t;
}
function Saturn_Z4($t) // 22 terms of order 4
{
$Z4 = 0.00000789033*cos(1.11928782644 + 206.1855484372*$t);
$Z4 += 0.00000281365*cos(3.13274851308 + 213.299095438*$t);
$Z4 -= 0.00000169515;
$Z4 += 0.00000157511*cos(2.46634171520 + 220.4126424388*$t);
$Z4 += 0.00000046995*cos(1.27259130638 + 199.0720014364*$t);
$Z4 += 0.00000043842*cos(0.38587829145 + 419.4846438752*$t);
$Z4 += 0.00000043114*cos(2.62919688921 + 227.5261894396*$t);
$Z4 += 0.00000028988*cos(1.55482750505 + 433.7117378768*$t);
$Z4 += 0.00000009447*cos(3.85114048856 + 14.2270940016*$t);
$Z4 += 0.00000006018*cos(1.29220324867 + 426.598190876*$t);
$Z4 += 0.00000007462*cos(3.20599530963 + 7.1135470008*$t);
$Z4 += 0.00000004617*cos(0.67712478942 + 647.0108333148*$t);
$Z4 += 0.00000005282*cos(1.71952902559 + 440.8252848776*$t);
$Z4 += 0.00000003522*cos(6.19992669453 + 639.897286314*$t);
$Z4 += 0.00000002258*cos(0.44292528032 + 412.3710968744*$t);
$Z4 += 0.00000002256*cos(2.11084590211 + 210.1177017003*$t);
$Z4 += 0.00000002460*cos(2.50380847653 + 234.6397364404*$t);
$Z4 += 0.00000001239*cos(5.78004218066 + 110.2063212194*$t);
$Z4 += 0.00000001449*cos(5.96384491391 + 216.4804891757*$t);
$Z4 += 0.00000001322*cos(0.54271370335 + 853.196381752*$t);
$Z4 += 0.00000001151*cos(4.86229315211 + 117.3198682202*$t);
$Z4 += 0.00000001045*cos(5.61649418233 + 316.3918696566*$t);
return $Z4*$t*$t*$t*$t;
}
function Saturn_Z5($t) // 9 terms of order 5
{
$Z5 = 0.00000077433*cos(2.81859989913 + 206.1855484372*$t);
$Z5 -= 0.00000013826;
$Z5 += 0.00000009303*cos(0.47844462514 + 220.4126424388*$t);
$Z5 += 0.00000007840*cos(2.99415198633 + 199.0720014364*$t);
$Z5 += 0.00000005604*cos(0.80222427065 + 227.5261894396*$t);
$Z5 += 0.00000002881*cos(6.00054088318 + 433.7117378768*$t);
$Z5 += 0.00000001362*cos(2.58324584516 + 419.4846438752*$t);
$Z5 += 0.00000000968*cos(5.23916441152 + 213.299095438*$t);
$Z5 += 0.00000000867*cos(5.81659714144 + 7.1135470008*$t);
return $Z5*$t*$t*$t*$t*$t;
}
?>