<?PHP

/*

   ******************************************************
   NEPTUNE

   Heliocentric Coords Module - VSOP 87 Theory - Series C

   Heliocentric rectangular X,Y,Z,R coordinates for the
   mean dynamical ecliptic and equinox of the date.

   Module Range: 4000 BC  to  8000 AD

   Written in PHP v5.2.5

   This source code is released to the public domain.

   Jay Tanner
   VSOP87@NeoProgrammics.com

   ******************************************************

*/

   function Neptune_hXYZR($JDArg)
{

// Compute time in Julian millennia from J2000.0
   $t = ($JDArg - 2451545.0) / 365250.0;

// Compute the heliocentric coordinates for time ($t).
   $hX = Neptune_X0($t) + Neptune_X1($t) + Neptune_X2($t)
       + Neptune_X3($t) + Neptune_X4($t) + Neptune_X5($t);

   $hY = Neptune_Y0($t) + Neptune_Y1($t) + Neptune_Y2($t)
       + Neptune_Y3($t) + Neptune_Y4($t) + Neptune_Y5($t);

   $hZ = Neptune_Z0($t) + Neptune_Z1($t) + Neptune_Z2($t)
       + Neptune_Z3($t) + Neptune_Z4($t) + Neptune_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";

}




/*

   Neptune - VSOP87 Series Version C - 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 Neptune_X0($t) // 821 terms of order 0
{
   $X0  = 30.05973100580*cos(5.31188633083 + 38.3768531213*$t);
   $X0 += 0.40567587218*cos(3.98149970131 + 0.2438174835*$t);
   $X0 += 0.13506026414*cos(3.50055820972 + 76.50988875911*$t);
   $X0 += 0.15716341901*cos(0.11310077968 + 36.892380413*$t);
   $X0 += 0.14935642614*cos(1.08477702063 + 39.86132582961*$t);
   $X0 += 0.02590782232*cos(1.99609768221 + 1.7282901918*$t);
   $X0 += 0.01073890204*cos(5.38477153556 + 75.0254160508*$t);
   $X0 += 0.00816388197*cos(0.78185518038 + 3.21276290011*$t);
   $X0 += 0.00702768075*cos(1.45363642119 + 35.40790770471*$t);
   $X0 += 0.00687594822*cos(0.72075739344 + 37.88921815429*$t);
   $X0 += 0.00565555652*cos(5.98943773879 + 41.3457985379*$t);
   $X0 += 0.00495650075*cos(0.59957534348 + 529.9347825781*$t);
   $X0 += 0.00306025380*cos(0.39916788140 + 73.5409433425*$t);
   $X0 += 0.00272446904*cos(0.87404115637 + 213.5429129215*$t);
   $X0 += 0.00135892298*cos(5.54654979922 + 77.9943614674*$t);
   $X0 += 0.00122117697*cos(1.30863876781 + 34.9202727377*$t);
   $X0 += 0.00090968285*cos(1.68886748674 + 114.6429243969*$t);
   $X0 += 0.00068915400*cos(5.83470374400 + 4.6972356084*$t);
   $X0 += 0.00040370680*cos(2.66129691063 + 33.9234349964*$t);
   $X0 += 0.00028891307*cos(4.78947715515 + 42.83027124621*$t);
   $X0 += 0.00029247752*cos(1.62319522731 + 72.05647063421*$t);
   $X0 += 0.00025576289*cos(1.48342967006 + 71.5688356672*$t);
   $X0 += 0.00020517968*cos(2.55621077117 + 33.43580002939*$t);
   $X0 += 0.00012614154*cos(3.56929744338 + 113.15845168861*$t);
   $X0 += 0.00012788929*cos(2.73769634046 + 111.67397898031*$t);
   $X0 += 0.00012013477*cos(0.94915799508 + 1059.6257476727*$t);
   $X0 += 0.00009854638*cos(0.25713641240 + 36.404745446*$t);
   $X0 += 0.00008385825*cos(1.65242210861 + 108.2173985967*$t);
   $X0 += 0.00007577585*cos(0.09970777629 + 426.8420083595*$t);
   $X0 += 0.00006452053*cos(4.62556526073 + 6.1817083167*$t);
   $X0 += 0.00006551074*cos(1.91884050790 + 1.24065522479*$t);
   $X0 += 0.00004652534*cos(0.10344003066 + 37.8555882595*$t);
   $X0 += 0.00004732958*cos(4.09711900918 + 79.47883417571*$t);
   $X0 += 0.00004557247*cos(1.09712661798 + 38.89811798311*$t);
   $X0 += 0.00004322550*cos(2.37744779374 + 38.32866901151*$t);
   $X0 += 0.00004315539*cos(5.10473140788 + 38.4250372311*$t);
   $X0 += 0.00004089036*cos(1.99429063701 + 37.4136452748*$t);
   $X0 += 0.00004248658*cos(5.63379709294 + 28.81562556571*$t);
   $X0 += 0.00004622142*cos(2.73995451568 + 70.08436295889*$t);
   $X0 += 0.00003926447*cos(5.48975060892 + 39.34006096781*$t);
   $X0 += 0.00003148422*cos(5.18755364576 + 76.0222537921*$t);
   $X0 += 0.00003940981*cos(2.29766376691 + 98.6561710411*$t);
   $X0 += 0.00003323363*cos(4.68776245279 + 4.4366031775*$t);
   $X0 += 0.00003282964*cos(2.81551282614 + 39.3736908626*$t);
   $X0 += 0.00003110464*cos(1.84416897204 + 47.9380806769*$t);
   $X0 += 0.00002927062*cos(2.83767313961 + 70.5719979259*$t);
   $X0 += 0.00002748919*cos(3.86990252936 + 32.4389622881*$t);
   $X0 += 0.00003316668*cos(1.82194084200 + 144.8659615262*$t);
   $X0 += 0.00002822405*cos(3.78131048254 + 31.9513273211*$t);
   $X0 += 0.00002695972*cos(3.85276301548 + 110.189506272*$t);
   $X0 += 0.00002522990*cos(4.66308619966 + 311.9552664791*$t);
   $X0 += 0.00001888129*cos(3.20464683230 + 35.9291725665*$t);
   $X0 += 0.00001648229*cos(4.07040254381 + 30.300098274*$t);
   $X0 += 0.00001826545*cos(3.58021128918 + 44.31474395451*$t);
   $X0 += 0.00001956241*cos(4.14516146871 + 206.42936592071*$t);
   $X0 += 0.00001681257*cos(4.27560127770 + 40.8245336761*$t);
   $X0 += 0.00001533383*cos(1.17732213608 + 38.26497853671*$t);
   $X0 += 0.00001893076*cos(0.75017402977 + 220.6564599223*$t);
   $X0 += 0.00001527526*cos(0.02173638301 + 38.4887277059*$t);
   $X0 += 0.00002085691*cos(1.56948272604 + 149.8070146181*$t);
   $X0 += 0.00002070612*cos(2.82581806721 + 136.78920667889*$t);
   $X0 += 0.00001535699*cos(0.61413315675 + 73.0533083755*$t);
   $X0 += 0.00001667976*cos(2.91712458990 + 106.73292588839*$t);
   $X0 += 0.00001289620*cos(3.39708861100 + 46.4536079686*$t);
   $X0 += 0.00001559811*cos(0.55870841967 + 38.11622069041*$t);
   $X0 += 0.00001545705*cos(0.64028776037 + 38.6374855522*$t);
   $X0 += 0.00001435033*cos(0.72855949679 + 522.8212355773*$t);
   $X0 += 0.00001406206*cos(3.61717027558 + 537.0483295789*$t);
   $X0 += 0.00001256446*cos(2.70907758736 + 34.1840674273*$t);
   $X0 += 0.00001387973*cos(3.71843398082 + 116.12739710521*$t);
   $X0 += 0.00001457739*cos(1.98981635014 + 181.5145244557*$t);
   $X0 += 0.00001228429*cos(2.78646343835 + 72.31710306511*$t);
   $X0 += 0.00001140665*cos(3.96643713353 + 7.83293736379*$t);
   $X0 += 0.00001080801*cos(4.75483465055 + 42.5696388153*$t);
   $X0 += 0.00001201409*cos(0.74547986507 + 2.7251279331*$t);
   $X0 += 0.00001228671*cos(2.65249731727 + 148.32254190981*$t);
   $X0 += 0.00000722014*cos(6.16806714444 + 152.77596003471*$t);
   $X0 += 0.00000608545*cos(4.49536985567 + 35.4560918145*$t);
   $X0 += 0.00000722865*cos(3.09340262825 + 143.38148881789*$t);
   $X0 += 0.00000632820*cos(3.41702130042 + 7.66618102501*$t);
   $X0 += 0.00000642369*cos(3.97490787694 + 68.5998902506*$t);
   $X0 += 0.00000553789*cos(2.98606728111 + 41.2976144281*$t);
   $X0 += 0.00000682276*cos(2.15806346682 + 218.1630873852*$t);
   $X0 += 0.00000463186*cos(2.74420554348 + 31.7845709823*$t);
   $X0 += 0.00000521560*cos(0.34813640632 + 0.719390363*$t);
   $X0 += 0.00000437892*cos(1.29807722623 + 1589.3167127673*$t);
   $X0 += 0.00000398091*cos(5.50783691510 + 6.3484646555*$t);
   $X0 += 0.00000384065*cos(4.72632236146 + 44.96913526031*$t);
   $X0 += 0.00000395583*cos(5.05527677390 + 108.70503356371*$t);
   $X0 += 0.00000327446*cos(2.69199709491 + 60.52313540329*$t);
   $X0 += 0.00000358824*cos(4.99912098256 + 30.4668546128*$t);
   $X0 += 0.00000315179*cos(0.17468500209 + 74.53778108379*$t);
   $X0 += 0.00000343384*cos(1.74645896957 + 0.7650823453*$t);
   $X0 += 0.00000399611*cos(5.33540800911 + 31.2633061205*$t);
   $X0 += 0.00000314611*cos(2.98803024638 + 419.72846135871*$t);
   $X0 += 0.00000347596*cos(3.26643963659 + 180.03005174739*$t);
   $X0 += 0.00000382279*cos(0.21764578681 + 487.1213262793*$t);
   $X0 += 0.00000300918*cos(4.04922612099 + 69.0875252176*$t);
   $X0 += 0.00000340448*cos(3.90546849629 + 146.8380692015*$t);
   $X0 += 0.00000298710*cos(5.18013539651 + 84.5866436064*$t);
   $X0 += 0.00000290629*cos(1.74873675275 + 110.45013870291*$t);
   $X0 += 0.00000336211*cos(2.14815098729 + 45.49040012211*$t);
   $X0 += 0.00000305606*cos(5.63265481978 + 640.1411037975*$t);
   $X0 += 0.00000333702*cos(2.32938316969 + 254.8116503147*$t);
   $X0 += 0.00000268060*cos(3.30852201658 + 37.0042549976*$t);
   $X0 += 0.00000264760*cos(4.12724058864 + 39.749451245*$t);
   $X0 += 0.00000315240*cos(2.72241788492 + 388.70897272171*$t);
   $X0 += 0.00000227098*cos(4.59157281152 + 273.8222308413*$t);
   $X0 += 0.00000306112*cos(1.75345186469 + 6283.3196674749*$t);
   $X0 += 0.00000284373*cos(3.36139825385 + 12.77399045571*$t);
   $X0 += 0.00000221105*cos(3.50940363876 + 213.0552779545*$t);
   $X0 += 0.00000242568*cos(2.06437650010 + 14.258463164*$t);
   $X0 += 0.00000241087*cos(4.16115355874 + 105.2484531801*$t);
   $X0 += 0.00000226136*cos(2.83815938853 + 80.963306884*$t);
   $X0 += 0.00000245904*cos(0.54462524204 + 27.3311528574*$t);
   $X0 += 0.00000265825*cos(4.10952660358 + 944.7390057923*$t);
   $X0 += 0.00000207893*cos(5.07812851336 + 30.95448957981*$t);
   $X0 += 0.00000214661*cos(2.65402494691 + 316.6356871401*$t);
   $X0 += 0.00000190638*cos(2.32667703756 + 69.3963417583*$t);
   $X0 += 0.00000246295*cos(1.98638488517 + 102.84895673509*$t);
   $X0 += 0.00000202915*cos(0.60029260077 + 415.04804069769*$t);
   $X0 += 0.00000176465*cos(0.14731292877 + 36.7805058284*$t);
   $X0 += 0.00000193886*cos(3.35476299352 + 174.9222423167*$t);
   $X0 += 0.00000175209*cos(1.12575693515 + 39.97320041421*$t);
   $X0 += 0.00000177868*cos(3.43923391414 + 216.67861467689*$t);
   $X0 += 0.00000138494*cos(5.45265920432 + 75.98862389731*$t);
   $X0 += 0.00000152234*cos(4.81662104772 + 11.2895177474*$t);
   $X0 += 0.00000147648*cos(1.68543706672 + 151.2914873264*$t);
   $X0 += 0.00000156202*cos(3.65252575052 + 146.3504342345*$t);
   $X0 += 0.00000152289*cos(0.07345728764 + 23.87457247379*$t);
   $X0 += 0.00000177911*cos(3.17643554721 + 10213.5293636945*$t);
   $X0 += 0.00000162474*cos(4.13351391379 + 63.9797157869*$t);
   $X0 += 0.00000121226*cos(5.10584286197 + 38.16440480021*$t);
   $X0 += 0.00000129049*cos(3.80684906955 + 37.1048287341*$t);
   $X0 += 0.00000120334*cos(2.37637214462 + 38.5893014424*$t);
   $X0 += 0.00000168977*cos(2.49551838497 + 291.4602132442*$t);
   $X0 += 0.00000121138*cos(1.49657109299 + 33.26904369061*$t);
   $X0 += 0.00000129366*cos(2.36903010922 + 45.7992166628*$t);
   $X0 += 0.00000144682*cos(0.63023431786 + 49.42255338521*$t);
   $X0 += 0.00000122915*cos(3.67433526761 + 39.6488775085*$t);
   $X0 += 0.00000113400*cos(0.42160185021 + 83.1021708981*$t);
   $X0 += 0.00000154892*cos(1.74989069653 + 77.4730966056*$t);
   $X0 += 0.00000106737*cos(0.57437068095 + 4.8639919472*$t);
   $X0 += 0.00000104756*cos(5.96272070512 + 43.484662552*$t);
   $X0 += 0.00000125142*cos(5.82780261996 + 4.2096006414*$t);
   $X0 += 0.00000103541*cos(5.25634741505 + 41.08516610701*$t);
   $X0 += 0.00000133573*cos(3.92147215781 + 182.998997164*$t);
   $X0 += 0.00000103627*cos(2.29256111601 + 35.6685401356*$t);
   $X0 += 0.00000116874*cos(5.41378396536 + 62.4952430786*$t);
   $X0 += 0.00000098063*cos(3.25654027665 + 9.8050450391*$t);
   $X0 += 0.00000111411*cos(4.34345309647 + 141.8970161096*$t);
   $X0 += 0.00000114294*cos(5.56228935636 + 633.0275567967*$t);
   $X0 += 0.00000104705*cos(6.26072139356 + 433.9555553603*$t);
   $X0 += 0.00000121306*cos(1.44892345337 + 40.8581635709*$t);
   $X0 += 0.00000096954*cos(6.17373469303 + 1052.51220067191*$t);
   $X0 += 0.00000085104*cos(4.79018222360 + 36.6799320919*$t);
   $X0 += 0.00000085209*cos(5.94497188324 + 105.76971804189*$t);
   $X0 += 0.00000085291*cos(2.59495207397 + 109.701871305*$t);
   $X0 += 0.00000083260*cos(0.00625676877 + 529.44714761109*$t);
   $X0 += 0.00000080200*cos(2.69199769694 + 40.07377415071*$t);
   $X0 += 0.00000107927*cos(0.01570870082 + 1162.7185218913*$t);
   $X0 += 0.00000095241*cos(3.61102256601 + 253.32717760639*$t);
   $X0 += 0.00000089535*cos(3.25178384851 + 32.9602271499*$t);
   $X0 += 0.00000089793*cos(2.76430560225 + 65.46418849521*$t);
   $X0 += 0.00000072027*cos(0.11366576076 + 36.9405645228*$t);
   $X0 += 0.00000080381*cos(5.21057317852 + 67.1154175423*$t);
   $X0 += 0.00000099502*cos(2.53010647936 + 453.1810763355*$t);
   $X0 += 0.00000088685*cos(1.33848394125 + 251.6759485593*$t);
   $X0 += 0.00000094971*cos(4.11602347578 + 219.6475600935*$t);
   $X0 += 0.00000077015*cos(5.30660266172 + 5.6604434549*$t);
   $X0 += 0.00000069098*cos(1.84984192453 + 22.3900997655*$t);
   $X0 += 0.00000079079*cos(4.12824954018 + 44.48150029329*$t);
   $X0 += 0.00000069159*cos(3.95901333551 + 1066.7392946735*$t);
   $X0 += 0.00000064446*cos(4.03076164648 + 66.9486612035*$t);
   $X0 += 0.00000088518*cos(2.66179796694 + 328.1087761737*$t);
   $X0 += 0.00000065817*cos(1.42821476263 + 36.3711155512*$t);
   $X0 += 0.00000071422*cos(4.23104971231 + 43.79347909271*$t);
   $X0 += 0.00000063298*cos(2.21146718451 + 9.1506537333*$t);
   $X0 += 0.00000077320*cos(0.26842720811 + 97.17169833279*$t);
   $X0 += 0.00000073912*cos(1.72397638430 + 2.6769438233*$t);
   $X0 += 0.00000073965*cos(5.55809543248 + 2.9521304692*$t);
   $X0 += 0.00000056194*cos(4.45857439361 + 949.4194264533*$t);
   $X0 += 0.00000059173*cos(1.41372632607 + 100.14064374939*$t);
   $X0 += 0.00000067507*cos(3.94700376513 + 7.14491616321*$t);
   $X0 += 0.00000071718*cos(0.93392607299 + 2.20386307129*$t);
   $X0 += 0.00000063606*cos(5.17175542607 + 25.8466801491*$t);
   $X0 += 0.00000071523*cos(2.05830478088 + 662.28738607949*$t);
   $X0 += 0.00000057219*cos(0.88485013288 + 15.7429358723*$t);
   $X0 += 0.00000050322*cos(1.08310288762 + 37.15301284391*$t);
   $X0 += 0.00000066615*cos(3.42462264660 + 846.3266522347*$t);
   $X0 += 0.00000056220*cos(4.52386924168 + 178.5455790391*$t);
   $X0 += 0.00000067883*cos(3.88546727303 + 224.5886131854*$t);
   $X0 += 0.00000057761*cos(5.16493680948 + 145.35359649321*$t);
   $X0 += 0.00000053973*cos(6.25404762289 + 107.2205608554*$t);
   $X0 += 0.00000057588*cos(4.84839311245 + 25.3590451821*$t);
   $X0 += 0.00000049026*cos(1.27836371915 + 19.2543980101*$t);
   $X0 += 0.00000063036*cos(4.29760573349 + 256.296123023*$t);
   $X0 += 0.00000045304*cos(0.86492921312 + 4.1759707466*$t);
   $X0 += 0.00000045669*cos(2.17547535945 + 117.6118698135*$t);
   $X0 += 0.00000052821*cos(3.77933473571 + 289.97574053589*$t);
   $X0 += 0.00000044016*cos(2.25498623278 + 32.7477788288*$t);
   $X0 += 0.00000042933*cos(6.21504221321 + 28.98238190449*$t);
   $X0 += 0.00000038369*cos(0.36602717013 + 39.6006933987*$t);
   $X0 += 0.00000038805*cos(4.12403932769 + 103.3365917021*$t);
   $X0 += 0.00000037679*cos(3.40097359574 + 9.3174100721*$t);
   $X0 += 0.00000040292*cos(6.03933270535 + 111.18634401329*$t);
   $X0 += 0.00000050011*cos(6.19966711969 + 221.61966776881*$t);
   $X0 += 0.00000037056*cos(4.63008749202 + 8.32057233081*$t);
   $X0 += 0.00000036562*cos(0.18548635975 + 448.98829064149*$t);
   $X0 += 0.00000044628*cos(3.82762130859 + 525.2543619171*$t);
   $X0 += 0.00000038213*cos(0.28030378709 + 75.54668091261*$t);
   $X0 += 0.00000045963*cos(4.06403723861 + 183.486632131*$t);
   $X0 += 0.00000048222*cos(2.81328685847 + 364.7573391032*$t);
   $X0 += 0.00000038164*cos(5.23367149002 + 44.00592741381*$t);
   $X0 += 0.00000047779*cos(6.19272750750 + 3340.8562441833*$t);
   $X0 += 0.00000042228*cos(5.64690940917 + 77.0311536209*$t);
   $X0 += 0.00000035247*cos(0.20766845689 + 34.7535163989*$t);
   $X0 += 0.00000046804*cos(3.96902162832 + 33.6964324603*$t);
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   $X0 += 0.00000003211*cos(5.64833047248 + 416.532513406*$t);
   $X0 += 0.00000003265*cos(1.54950325507 + 24.7347144563*$t);
   $X0 += 0.00000002644*cos(1.01963899758 + 508.5941415757*$t);
   $X0 += 0.00000002764*cos(4.98225869197 + 410.59462257279*$t);
   $X0 += 0.00000003428*cos(5.71088563789 + 1012.6195056799*$t);
   $X0 += 0.00000002614*cos(4.07639961382 + 213.5910970313*$t);
   $X0 += 0.00000003469*cos(5.28643352424 + 24.14975911971*$t);
   $X0 += 0.00000002606*cos(0.81160096517 + 213.4947288117*$t);
   $X0 += 0.00000003444*cos(2.56432157215 + 891.57323487331*$t);
   $X0 += 0.00000002540*cos(4.32167771768 + 564.8718702632*$t);
   $X0 += 0.00000002540*cos(4.32167771768 + 565.35950523021*$t);
   $X0 += 0.00000002754*cos(2.69535555411 + 57.5541899867*$t);
   $X0 += 0.00000002531*cos(0.59020723407 + 800.5924346291*$t);
   $X0 += 0.00000002557*cos(0.66999256840 + 341.49028240779*$t);
   $X0 += 0.00000002601*cos(4.54885591305 + 261.2371761149*$t);
   $X0 += 0.00000003027*cos(0.20183300410 + 331.07772159029*$t);
   $X0 += 0.00000002494*cos(0.58142193078 + 203.9816853659*$t);
   $X0 += 0.00000002590*cos(1.76325981719 + 1190.5420625756*$t);
   $X0 += 0.00000003494*cos(2.90876238684 + 534.0793841623*$t);
   $X0 += 0.00000003144*cos(0.01981710217 + 1503.9649868156*$t);
   $X0 += 0.00000002818*cos(3.61898449244 + 49.31067880061*$t);
   $X0 += 0.00000002791*cos(4.48606671949 + 288.32451148881*$t);
   $X0 += 0.00000002471*cos(1.23009614301 + 411.11588743459*$t);
   $X0 += 0.00000003059*cos(3.30977686438 + 172.48911597691*$t);
   $X0 += 0.00000002972*cos(0.30229231666 + 569.29165849331*$t);
   $X0 += 0.00000003418*cos(5.40293550246 + 638.3959986583*$t);
   $X0 += 0.00000002541*cos(4.99016167757 + 1448.09090291091*$t);
   $X0 += 0.00000002663*cos(0.43151826022 + 573.6968925084*$t);
   $X0 += 0.00000002439*cos(4.39632185677 + 1625.9652756968*$t);
   $X0 += 0.00000002739*cos(5.72535305895 + 112.8832650427*$t);
   $X0 += 0.00000002821*cos(5.66863744979 + 402.93606672331*$t);
   $X0 += 0.00000003412*cos(1.27007980380 + 772.8325844196*$t);
   $X0 += 0.00000002624*cos(5.85528852490 + 1624.4808029885*$t);
   $X0 += 0.00000003170*cos(0.53682796950 + 1011.13503297159*$t);
   $X0 += 0.00000002908*cos(4.60949958082 + 635.94831810351*$t);
   $X0 += 0.00000002664*cos(2.68003479349 + 409.41896640519*$t);
   $X0 += 0.00000003091*cos(1.88245278611 + 379.25961975071*$t);
   $X0 += 0.00000003301*cos(1.91350932819 + 19.7936613644*$t);
   $X0 += 0.00000003176*cos(3.29730129609 + 300.9095662152*$t);
   $X0 += 0.00000003022*cos(5.94822554077 + 52.0189917863*$t);
   $X0 += 0.00000002890*cos(1.53549747897 + 293.4323209195*$t);
   $X0 += 0.00000002698*cos(1.69370735844 + 78149.06650032569*$t);
   $X0 += 0.00000002558*cos(0.74578099458 + 1371.3371966683*$t);
   $X0 += 0.00000002619*cos(3.80578981072 + 202.0095776906*$t);
   $X0 += 0.00000003176*cos(3.75055063339 + 10101.61156723069*$t);
   $X0 += 0.00000003341*cos(2.34080319182 + 345.8955164229*$t);
   $X0 += 0.00000002373*cos(4.96475711609 + 130.8513158457*$t);
   $X0 += 0.00000002644*cos(2.68099240015 + 305.10235190919*$t);
   $X0 += 0.00000003339*cos(4.63303989765 + 2849.2983147265*$t);
   $X0 += 0.00000002410*cos(1.58163612779 + 951.8525527931*$t);
   $X0 += 0.00000003303*cos(2.25771292490 + 769.5729459921*$t);
   $X0 += 0.00000003302*cos(4.85894681967 + 90.1520274241*$t);
   $X0 += 0.00000002416*cos(6.00635580174 + 527.929045008*$t);
   $X0 += 0.00000002361*cos(5.34789183737 + 905.1214974462*$t);
   $X0 += 0.00000002737*cos(4.77190944455 + 1206.2199993907*$t);
   $X0 += 0.00000002441*cos(3.82975575752 + 246.73489546739*$t);
   $X0 += 0.00000002441*cos(0.68816310393 + 247.2225304344*$t);
   $X0 += 0.00000002957*cos(4.25832811500 + 238.23075185041*$t);
   $X0 += 0.00000003263*cos(0.98630889937 + 1506.93393223219*$t);
   $X0 += 0.00000003293*cos(5.93270574395 + 66.1522096958*$t);
   $X0 += 0.00000003241*cos(3.43806050184 + 978.4186233052*$t);
   $X0 += 0.00000003149*cos(3.64971867049 + 271.9103693633*$t);
   $X0 += 0.00000003149*cos(3.64971867050 + 271.4227343963*$t);
   $X0 += 0.00000002328*cos(5.07609916236 + 31.73887900*$t);
   $X0 += 0.00000002372*cos(0.68652074740 + 309.0345051723*$t);
   $X0 += 0.00000002372*cos(3.82811340099 + 309.5221401393*$t);
   $X0 += 0.00000002369*cos(4.33012817739 + 418.9801939608*$t);
   $X0 += 0.00000003007*cos(4.64009260533 + 1437.7814079574*$t);
   $X0 += 0.00000003034*cos(5.98346126252 + 330.8627811417*$t);
   $X0 += 0.00000002345*cos(2.80677153952 + 453.9318358609*$t);
   $X0 += 0.00000003118*cos(3.73398781358 + 1434.81246254079*$t);
   $X0 += 0.00000002324*cos(3.85931736808 + 495.2462652364*$t);
   $X0 += 0.00000002340*cos(5.41992470939 + 452.43031681009*$t);
   $X0 += 0.00000002336*cos(0.04655833240 + 189.591279303*$t);
   $X0 += 0.00000002920*cos(3.78758562864 + 1549.69920442121*$t);
   $X0 += 0.00000002494*cos(0.79353025531 + 1187.57311715899*$t);
   $X0 += 0.00000002692*cos(4.17807622816 + 425.13053311509*$t);
   $X0 += 0.00000002874*cos(4.63267401857 + 1654.2764513481*$t);
   $X0 += 0.00000002809*cos(5.67077170621 + 317.5843407716*$t);
   $X0 += 0.00000002735*cos(3.93990204220 + 1513.05064149171*$t);
   $X0 += 0.00000002949*cos(6.26993364897 + 186.71620997851*$t);
   $X0 += 0.00000002320*cos(0.74326897219 + 487.38195871019*$t);
   $X0 += 0.00000003113*cos(6.20902109610 + 353.28425006961*$t);
   $X0 += 0.00000003086*cos(4.87476303199 + 1230.5990217789*$t);
   $X0 += 0.00000002722*cos(2.16494792915 + 49.6831858161*$t);
   $X0 += 0.00000003064*cos(3.68765217385 + 133.13224006171*$t);
   $X0 += 0.00000003064*cos(3.68765217385 + 132.64460509469*$t);
   $X0 += 0.00000002470*cos(2.78243316001 + 532.3824631329*$t);
   $X0 += 0.00000002640*cos(0.51790972890 + 394.33804701421*$t);
   $X0 += 0.00000002252*cos(1.84613004390 + 22.6507321964*$t);
   $X0 += 0.00000003151*cos(5.26039361613 + 859.77184894361*$t);
   $X0 += 0.00000002671*cos(0.92145640556 + 37.3679532925*$t);
   $X0 += 0.00000002380*cos(0.86687455354 + 429.2751346993*$t);
   $X0 += 0.00000002655*cos(2.72088152594 + 484.1523808627*$t);
   $X0 += 0.00000003005*cos(3.02367934874 + 1929.33933741419*$t);
   $X0 += 0.00000002550*cos(5.60497907633 + 496.9431862658*$t);
   $X0 += 0.00000002290*cos(3.41120190653 + 455.18681390559*$t);
   $X0 += 0.00000002608*cos(3.85525903926 + 422.9580392062*$t);
   $X0 += 0.00000002226*cos(2.09977531258 + 47.82620609231*$t);
   $X0 += 0.00000002233*cos(4.94028872789 + 877.3461408717*$t);
   $X0 += 0.00000002764*cos(0.83501700112 + 356.68058425589*$t);
   $X0 += 0.00000002719*cos(1.98953734068 + 177.5823711926*$t);
   $X0 += 0.00000002999*cos(2.06885612973 + 1926.37039199759*$t);
   $X0 += 0.00000002693*cos(3.57972778548 + 6284.8041401832*$t);
   $X0 += 0.00000002369*cos(1.19578023344 + 70.88081446661*$t);
   $X0 += 0.00000002498*cos(3.71851216671 + 315.1512144318*$t);
   $X0 += 0.00000002204*cos(3.20466206592 + 442.886135597*$t);
   $X0 += 0.00000002261*cos(3.32534753019 + 621.2335891349*$t);
   $X0 += 0.00000002213*cos(6.16263836668 + 1189.0575898673*$t);
   $X0 += 0.00000002492*cos(2.67366070604 + 406.9712858504*$t);
   $X0 += 0.00000002976*cos(1.45402284302 + 1014.1039783882*$t);
   $X0 += 0.00000002840*cos(5.35710509350 + 522.3336006103*$t);
   $X0 += 0.00000002340*cos(1.72448626630 + 440.43845504219*$t);
   $X0 += 0.00000003012*cos(1.13512104183 + 15.9096922111*$t);
   $X0 += 0.00000003012*cos(4.27671369542 + 16.3973271781*$t);
   $X0 += 0.00000002372*cos(0.24227395275 + 132.5964209849*$t);
   $X0 += 0.00000002232*cos(2.42168492591 + 158.12984768129*$t);
   $X0 += 0.00000002961*cos(4.37134416172 + 286.3524038135*$t);
   $X0 += 0.00000002961*cos(4.37134416172 + 286.8400387805*$t);
   return $X0;
}



   function Neptune_X1($t) // 342 terms of order 1
{
   $X1  = 0.00357822049*cos(4.60537437341 + 0.2438174835*$t);
   $X1 += 0.00256200629*cos(2.01693264233 + 36.892380413*$t);
   $X1 += 0.00242677799*cos(5.46293481092 + 39.86132582961*$t);
   $X1 += 0.00106073143*cos(3.07856435709 + 37.88921815429*$t);
   $X1 += 0.00103735195*cos(6.08270773807 + 38.3768531213*$t);
   $X1 += 0.00118508231*cos(2.88623136735 + 76.50988875911*$t);
   $X1 += 0.00021930692*cos(3.20019569049 + 35.40790770471*$t);
   $X1 += 0.00017445772*cos(4.26396070854 + 41.3457985379*$t);
   $X1 += 0.00013038843*cos(5.36684741537 + 3.21276290011*$t);
   $X1 += 0.00004928885*cos(2.08893204170 + 73.5409433425*$t);
   $X1 += 0.00002742686*cos(4.06389633495 + 77.9943614674*$t);
   $X1 += 0.00002155134*cos(4.11881068429 + 4.6972356084*$t);
   $X1 += 0.00001882800*cos(4.42038284259 + 33.9234349964*$t);
   $X1 += 0.00001572888*cos(1.07810551784 + 114.6429243969*$t);
   $X1 += 0.00001326507*cos(6.02985868883 + 75.0254160508*$t);
   $X1 += 0.00001343094*cos(3.03838214796 + 42.83027124621*$t);
   $X1 += 0.00000897979*cos(4.26993024752 + 426.8420083595*$t);
   $X1 += 0.00000865617*cos(1.66618456177 + 37.8555882595*$t);
   $X1 += 0.00000849963*cos(5.81599535394 + 38.89811798311*$t);
   $X1 += 0.00000922754*cos(3.34516686314 + 72.05647063421*$t);
   $X1 += 0.00000726258*cos(4.24833812431 + 36.404745446*$t);
   $X1 += 0.00000778220*cos(5.84479856092 + 206.42936592071*$t);
   $X1 += 0.00000754025*cos(5.33205816073 + 220.6564599223*$t);
   $X1 += 0.00000607406*cos(0.10576615596 + 1059.6257476727*$t);
   $X1 += 0.00000571831*cos(2.42930874906 + 522.8212355773*$t);
   $X1 += 0.00000560995*cos(1.91555986158 + 537.0483295789*$t);
   $X1 += 0.00000501078*cos(1.71335109406 + 28.81562556571*$t);
   $X1 += 0.00000493238*cos(5.24702261334 + 39.3736908626*$t);
   $X1 += 0.00000474802*cos(4.40715596351 + 98.6561710411*$t);
   $X1 += 0.00000453975*cos(1.71443209341 + 35.9291725665*$t);
   $X1 += 0.00000471731*cos(4.84217171915 + 1.7282901918*$t);
   $X1 += 0.00000410057*cos(5.76579953705 + 40.8245336761*$t);
   $X1 += 0.00000366899*cos(5.76755572930 + 47.9380806769*$t);
   $X1 += 0.00000450109*cos(1.25670451550 + 76.0222537921*$t);
   $X1 += 0.00000354347*cos(6.27109348494 + 1.24065522479*$t);
   $X1 += 0.00000300159*cos(2.88687992256 + 6.1817083167*$t);
   $X1 += 0.00000327501*cos(4.20479564636 + 33.43580002939*$t);
   $X1 += 0.00000174973*cos(5.64027558321 + 32.4389622881*$t);
   $X1 += 0.00000171503*cos(4.43985554308 + 34.1840674273*$t);
   $X1 += 0.00000156749*cos(2.59545084410 + 79.47883417571*$t);
   $X1 += 0.00000152549*cos(0.58219894744 + 30.300098274*$t);
   $X1 += 0.00000150775*cos(3.03954929901 + 42.5696388153*$t);
   $X1 += 0.00000162280*cos(0.79977049351 + 31.2633061205*$t);
   $X1 += 0.00000131609*cos(1.62895622934 + 7.83293736379*$t);
   $X1 += 0.00000136159*cos(4.57878446789 + 70.5719979259*$t);
   $X1 += 0.00000134616*cos(0.39184091634 + 45.49040012211*$t);
   $X1 += 0.00000116304*cos(0.61710594601 + 46.4536079686*$t);
   $X1 += 0.00000115918*cos(1.81843338530 + 44.31474395451*$t);
   $X1 += 0.00000110293*cos(6.26561089969 + 35.4560918145*$t);
   $X1 += 0.00000099282*cos(5.06218386285 + 2.7251279331*$t);
   $X1 += 0.00000099914*cos(1.21626942611 + 41.2976144281*$t);
   $X1 += 0.00000108706*cos(3.09142093314 + 113.15845168861*$t);
   $X1 += 0.00000088965*cos(4.26680850699 + 60.52313540329*$t);
   $X1 += 0.00000086886*cos(5.46872067794 + 31.9513273211*$t);
   $X1 += 0.00000072232*cos(3.50587405737 + 640.1411037975*$t);
   $X1 += 0.00000086985*cos(4.80098575405 + 419.72846135871*$t);
   $X1 += 0.00000073430*cos(4.36511226727 + 70.08436295889*$t);
   $X1 += 0.00000053395*cos(4.46520807878 + 433.9555553603*$t);
   $X1 += 0.00000057451*cos(1.08003733120 + 213.5429129215*$t);
   $X1 += 0.00000051458*cos(4.01726374522 + 69.3963417583*$t);
   $X1 += 0.00000048797*cos(6.01365170443 + 111.67397898031*$t);
   $X1 += 0.00000048557*cos(6.24808481100 + 2.6769438233*$t);
   $X1 += 0.00000042206*cos(3.23823062186 + 74.53778108379*$t);
   $X1 += 0.00000042550*cos(1.67247318349 + 7.66618102501*$t);
   $X1 += 0.00000039462*cos(5.84051041865 + 31.7845709823*$t);
   $X1 += 0.00000039445*cos(0.94630986910 + 12.77399045571*$t);
   $X1 += 0.00000042389*cos(5.59019905902 + 110.189506272*$t);
   $X1 += 0.00000044118*cos(0.44615133445 + 1589.3167127673*$t);
   $X1 += 0.00000037988*cos(2.73850879415 + 6.3484646555*$t);
   $X1 += 0.00000037802*cos(5.98781130211 + 14.258463164*$t);
   $X1 += 0.00000036280*cos(6.27894536142 + 273.8222308413*$t);
   $X1 += 0.00000037247*cos(4.62968774107 + 73.0533083755*$t);
   $X1 += 0.00000036282*cos(2.85336450932 + 84.5866436064*$t);
   $X1 += 0.00000040018*cos(4.27418471085 + 4.4366031775*$t);
   $X1 += 0.00000032400*cos(1.64328879813 + 44.96913526031*$t);
   $X1 += 0.00000031842*cos(5.16652228087 + 34.9202727377*$t);
   $X1 += 0.00000032037*cos(2.94551844856 + 27.3311528574*$t);
   $X1 += 0.00000034456*cos(3.37152599360 + 529.9347825781*$t);
   $X1 += 0.00000031208*cos(1.73420111381 + 1052.51220067191*$t);
   $X1 += 0.00000030002*cos(2.33639558082 + 1066.7392946735*$t);
   $X1 += 0.00000033805*cos(6.04114496470 + 149.8070146181*$t);
   $X1 += 0.00000033096*cos(2.45794089359 + 116.12739710521*$t);
   $X1 += 0.00000030571*cos(4.02151161164 + 22.3900997655*$t);
   $X1 += 0.00000024020*cos(0.23821463973 + 63.9797157869*$t);
   $X1 += 0.00000023780*cos(4.34619784366 + 105.76971804189*$t);
   $X1 += 0.00000023110*cos(2.51348904373 + 23.87457247379*$t);
   $X1 += 0.00000022233*cos(1.21582777350 + 174.9222423167*$t);
   $X1 += 0.00000021377*cos(3.74139728076 + 316.6356871401*$t);
   $X1 += 0.00000025400*cos(4.52702077197 + 106.73292588839*$t);
   $X1 += 0.00000020754*cos(0.94473828111 + 5.6604434549*$t);
   $X1 += 0.00000025572*cos(5.46068636869 + 529.44714761109*$t);
   $X1 += 0.00000019878*cos(1.01805940417 + 32.9602271499*$t);
   $X1 += 0.00000019754*cos(4.49000124955 + 49.42255338521*$t);
   $X1 += 0.00000019241*cos(6.01413524726 + 7.14491616321*$t);
   $X1 += 0.00000017979*cos(1.48478132886 + 62.4952430786*$t);
   $X1 += 0.00000019513*cos(5.64767624982 + 68.5998902506*$t);
   $X1 += 0.00000018273*cos(5.20130356006 + 227.77000692311*$t);
   $X1 += 0.00000017552*cos(5.80350239388 + 69.0875252176*$t);
   $X1 += 0.00000016704*cos(3.94483252805 + 40.8581635709*$t);
   $X1 += 0.00000016996*cos(1.10449263633 + 91.54262404029*$t);
   $X1 += 0.00000016800*cos(0.51632981099 + 30.4668546128*$t);
   $X1 += 0.00000016800*cos(0.51632981099 + 30.95448957981*$t);
   $X1 += 0.00000016400*cos(5.02426208775 + 33.26904369061*$t);
   $X1 += 0.00000017242*cos(0.18352088447 + 11.55015017831*$t);
   $X1 += 0.00000015590*cos(1.99260946960 + 37.1048287341*$t);
   $X1 += 0.00000015590*cos(5.48957045033 + 39.6488775085*$t);
   $X1 += 0.00000015469*cos(0.19931591320 + 43.79347909271*$t);
   $X1 += 0.00000016590*cos(2.76837508684 + 33.71098667531*$t);
   $X1 += 0.00000019347*cos(5.63498287914 + 152.77596003471*$t);
   $X1 += 0.00000014994*cos(2.71995630411 + 319.06881347989*$t);
   $X1 += 0.00000014395*cos(0.95950619453 + 110.45013870291*$t);
   $X1 += 0.00000015528*cos(1.16348592635 + 79.43065006591*$t);
   $X1 += 0.00000013727*cos(2.45811249773 + 43.484662552*$t);
   $X1 += 0.00000013988*cos(3.96979676090 + 4.2096006414*$t);
   $X1 += 0.00000014467*cos(0.42164709009 + 108.70503356371*$t);
   $X1 += 0.00000016652*cos(3.17617180933 + 304.84171947829*$t);
   $X1 += 0.00000015153*cos(3.21783791411 + 72.31710306511*$t);
   $X1 += 0.00000012810*cos(2.37864271463 + 11.2895177474*$t);
   $X1 += 0.00000012751*cos(0.61424962834 + 45.7992166628*$t);
   $X1 += 0.00000013293*cos(4.71511827202 + 43.0427195673*$t);
   $X1 += 0.00000012751*cos(2.55685741962 + 515.70768857651*$t);
   $X1 += 0.00000011616*cos(2.50185569269 + 97.17169833279*$t);
   $X1 += 0.00000011538*cos(6.20327139591 + 633.0275567967*$t);
   $X1 += 0.00000011046*cos(1.26188662646 + 25.8466801491*$t);
   $X1 += 0.00000011032*cos(3.82567311622 + 4.8639919472*$t);
   $X1 += 0.00000011189*cos(3.94939417077 + 83.1021708981*$t);
   $X1 += 0.00000010860*cos(0.38739756984 + 9.8050450391*$t);
   $X1 += 0.00000010958*cos(1.48375898962 + 415.04804069769*$t);
   $X1 += 0.00000010244*cos(0.26615444717 + 71.09326278771*$t);
   $X1 += 0.00000011427*cos(1.50679043329 + 129.6756596781*$t);
   $X1 += 0.00000009895*cos(5.62468142972 + 251.6759485593*$t);
   $X1 += 0.00000009802*cos(1.83814841533 + 44.48150029329*$t);
   $X1 += 0.00000011029*cos(4.69741395112 + 143.38148881789*$t);
   $X1 += 0.00000009235*cos(5.99370019321 + 199.3158189199*$t);
   $X1 += 0.00000008899*cos(3.54958918415 + 7.3573644843*$t);
   $X1 += 0.00000007746*cos(5.89688581764 + 103.3365917021*$t);
   $X1 += 0.00000008691*cos(3.86130807292 + 32.7477788288*$t);
   $X1 += 0.00000007714*cos(5.08136079606 + 65.46418849521*$t);
   $X1 += 0.00000008007*cos(1.80952555463 + 544.1618765797*$t);
   $X1 += 0.00000007513*cos(1.47497152514 + 69.6087900794*$t);
   $X1 += 0.00000007336*cos(5.00489054996 + 15.7429358723*$t);
   $X1 += 0.00000007195*cos(6.14029832936 + 949.4194264533*$t);
   $X1 += 0.00000009601*cos(0.96952505042 + 80.963306884*$t);
   $X1 += 0.00000008094*cos(3.27383873772 + 526.7533888404*$t);
   $X1 += 0.00000008109*cos(1.06293290956 + 533.1161763158*$t);
   $X1 += 0.00000006906*cos(5.27751864757 + 137.2768416459*$t);
   $X1 += 0.00000007455*cos(5.82601593331 + 105.2484531801*$t);
   $X1 += 0.00000007826*cos(4.02401038086 + 77.0311536209*$t);
   $X1 += 0.00000006529*cos(0.86598314454 + 65.2035560643*$t);
   $X1 += 0.00000007134*cos(3.62090018772 + 44.00592741381*$t);
   $X1 += 0.00000006186*cos(2.42103444520 + 31.4757544416*$t);
   $X1 += 0.00000006186*cos(2.42103444520 + 30.9881194746*$t);
   $X1 += 0.00000007698*cos(0.17876132177 + 14.47091148511*$t);
   $X1 += 0.00000007434*cos(5.53413189412 + 146.8380692015*$t);
   $X1 += 0.00000006317*cos(0.53538901275 + 66.9486612035*$t);
   $X1 += 0.00000006903*cos(6.20818943193 + 75.98862389731*$t);
   $X1 += 0.00000005591*cos(1.90701487438 + 448.98829064149*$t);
   $X1 += 0.00000006425*cos(5.04706195455 + 678.27413943531*$t);
   $X1 += 0.00000005483*cos(3.18327336885 + 34.44469985821*$t);
   $X1 += 0.00000005483*cos(4.29890655108 + 42.3090063844*$t);
   $X1 += 0.00000005519*cos(2.84195707915 + 853.4401992355*$t);
   $X1 += 0.00000005483*cos(3.53790147295 + 100.14064374939*$t);
   $X1 += 0.00000005483*cos(3.53790147295 + 100.6282787164*$t);
   $X1 += 0.00000006288*cos(1.03240051727 + 143.9027536797*$t);
   $X1 += 0.00000006239*cos(5.78066710550 + 17.76992530181*$t);
   $X1 += 0.00000005246*cos(5.09114965169 + 209.6107596584*$t);
   $X1 += 0.00000005331*cos(3.26471064810 + 45.9659730016*$t);
   $X1 += 0.00000005131*cos(6.10583196953 + 217.4750661846*$t);
   $X1 += 0.00000005325*cos(4.39759756568 + 19.2543980101*$t);
   $X1 += 0.00000005172*cos(0.86928942503 + 25.3590451821*$t);
   $X1 += 0.00000005139*cos(2.60427452606 + 6.86972951729*$t);
   $X1 += 0.00000005992*cos(1.19287924990 + 9.3174100721*$t);
   $X1 += 0.00000005011*cos(3.34804654196 + 38.85242600079*$t);
   $X1 += 0.00000004975*cos(1.43964900757 + 525.2543619171*$t);
   $X1 += 0.00000004910*cos(5.04787040559 + 45.277951801*$t);
   $X1 += 0.00000005250*cos(4.87798510402 + 0.719390363*$t);
   $X1 += 0.00000004731*cos(1.56230403811 + 40.3825906914*$t);
   $X1 += 0.00000004731*cos(2.77828322823 + 36.3711155512*$t);
   $X1 += 0.00000005910*cos(6.11804979728 + 6168.43292559449*$t);
   $X1 += 0.00000004700*cos(6.23394030506 + 50.9070260935*$t);
   $X1 += 0.00000005127*cos(0.06949696047 + 140.9338082631*$t);
   $X1 += 0.00000005321*cos(3.67018745291 + 1104.87233031131*$t);
   $X1 += 0.00000006339*cos(2.59865692618 + 10175.3963280567*$t);
   $X1 += 0.00000004983*cos(3.03193615352 + 1090.6452363097*$t);
   $X1 += 0.00000005487*cos(4.85218420019 + 180.03005174739*$t);
   $X1 += 0.00000004560*cos(3.95095239655 + 323.74923414091*$t);
   $X1 += 0.00000004689*cos(1.24271255508 + 1068.22376738181*$t);
   $X1 += 0.00000005562*cos(1.26401999292 + 10098.64262181409*$t);
   $X1 += 0.00000004432*cos(2.40638908148 + 415.7963080956*$t);
   $X1 += 0.00000004456*cos(6.17485306628 + 235.68919520349*$t);
   $X1 += 0.00000004289*cos(5.97528879519 + 1051.0277279636*$t);
   $X1 += 0.00000004145*cos(3.13378236518 + 33.6964324603*$t);
   $X1 += 0.00000004167*cos(1.72807331665 + 416.532513406*$t);
   $X1 += 0.00000004107*cos(2.49036069416 + 61.01077037031*$t);
   $X1 += 0.00000004088*cos(5.45739808026 + 423.66061462181*$t);
   $X1 += 0.00000005027*cos(4.43953537205 + 21.7020785649*$t);
   $X1 += 0.00000004030*cos(5.01269280095 + 216.72430665921*$t);
   $X1 += 0.00000004278*cos(4.65333719777 + 310.4707937708*$t);
   $X1 += 0.00000004013*cos(1.39689438468 + 104275.10267753768*$t);
   $X1 += 0.00000004505*cos(1.22507263591 + 291.9478482112*$t);
   $X1 += 0.00000003959*cos(6.18034607330 + 210.36151918381*$t);
   $X1 += 0.00000003962*cos(4.02082978591 + 978.93988816699*$t);
   $X1 += 0.00000005561*cos(1.74843583918 + 1409.47023230609*$t);
   $X1 += 0.00000005073*cos(3.58205424554 + 1498.3359125231*$t);
   $X1 += 0.00000004227*cos(1.48715312131 + 534.38820070301*$t);
   $X1 += 0.00000004054*cos(4.02884108627 + 430.02340209721*$t);
   $X1 += 0.00000003863*cos(2.24264031920 + 1127.50624756031*$t);
   $X1 += 0.00000004367*cos(1.71153359581 + 58.9837809408*$t);
   $X1 += 0.00000004694*cos(3.33961949377 + 77.5067265004*$t);
   $X1 += 0.00000004144*cos(3.59057653937 + 518.1408149163*$t);
   $X1 += 0.00000004289*cos(3.29776439152 + 921.3206991231*$t);
   $X1 += 0.00000004039*cos(3.79987840474 + 1622.76932774409*$t);
   $X1 += 0.00000005180*cos(5.37115331697 + 99.1438060081*$t);
   $X1 += 0.00000004845*cos(6.04321981604 + 136.78920667889*$t);
   $X1 += 0.00000004827*cos(2.78459346340 + 418.2439886504*$t);
   $X1 += 0.00000003722*cos(0.22932453326 + 1065.2548219652*$t);
   $X1 += 0.00000004729*cos(3.76762324044 + 421.212934067*$t);
   $X1 += 0.00000003490*cos(5.25995346649 + 986.8041946932*$t);
   $X1 += 0.00000003715*cos(6.02151166051 + 254.10907489909*$t);
   $X1 += 0.00000003488*cos(1.23861297869 + 187.9400502559*$t);
   $X1 += 0.00000003989*cos(3.79961685835 + 95.7354097343*$t);
   $X1 += 0.00000003603*cos(0.65230587403 + 67.1154175423*$t);
   $X1 += 0.00000003530*cos(2.51065807549 + 24.36220744081*$t);
   $X1 += 0.00000003538*cos(3.09031960755 + 57.4993082325*$t);
   $X1 += 0.00000003838*cos(1.99815683749 + 979.90309601349*$t);
   $X1 += 0.00000003615*cos(3.17553643085 + 493.2862196486*$t);
   $X1 += 0.00000003457*cos(0.22865254260 + 807.70598162989*$t);
   $X1 += 0.00000003648*cos(3.01000228275 + 647.25465079831*$t);
   $X1 += 0.00000004048*cos(4.68171378592 + 979.69064769239*$t);
   $X1 += 0.00000004414*cos(3.57495606042 + 1062.59469308931*$t);
   $X1 += 0.00000003631*cos(2.31921127570 + 486.1726726478*$t);
   $X1 += 0.00000003347*cos(5.70639780704 + 151.2914873264*$t);
   $X1 += 0.00000003305*cos(0.52158954660 + 1544.07013012871*$t);
   $X1 += 0.00000003428*cos(1.68792809396 + 107.2205608554*$t);
   $X1 += 0.00000003286*cos(5.12949558917 + 1131.6990332543*$t);
   $X1 += 0.00000003389*cos(1.65565102713 + 28.98238190449*$t);
   $X1 += 0.00000003353*cos(3.87388681549 + 10289.7954349701*$t);
   $X1 += 0.00000003214*cos(2.40799794941 + 569.5522909242*$t);
   $X1 += 0.00000003210*cos(5.76688710335 + 114.1552894299*$t);
   $X1 += 0.00000003353*cos(3.19692974184 + 157.8837694654*$t);
   $X1 += 0.00000003339*cos(3.69632773816 + 443.0985839181*$t);
   $X1 += 0.00000003188*cos(1.05807532391 + 361.13400238079*$t);
   $X1 += 0.00000003390*cos(0.82325646834 + 1558.2972241303*$t);
   $X1 += 0.00000003933*cos(0.51543027693 + 313.43973918739*$t);
   $X1 += 0.00000003131*cos(5.23811887945 + 275.3067035496*$t);
   $X1 += 0.00000003156*cos(4.66486358528 + 431.8404353331*$t);
   $X1 += 0.00000003993*cos(3.33001170426 + 67.6366824041*$t);
   $X1 += 0.00000003708*cos(1.81916567333 + 500.39976664941*$t);
   $X1 += 0.00000004051*cos(2.84746860357 + 59.038662695*$t);
   $X1 += 0.00000003757*cos(3.59917867608 + 296.4012663361*$t);
   $X1 += 0.00000003138*cos(5.35145867078 + 347.1193567003*$t);
   $X1 += 0.00000003086*cos(3.24315098824 + 392.9017584157*$t);
   $X1 += 0.00000003466*cos(0.02941146445 + 215.1941419686*$t);
   $X1 += 0.00000003139*cos(4.67079139650 + 159.36824217371*$t);
   $X1 += 0.00000003466*cos(1.90282193275 + 2145.34674583789*$t);
   $X1 += 0.00000003737*cos(1.95939265626 + 449.0364747513*$t);
   $X1 += 0.00000003286*cos(3.39700619187 + 435.44002806861*$t);
   $X1 += 0.00000003043*cos(3.45909355839 + 2.20386307129*$t);
   $X1 += 0.00000003999*cos(1.21766663097 + 6245.1866318371*$t);
   $X1 += 0.00000003999*cos(4.35925928456 + 6244.69899687009*$t);
   $X1 += 0.00000002999*cos(1.64598289911 + 526.00262931501*$t);
   $X1 += 0.00000003014*cos(3.95092279768 + 1054.94532701169*$t);
   $X1 += 0.00000003091*cos(2.95397758261 + 42.997027585*$t);
   $X1 += 0.00000003274*cos(1.10162661548 + 736.1203310153*$t);
   $X1 += 0.00000002965*cos(2.69144881941 + 533.8669358412*$t);
   $X1 += 0.00000003149*cos(0.77764778909 + 103.7639804718*$t);
   $X1 += 0.00000003610*cos(3.04477019722 + 55.05162767771*$t);
   $X1 += 0.00000002937*cos(4.36852075939 + 385.2523923381*$t);
   $X1 += 0.00000002903*cos(5.92315544183 + 117.5636857037*$t);
   $X1 += 0.00000002968*cos(2.85171539624 + 613.31440085451*$t);
   $X1 += 0.00000003097*cos(2.85040396879 + 1395.24313830449*$t);
   $X1 += 0.00000002931*cos(5.17875295945 + 202.4972126576*$t);
   $X1 += 0.00000003013*cos(3.06605929280 + 121.2352065359*$t);
   $X1 += 0.00000003206*cos(1.29027400076 + 53.40958840249*$t);
   $X1 += 0.00000003269*cos(5.16847517364 + 480.00777927849*$t);
   $X1 += 0.00000003948*cos(3.85972628729 + 112.8832650427*$t);
   $X1 += 0.00000002824*cos(1.57846497121 + 176.406715025*$t);
   $X1 += 0.00000002827*cos(1.93940329091 + 429.81095377611*$t);
   $X1 += 0.00000003348*cos(5.12243609352 + 6284.8041401832*$t);
   $X1 += 0.00000002862*cos(0.86276885894 + 384.02855206069*$t);
   $X1 += 0.00000003228*cos(0.42457598020 + 52.6039471229*$t);
   $X1 += 0.00000003446*cos(3.75606585057 + 62.0076081116*$t);
   $X1 += 0.00000003096*cos(3.26760360935 + 71.82946809809*$t);
   $X1 += 0.00000003031*cos(4.66996407487 + 494.2348732801*$t);
   $X1 += 0.00000003021*cos(1.39292760491 + 328.5964111407*$t);
   $X1 += 0.00000002731*cos(2.36952809744 + 432.471082652*$t);
   $X1 += 0.00000003171*cos(0.25949036332 + 10215.0138364028*$t);
   $X1 += 0.00000002674*cos(0.72177739894 + 158.12984768129*$t);
   $X1 += 0.00000002901*cos(5.80027365050 + 559.4697985068*$t);
   $X1 += 0.00000002631*cos(5.78146252380 + 2008.8013566425*$t);
   $X1 += 0.00000002695*cos(5.11715867535 + 81.61769818981*$t);
   $X1 += 0.00000002695*cos(1.97556602176 + 81.13006322279*$t);
   $X1 += 0.00000002721*cos(2.68965946829 + 326.1823604807*$t);
   $X1 += 0.00000002775*cos(5.84695952836 + 457.8614969965*$t);
   $X1 += 0.00000003054*cos(1.52217085552 + 6281.8351947666*$t);
   $X1 += 0.00000002852*cos(4.47706032032 + 186.71620997851*$t);
   $X1 += 0.00000002538*cos(0.16145086268 + 111.18634401329*$t);
   $X1 += 0.00000002835*cos(4.50055998275 + 419.50145882259*$t);
   $X1 += 0.00000002868*cos(2.09813621145 + 844.56699288049*$t);
   $X1 += 0.00000002530*cos(1.04013419881 + 1050.7525413177*$t);
   $X1 += 0.00000002843*cos(2.58892628620 + 830.3398988789*$t);
   $X1 += 0.00000002848*cos(3.12250765680 + 659.36662477269*$t);
   $X1 += 0.00000003031*cos(4.13022602708 + 406.3469551246*$t);
   $X1 += 0.00000002907*cos(5.28583383732 + 573.6968925084*$t);
   $X1 += 0.00000002536*cos(3.44172011173 + 82.6145359311*$t);
   $X1 += 0.00000002957*cos(0.45041658093 + 947.70795120889*$t);
   $X1 += 0.00000003321*cos(2.30536254604 + 449.9996825978*$t);
   $X1 += 0.00000003117*cos(3.17172140219 + 457.32567791969*$t);
   $X1 += 0.00000002902*cos(2.94761781535 + 10212.0448909862*$t);
   $X1 += 0.00000002459*cos(2.17142711813 + 450.73339578069*$t);
   $X1 += 0.00000002557*cos(2.89791026532 + 525.4813644532*$t);
   $X1 += 0.00000002624*cos(1.78027142371 + 946.2234785006*$t);
   $X1 += 0.00000002417*cos(4.80936350850 + 351.5727748252*$t);
   $X1 += 0.00000002454*cos(4.84992044892 + 196.01680510321*$t);
   $X1 += 0.00000002585*cos(0.99587951695 + 248.70700314271*$t);
   $X1 += 0.00000002549*cos(1.80324449988 + 1062.80714141041*$t);
   $X1 += 0.00000002615*cos(2.49010683388 + 425.13053311509*$t);
   $X1 += 0.00000002387*cos(3.61270640757 + 654.3681977991*$t);
   $X1 += 0.00000002439*cos(6.16957116292 + 462.74230389109*$t);
   $X1 += 0.00000002367*cos(4.32238656757 + 107.52937739611*$t);
   $X1 += 0.00000002538*cos(2.61932649618 + 481.2316195559*$t);
   $X1 += 0.00000002479*cos(1.99143603619 + 205.9417309537*$t);
   $X1 += 0.00000002791*cos(0.73480816467 + 24.14975911971*$t);
   $X1 += 0.00000002626*cos(1.16663444616 + 213.0552779545*$t);
   $X1 += 0.00000002445*cos(4.84988920933 + 146.87169909629*$t);
   $X1 += 0.00000002575*cos(1.89431453798 + 86.07111631471*$t);
   $X1 += 0.00000003120*cos(5.91742201237 + 456.36247007319*$t);
   $X1 += 0.00000002587*cos(0.02224873460 + 400.8209466961*$t);
   $X1 += 0.00000002261*cos(4.82066845150 + 644.33388949151*$t);
   $X1 += 0.00000002796*cos(5.01395178381 + 216.67861467689*$t);
   $X1 += 0.00000002896*cos(2.29072801127 + 1685.2959399851*$t);
   $X1 += 0.00000002453*cos(3.24288673382 + 109.9625037359*$t);
   $X1 += 0.00000002325*cos(4.96633817815 + 442.886135597*$t);
   $X1 += 0.00000002387*cos(5.32424727918 + 599.0873068529*$t);
   $X1 += 0.00000002873*cos(3.56351208170 + 834.5326845729*$t);
   $X1 += 0.00000002963*cos(0.77021714990 + 2119.00767786191*$t);
   $X1 += 0.00000002233*cos(5.94426610995 + 709.29362807231*$t);
   $X1 += 0.00000002337*cos(4.30558394222 + 210.5739675049*$t);
   $X1 += 0.00000002259*cos(3.67528651606 + 29.5036467663*$t);
   $X1 += 0.00000002300*cos(0.62755545112 + 986.0534351678*$t);
   $X1 += 0.00000002199*cos(2.78438991669 + 606.2008538537*$t);
   $X1 += 0.00000002325*cos(3.26991047297 + 109.701871305*$t);
   return $X1*$t;
}



   function Neptune_X2($t) // 113 terms of order 2
{
   $X2  = 0.01620002167*cos(0.60038473142 + 38.3768531213*$t);
   $X2 += 0.00028138323*cos(5.58440767451 + 0.2438174835*$t);
   $X2 += 0.00012318619*cos(2.58513114618 + 39.86132582961*$t);
   $X2 += 0.00008346956*cos(5.13440715484 + 37.88921815429*$t);
   $X2 += 0.00005131003*cos(5.12974075920 + 76.50988875911*$t);
   $X2 += 0.00004109792*cos(1.46495026130 + 36.892380413*$t);
   $X2 += 0.00001369663*cos(3.55762715050 + 1.7282901918*$t);
   $X2 += 0.00000633706*cos(2.38135108376 + 3.21276290011*$t);
   $X2 += 0.00000583006*cos(1.54592369321 + 41.3457985379*$t);
   $X2 += 0.00000546517*cos(0.70972594452 + 75.0254160508*$t);
   $X2 += 0.00000246224*cos(2.44618778574 + 213.5429129215*$t);
   $X2 += 0.00000159773*cos(1.26414365966 + 206.42936592071*$t);
   $X2 += 0.00000156619*cos(3.61656709171 + 220.6564599223*$t);
   $X2 += 0.00000191674*cos(2.17166123081 + 529.9347825781*$t);
   $X2 += 0.00000188212*cos(4.43184732741 + 35.40790770471*$t);
   $X2 += 0.00000117788*cos(4.12530218101 + 522.8212355773*$t);
   $X2 += 0.00000114488*cos(0.05081176794 + 35.9291725665*$t);
   $X2 += 0.00000112666*cos(0.21220394551 + 537.0483295789*$t);
   $X2 += 0.00000105949*cos(1.13080468733 + 40.8245336761*$t);
   $X2 += 0.00000077696*cos(0.84633184914 + 77.9943614674*$t);
   $X2 += 0.00000090798*cos(2.05479887039 + 73.5409433425*$t);
   $X2 += 0.00000067696*cos(2.44679430551 + 426.8420083595*$t);
   $X2 += 0.00000074860*cos(1.44346648461 + 4.6972356084*$t);
   $X2 += 0.00000064717*cos(6.06001471150 + 34.9202727377*$t);
   $X2 += 0.00000051378*cos(6.13002795973 + 36.404745446*$t);
   $X2 += 0.00000050205*cos(0.67007332287 + 42.83027124621*$t);
   $X2 += 0.00000040929*cos(6.22049348014 + 33.9234349964*$t);
   $X2 += 0.00000036136*cos(6.15460243008 + 98.6561710411*$t);
   $X2 += 0.00000033953*cos(5.02568302050 + 1059.6257476727*$t);
   $X2 += 0.00000034603*cos(3.26702076082 + 76.0222537921*$t);
   $X2 += 0.00000035441*cos(2.49518827466 + 31.2633061205*$t);
   $X2 += 0.00000029614*cos(3.34814694529 + 28.81562556571*$t);
   $X2 += 0.00000031027*cos(4.97087448592 + 45.49040012211*$t);
   $X2 += 0.00000035521*cos(1.13028002523 + 39.3736908626*$t);
   $X2 += 0.00000025488*cos(4.04320892614 + 47.9380806769*$t);
   $X2 += 0.00000020115*cos(3.93227849656 + 1.24065522479*$t);
   $X2 += 0.00000014328*cos(2.73754899228 + 433.9555553603*$t);
   $X2 += 0.00000015503*cos(3.13160557995 + 114.6429243969*$t);
   $X2 += 0.00000016998*cos(0.93393874821 + 33.43580002939*$t);
   $X2 += 0.00000013166*cos(0.39556817176 + 419.72846135871*$t);
   $X2 += 0.00000013053*cos(6.11304367644 + 60.52313540329*$t);
   $X2 += 0.00000010637*cos(5.94332175983 + 34.1840674273*$t);
   $X2 += 0.00000009610*cos(1.65699013342 + 640.1411037975*$t);
   $X2 += 0.00000009354*cos(1.41415954295 + 42.5696388153*$t);
   $X2 += 0.00000011447*cos(6.19793150566 + 71.5688356672*$t);
   $X2 += 0.00000008454*cos(2.75562169800 + 2.7251279331*$t);
   $X2 += 0.00000009012*cos(4.44112001347 + 72.05647063421*$t);
   $X2 += 0.00000009594*cos(5.79483289118 + 69.3963417583*$t);
   $X2 += 0.00000007419*cos(3.49645345230 + 227.77000692311*$t);
   $X2 += 0.00000006800*cos(5.14250085135 + 113.15845168861*$t);
   $X2 += 0.00000006267*cos(0.79586518424 + 1066.7392946735*$t);
   $X2 += 0.00000006895*cos(4.31090775556 + 111.67397898031*$t);
   $X2 += 0.00000005770*cos(1.23253284004 + 32.4389622881*$t);
   $X2 += 0.00000005686*cos(2.23805923850 + 30.300098274*$t);
   $X2 += 0.00000006679*cos(4.85529332414 + 258.78949556011*$t);
   $X2 += 0.00000007799*cos(1.58396135295 + 7.3573644843*$t);
   $X2 += 0.00000005906*cos(5.92485931723 + 44.31474395451*$t);
   $X2 += 0.00000005606*cos(5.17941805418 + 46.4536079686*$t);
   $X2 += 0.00000005525*cos(3.61911776351 + 1052.51220067191*$t);
   $X2 += 0.00000007257*cos(0.17315189128 + 1097.7587833105*$t);
   $X2 += 0.00000005427*cos(1.80586256737 + 105.76971804189*$t);
   $X2 += 0.00000005179*cos(4.25986194250 + 515.70768857651*$t);
   $X2 += 0.00000005163*cos(6.27919257182 + 7.83293736379*$t);
   $X2 += 0.00000004688*cos(2.52139212878 + 222.14093263061*$t);
   $X2 += 0.00000005379*cos(5.86341629561 + 22.3900997655*$t);
   $X2 += 0.00000004607*cos(4.89100806572 + 549.1603035533*$t);
   $X2 += 0.00000004101*cos(0.29016053329 + 213.0552779545*$t);
   $X2 += 0.00000004262*cos(5.51395238453 + 204.9448932124*$t);
   $X2 += 0.00000003916*cos(0.21419544093 + 207.913838629*$t);
   $X2 += 0.00000004089*cos(4.97684127402 + 304.84171947829*$t);
   $X2 += 0.00000003729*cos(1.40848954224 + 199.3158189199*$t);
   $X2 += 0.00000003680*cos(5.54809318630 + 1589.3167127673*$t);
   $X2 += 0.00000003702*cos(1.01863119774 + 319.06881347989*$t);
   $X2 += 0.00000004832*cos(1.26423594188 + 215.0273856298*$t);
   $X2 += 0.00000003474*cos(1.17401543445 + 103.3365917021*$t);
   $X2 += 0.00000003298*cos(0.10619126376 + 544.1618765797*$t);
   $X2 += 0.00000004521*cos(0.07911565781 + 108.2173985967*$t);
   $X2 += 0.00000003967*cos(2.67776762695 + 944.7390057923*$t);
   $X2 += 0.00000004059*cos(3.01104350847 + 149.8070146181*$t);
   $X2 += 0.00000004009*cos(5.61852534309 + 533.1161763158*$t);
   $X2 += 0.00000003288*cos(1.44957894842 + 407.9344936969*$t);
   $X2 += 0.00000003976*cos(5.00221858099 + 526.7533888404*$t);
   $X2 += 0.00000003343*cos(0.65785646071 + 531.4192552864*$t);
   $X2 += 0.00000003932*cos(3.66244745467 + 91.54262404029*$t);
   $X2 += 0.00000003478*cos(6.19876429652 + 6.1817083167*$t);
   $X2 += 0.00000002967*cos(1.04478648324 + 860.55374623631*$t);
   $X2 += 0.00000003058*cos(0.02482940557 + 342.9747551161*$t);
   $X2 += 0.00000003974*cos(2.04910269520 + 335.8612081153*$t);
   $X2 += 0.00000002849*cos(0.86611245106 + 666.4801717735*$t);
   $X2 += 0.00000002999*cos(1.27874757189 + 937.62545879149*$t);
   $X2 += 0.00000003008*cos(5.16783990611 + 74.53778108379*$t);
   $X2 += 0.00000003080*cos(3.04902400148 + 129.6756596781*$t);
   $X2 += 0.00000003346*cos(4.64303639862 + 1162.7185218913*$t);
   $X2 += 0.00000002625*cos(1.69459459452 + 273.8222308413*$t);
   $X2 += 0.00000002931*cos(1.57809055514 + 235.68919520349*$t);
   $X2 += 0.00000002579*cos(0.48473918174 + 1073.85284167431*$t);
   $X2 += 0.00000002550*cos(6.14366282644 + 26.58288545949*$t);
   $X2 += 0.00000002542*cos(4.22297682017 + 1265.81129610991*$t);
   $X2 += 0.00000002483*cos(1.73279038376 + 453.1810763355*$t);
   $X2 += 0.00000002732*cos(1.76626805419 + 563.38739755489*$t);
   $X2 += 0.00000002508*cos(1.67664275102 + 37.8555882595*$t);
   $X2 += 0.00000002508*cos(0.34076894500 + 425.35753565121*$t);
   $X2 += 0.00000002680*cos(5.74609617365 + 454.6655490438*$t);
   $X2 += 0.00000002511*cos(3.15018930028 + 209.6107596584*$t);
   $X2 += 0.00000002512*cos(1.74477024139 + 217.4750661846*$t);
   $X2 += 0.00000002552*cos(5.67032305105 + 79.47883417571*$t);
   $X2 += 0.00000002457*cos(2.67033044982 + 38.89811798311*$t);
   $X2 += 0.00000002343*cos(1.93599816349 + 981.3875687218*$t);
   $X2 += 0.00000002501*cos(1.67412173715 + 669.4009330803*$t);
   $X2 += 0.00000002330*cos(3.95065162563 + 38.32866901151*$t);
   $X2 += 0.00000002327*cos(0.39474993260 + 38.4250372311*$t);
   $X2 += 0.00000002481*cos(5.56752927904 + 655.1738390787*$t);
   $X2 += 0.00000002569*cos(4.22623902188 + 464.97504399731*$t);
   return $X2*$t*$t;
}



   function Neptune_X3($t) // 37 terms of order 3
{
   $X3  = 0.00000985355*cos(0.69240373955 + 38.3768531213*$t);
   $X3 += 0.00000482798*cos(0.83271959724 + 37.88921815429*$t);
   $X3 += 0.00000416447*cos(0.37037561694 + 0.2438174835*$t);
   $X3 += 0.00000303825*cos(0.53797420117 + 39.86132582961*$t);
   $X3 += 0.00000089203*cos(1.52338099991 + 36.892380413*$t);
   $X3 += 0.00000070862*cos(5.83899744010 + 76.50988875911*$t);
   $X3 += 0.00000028900*cos(5.65001946959 + 41.3457985379*$t);
   $X3 += 0.00000022279*cos(2.95886685234 + 206.42936592071*$t);
   $X3 += 0.00000021480*cos(1.87359273442 + 220.6564599223*$t);
   $X3 += 0.00000016157*cos(5.83581915834 + 522.8212355773*$t);
   $X3 += 0.00000015714*cos(4.76719570238 + 537.0483295789*$t);
   $X3 += 0.00000011404*cos(2.25961154910 + 35.40790770471*$t);
   $X3 += 0.00000013199*cos(0.06057423298 + 7.3573644843*$t);
   $X3 += 0.00000007024*cos(0.69890179308 + 3.21276290011*$t);
   $X3 += 0.00000006772*cos(1.19679143435 + 69.3963417583*$t);
   $X3 += 0.00000004517*cos(3.28893027439 + 45.49040012211*$t);
   $X3 += 0.00000004523*cos(4.18705629066 + 31.2633061205*$t);
   $X3 += 0.00000003682*cos(1.47261975259 + 98.6561710411*$t);
   $X3 += 0.00000003656*cos(0.60146659814 + 968.64494742849*$t);
   $X3 += 0.00000003927*cos(0.54740561653 + 426.8420083595*$t);
   $X3 += 0.00000003199*cos(1.67327016260 + 1519.6765535255*$t);
   $X3 += 0.00000003498*cos(3.27476696786 + 407.9344936969*$t);
   $X3 += 0.00000003304*cos(2.24745680549 + 422.1615876985*$t);
   $X3 += 0.00000003331*cos(1.97045240379 + 36.404745446*$t);
   $X3 += 0.00000003244*cos(2.85168281358 + 484.2005649725*$t);
   $X3 += 0.00000002689*cos(0.89932845788 + 441.06910236111*$t);
   $X3 += 0.00000003247*cos(1.76512860403 + 498.42765897409*$t);
   $X3 += 0.00000002651*cos(0.45669916115 + 304.84171947829*$t);
   $X3 += 0.00000002645*cos(5.61672793904 + 461.77909604459*$t);
   $X3 += 0.00000002542*cos(5.76347018476 + 444.5830566264*$t);
   $X3 += 0.00000002524*cos(0.75739625090 + 433.9555553603*$t);
   $X3 += 0.00000002472*cos(5.63416184223 + 319.06881347989*$t);
   $X3 += 0.00000002355*cos(0.46192754883 + 447.552002043*$t);
   $X3 += 0.00000002876*cos(5.22513442854 + 853.4401992355*$t);
   $X3 += 0.00000002279*cos(4.63709500769 + 458.810150628*$t);
   $X3 += 0.00000002147*cos(2.63611189369 + 175.40987728371*$t);
   $X3 += 0.00000002637*cos(3.63693499332 + 73.5409433425*$t);
   return $X3*$t*$t*$t;
}



   function Neptune_X4($t) // 14 terms of order 4
{
   $X4  = 0.00003455306*cos(3.61464892215 + 38.3768531213*$t);
   $X4 += 0.00000047405*cos(2.21390996774 + 0.2438174835*$t);
   $X4 += 0.00000021936*cos(2.72972488197 + 37.88921815429*$t);
   $X4 += 0.00000015596*cos(1.87854121560 + 76.50988875911*$t);
   $X4 += 0.00000017186*cos(5.53785371687 + 39.86132582961*$t);
   $X4 += 0.00000017459*cos(4.82899740364 + 36.892380413*$t);
   $X4 += 0.00000004229*cos(1.43245860878 + 515.70768857651*$t);
   $X4 += 0.00000004334*cos(5.41648117577 + 433.9555553603*$t);
   $X4 += 0.00000003547*cos(5.75561157107 + 989.98558843089*$t);
   $X4 += 0.00000003155*cos(4.85322840051 + 467.40817033709*$t);
   $X4 += 0.00000003017*cos(0.06479449145 + 227.77000692311*$t);
   $X4 += 0.00000002981*cos(0.29920864811 + 1.7282901918*$t);
   $X4 += 0.00000002295*cos(0.13749342692 + 220.6564599223*$t);
   $X4 += 0.00000002296*cos(4.70646260044 + 206.42936592071*$t);
   return $X4*$t*$t*$t*$t;
}



   function Neptune_X5($t) // 1 term of order 5
{
   $X5  = 0.00000026291*cos(3.71724730200 + 38.3768531213*$t);
   return $X5*$t*$t*$t*$t*$t;
}



   function Neptune_Y0($t) // 821 terms of order 0
{
   $Y0  = 30.05973100580*cos(3.74109000403 + 38.3768531213*$t);
   $Y0 += 0.40567587218*cos(2.41070337452 + 0.2438174835*$t);
   $Y0 += 0.13506026414*cos(1.92976188293 + 76.50988875911*$t);
   $Y0 += 0.15716341901*cos(4.82548976006 + 36.892380413*$t);
   $Y0 += 0.14935642614*cos(5.79716600101 + 39.86132582961*$t);
   $Y0 += 0.02590782232*cos(0.42530135542 + 1.7282901918*$t);
   $Y0 += 0.01073890204*cos(3.81397520876 + 75.0254160508*$t);
   $Y0 += 0.00816388197*cos(5.49424416077 + 3.21276290011*$t);
   $Y0 += 0.00702768075*cos(6.16602540157 + 35.40790770471*$t);
   $Y0 += 0.00687594822*cos(2.29155372023 + 37.88921815429*$t);
   $Y0 += 0.00565555652*cos(4.41864141199 + 41.3457985379*$t);
   $Y0 += 0.00495650075*cos(5.31196432386 + 529.9347825781*$t);
   $Y0 += 0.00306025380*cos(5.11155686178 + 73.5409433425*$t);
   $Y0 += 0.00272446904*cos(5.58643013675 + 213.5429129215*$t);
   $Y0 += 0.00135892298*cos(3.97575347243 + 77.9943614674*$t);
   $Y0 += 0.00122117697*cos(2.87943509460 + 34.9202727377*$t);
   $Y0 += 0.00090968285*cos(0.11807115994 + 114.6429243969*$t);
   $Y0 += 0.00068915400*cos(4.26390741720 + 4.6972356084*$t);
   $Y0 += 0.00040370680*cos(1.09050058383 + 33.9234349964*$t);
   $Y0 += 0.00028891307*cos(3.21868082836 + 42.83027124621*$t);
   $Y0 += 0.00029247752*cos(0.05239890051 + 72.05647063421*$t);
   $Y0 += 0.00025576289*cos(3.05422599686 + 71.5688356672*$t);
   $Y0 += 0.00020517968*cos(4.12700709797 + 33.43580002939*$t);
   $Y0 += 0.00012614154*cos(1.99850111659 + 113.15845168861*$t);
   $Y0 += 0.00012788929*cos(1.16690001367 + 111.67397898031*$t);
   $Y0 += 0.00012013477*cos(5.66154697546 + 1059.6257476727*$t);
   $Y0 += 0.00009854638*cos(1.82793273920 + 36.404745446*$t);
   $Y0 += 0.00008385825*cos(3.22321843541 + 108.2173985967*$t);
   $Y0 += 0.00007577585*cos(4.81209675667 + 426.8420083595*$t);
   $Y0 += 0.00006452053*cos(3.05476893393 + 6.1817083167*$t);
   $Y0 += 0.00006551074*cos(3.48963683470 + 1.24065522479*$t);
   $Y0 += 0.00004652534*cos(4.81582901104 + 37.8555882595*$t);
   $Y0 += 0.00004732958*cos(2.52632268239 + 79.47883417571*$t);
   $Y0 += 0.00004557247*cos(5.80951559837 + 38.89811798311*$t);
   $Y0 += 0.00004322550*cos(0.80665146695 + 38.32866901151*$t);
   $Y0 += 0.00004315539*cos(3.53393508109 + 38.4250372311*$t);
   $Y0 += 0.00004089036*cos(0.42349431022 + 37.4136452748*$t);
   $Y0 += 0.00004248658*cos(4.06300076615 + 28.81562556571*$t);
   $Y0 += 0.00004622142*cos(4.31075084247 + 70.08436295889*$t);
   $Y0 += 0.00003926447*cos(3.91895428213 + 39.34006096781*$t);
   $Y0 += 0.00003148422*cos(0.47516466537 + 76.0222537921*$t);
   $Y0 += 0.00003940981*cos(3.86846009370 + 98.6561710411*$t);
   $Y0 += 0.00003323363*cos(3.11696612599 + 4.4366031775*$t);
   $Y0 += 0.00003282964*cos(4.38630915294 + 39.3736908626*$t);
   $Y0 += 0.00003110464*cos(0.27337264525 + 47.9380806769*$t);
   $Y0 += 0.00002927062*cos(1.26687681282 + 70.5719979259*$t);
   $Y0 += 0.00002748919*cos(2.29910620256 + 32.4389622881*$t);
   $Y0 += 0.00003316668*cos(3.39273716880 + 144.8659615262*$t);
   $Y0 += 0.00002822405*cos(5.35210680933 + 31.9513273211*$t);
   $Y0 += 0.00002695972*cos(2.28196668869 + 110.189506272*$t);
   $Y0 += 0.00002522990*cos(6.23388252645 + 311.9552664791*$t);
   $Y0 += 0.00001888129*cos(1.63385050550 + 35.9291725665*$t);
   $Y0 += 0.00001648229*cos(2.49960621702 + 30.300098274*$t);
   $Y0 += 0.00001826545*cos(2.00941496239 + 44.31474395451*$t);
   $Y0 += 0.00001956241*cos(2.57436514192 + 206.42936592071*$t);
   $Y0 += 0.00001681257*cos(2.70480495091 + 40.8245336761*$t);
   $Y0 += 0.00001533383*cos(5.88971111646 + 38.26497853671*$t);
   $Y0 += 0.00001893076*cos(5.46256301015 + 220.6564599223*$t);
   $Y0 += 0.00001527526*cos(4.73412536340 + 38.4887277059*$t);
   $Y0 += 0.00002085691*cos(6.28187170642 + 149.8070146181*$t);
   $Y0 += 0.00002070612*cos(4.39661439400 + 136.78920667889*$t);
   $Y0 += 0.00001535699*cos(2.18492948354 + 73.0533083755*$t);
   $Y0 += 0.00001667976*cos(4.48792091670 + 106.73292588839*$t);
   $Y0 += 0.00001289620*cos(1.82629228420 + 46.4536079686*$t);
   $Y0 += 0.00001559811*cos(5.27109740006 + 38.11622069041*$t);
   $Y0 += 0.00001545705*cos(5.35267674075 + 38.6374855522*$t);
   $Y0 += 0.00001435033*cos(5.44094847718 + 522.8212355773*$t);
   $Y0 += 0.00001406206*cos(2.04637394879 + 537.0483295789*$t);
   $Y0 += 0.00001256446*cos(1.13828126057 + 34.1840674273*$t);
   $Y0 += 0.00001387973*cos(2.14763765402 + 116.12739710521*$t);
   $Y0 += 0.00001457739*cos(3.56061267693 + 181.5145244557*$t);
   $Y0 += 0.00001228429*cos(1.21566711155 + 72.31710306511*$t);
   $Y0 += 0.00001140665*cos(5.53723346032 + 7.83293736379*$t);
   $Y0 += 0.00001080801*cos(3.18403832376 + 42.5696388153*$t);
   $Y0 += 0.00001201409*cos(2.31627619186 + 2.7251279331*$t);
   $Y0 += 0.00001228671*cos(1.08170099047 + 148.32254190981*$t);
   $Y0 += 0.00000722014*cos(4.59727081765 + 152.77596003471*$t);
   $Y0 += 0.00000608545*cos(2.92457352888 + 35.4560918145*$t);
   $Y0 += 0.00000722865*cos(4.66419895504 + 143.38148881789*$t);
   $Y0 += 0.00000632820*cos(1.84622497362 + 7.66618102501*$t);
   $Y0 += 0.00000642369*cos(5.54570420373 + 68.5998902506*$t);
   $Y0 += 0.00000553789*cos(1.41527095431 + 41.2976144281*$t);
   $Y0 += 0.00000682276*cos(3.72885979362 + 218.1630873852*$t);
   $Y0 += 0.00000463186*cos(1.17340921668 + 31.7845709823*$t);
   $Y0 += 0.00000521560*cos(1.91893273311 + 0.719390363*$t);
   $Y0 += 0.00000437892*cos(6.01046620661 + 1589.3167127673*$t);
   $Y0 += 0.00000398091*cos(0.79544793472 + 6.3484646555*$t);
   $Y0 += 0.00000384065*cos(3.15552603467 + 44.96913526031*$t);
   $Y0 += 0.00000395583*cos(3.48448044710 + 108.70503356371*$t);
   $Y0 += 0.00000327446*cos(4.26279342171 + 60.52313540329*$t);
   $Y0 += 0.00000358824*cos(0.28673200218 + 30.4668546128*$t);
   $Y0 += 0.00000315179*cos(1.74548132888 + 74.53778108379*$t);
   $Y0 += 0.00000343384*cos(0.17566264278 + 0.7650823453*$t);
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   $Y0 += 0.00000003012*cos(2.70591736862 + 16.3973271781*$t);
   $Y0 += 0.00000002372*cos(1.81307027955 + 132.5964209849*$t);
   $Y0 += 0.00000002232*cos(3.99248125271 + 158.12984768129*$t);
   $Y0 += 0.00000002961*cos(5.94214048852 + 286.3524038135*$t);
   $Y0 += 0.00000002961*cos(2.80054783493 + 286.8400387805*$t);
   return $Y0;
}



   function Neptune_Y1($t) // 342 terms of order 1
{
   $Y1  = 0.00357822049*cos(3.03457804662 + 0.2438174835*$t);
   $Y1 += 0.00256200629*cos(0.44613631554 + 36.892380413*$t);
   $Y1 += 0.00242677799*cos(3.89213848413 + 39.86132582961*$t);
   $Y1 += 0.00106073143*cos(4.64936068389 + 37.88921815429*$t);
   $Y1 += 0.00103735195*cos(4.51191141127 + 38.3768531213*$t);
   $Y1 += 0.00118508231*cos(1.31543504055 + 76.50988875911*$t);
   $Y1 += 0.00021930692*cos(1.62939936370 + 35.40790770471*$t);
   $Y1 += 0.00017445772*cos(2.69316438174 + 41.3457985379*$t);
   $Y1 += 0.00013038843*cos(3.79605108858 + 3.21276290011*$t);
   $Y1 += 0.00004928885*cos(0.51813571490 + 73.5409433425*$t);
   $Y1 += 0.00002742686*cos(2.49310000815 + 77.9943614674*$t);
   $Y1 += 0.00002155134*cos(2.54801435750 + 4.6972356084*$t);
   $Y1 += 0.00001882800*cos(2.84958651579 + 33.9234349964*$t);
   $Y1 += 0.00001572888*cos(5.79049449823 + 114.6429243969*$t);
   $Y1 += 0.00001326507*cos(4.45906236203 + 75.0254160508*$t);
   $Y1 += 0.00001343094*cos(1.46758582116 + 42.83027124621*$t);
   $Y1 += 0.00000897979*cos(2.69913392072 + 426.8420083595*$t);
   $Y1 += 0.00000865617*cos(0.09538823497 + 37.8555882595*$t);
   $Y1 += 0.00000849963*cos(4.24519902715 + 38.89811798311*$t);
   $Y1 += 0.00000922754*cos(1.77437053635 + 72.05647063421*$t);
   $Y1 += 0.00000726258*cos(5.81913445111 + 36.404745446*$t);
   $Y1 += 0.00000778220*cos(4.27400223412 + 206.42936592071*$t);
   $Y1 += 0.00000754025*cos(3.76126183394 + 220.6564599223*$t);
   $Y1 += 0.00000607406*cos(4.81815513635 + 1059.6257476727*$t);
   $Y1 += 0.00000571831*cos(0.85851242227 + 522.8212355773*$t);
   $Y1 += 0.00000560995*cos(0.34476353479 + 537.0483295789*$t);
   $Y1 += 0.00000501078*cos(0.14255476727 + 28.81562556571*$t);
   $Y1 += 0.00000493238*cos(0.53463363296 + 39.3736908626*$t);
   $Y1 += 0.00000474802*cos(5.97795229031 + 98.6561710411*$t);
   $Y1 += 0.00000453975*cos(0.14363576661 + 35.9291725665*$t);
   $Y1 += 0.00000471731*cos(3.27137539235 + 1.7282901918*$t);
   $Y1 += 0.00000410057*cos(4.19500321025 + 40.8245336761*$t);
   $Y1 += 0.00000366899*cos(4.19675940250 + 47.9380806769*$t);
   $Y1 += 0.00000450109*cos(2.82750084230 + 76.0222537921*$t);
   $Y1 += 0.00000354347*cos(1.55870450456 + 1.24065522479*$t);
   $Y1 += 0.00000300159*cos(1.31608359577 + 6.1817083167*$t);
   $Y1 += 0.00000327501*cos(5.77559197316 + 33.43580002939*$t);
   $Y1 += 0.00000174973*cos(4.06947925642 + 32.4389622881*$t);
   $Y1 += 0.00000171503*cos(2.86905921629 + 34.1840674273*$t);
   $Y1 += 0.00000156749*cos(1.02465451730 + 79.47883417571*$t);
   $Y1 += 0.00000152549*cos(5.29458792782 + 30.300098274*$t);
   $Y1 += 0.00000150775*cos(1.46875297221 + 42.5696388153*$t);
   $Y1 += 0.00000162280*cos(5.51215947389 + 31.2633061205*$t);
   $Y1 += 0.00000131609*cos(3.19975255613 + 7.83293736379*$t);
   $Y1 += 0.00000136159*cos(3.00798814109 + 70.5719979259*$t);
   $Y1 += 0.00000134616*cos(5.10422989672 + 45.49040012211*$t);
   $Y1 += 0.00000116304*cos(5.32949492640 + 46.4536079686*$t);
   $Y1 += 0.00000115918*cos(0.24763705851 + 44.31474395451*$t);
   $Y1 += 0.00000110293*cos(4.69481457289 + 35.4560918145*$t);
   $Y1 += 0.00000099282*cos(0.34979488247 + 2.7251279331*$t);
   $Y1 += 0.00000099914*cos(5.92865840649 + 41.2976144281*$t);
   $Y1 += 0.00000108706*cos(1.52062460635 + 113.15845168861*$t);
   $Y1 += 0.00000088965*cos(5.83760483379 + 60.52313540329*$t);
   $Y1 += 0.00000086886*cos(0.75633169755 + 31.9513273211*$t);
   $Y1 += 0.00000072232*cos(1.93507773057 + 640.1411037975*$t);
   $Y1 += 0.00000086985*cos(3.23018942725 + 419.72846135871*$t);
   $Y1 += 0.00000073430*cos(5.93590859407 + 70.08436295889*$t);
   $Y1 += 0.00000053395*cos(2.89441175199 + 433.9555553603*$t);
   $Y1 += 0.00000057451*cos(5.79242631159 + 213.5429129215*$t);
   $Y1 += 0.00000051458*cos(2.44646741842 + 69.3963417583*$t);
   $Y1 += 0.00000048797*cos(4.44285537763 + 111.67397898031*$t);
   $Y1 += 0.00000048557*cos(1.53569583062 + 2.6769438233*$t);
   $Y1 += 0.00000042206*cos(4.80902694866 + 74.53778108379*$t);
   $Y1 += 0.00000042550*cos(0.10167685669 + 7.66618102501*$t);
   $Y1 += 0.00000039462*cos(4.26971409186 + 31.7845709823*$t);
   $Y1 += 0.00000039445*cos(5.65869884949 + 12.77399045571*$t);
   $Y1 += 0.00000042389*cos(4.01940273222 + 110.189506272*$t);
   $Y1 += 0.00000044118*cos(5.15854031484 + 1589.3167127673*$t);
   $Y1 += 0.00000037988*cos(4.30930512095 + 6.3484646555*$t);
   $Y1 += 0.00000037802*cos(4.41701497532 + 14.258463164*$t);
   $Y1 += 0.00000036280*cos(1.56655638104 + 273.8222308413*$t);
   $Y1 += 0.00000037247*cos(6.20048406786 + 73.0533083755*$t);
   $Y1 += 0.00000036282*cos(1.28256818253 + 84.5866436064*$t);
   $Y1 += 0.00000040018*cos(2.70338838405 + 4.4366031775*$t);
   $Y1 += 0.00000032400*cos(0.07249247133 + 44.96913526031*$t);
   $Y1 += 0.00000031842*cos(0.45413330049 + 34.9202727377*$t);
   $Y1 += 0.00000032037*cos(1.37472212177 + 27.3311528574*$t);
   $Y1 += 0.00000034456*cos(1.80072966680 + 529.9347825781*$t);
   $Y1 += 0.00000031208*cos(0.16340478702 + 1052.51220067191*$t);
   $Y1 += 0.00000030002*cos(0.76559925402 + 1066.7392946735*$t);
   $Y1 += 0.00000033805*cos(4.47034863791 + 149.8070146181*$t);
   $Y1 += 0.00000033096*cos(0.88714456679 + 116.12739710521*$t);
   $Y1 += 0.00000030571*cos(5.59230793843 + 22.3900997655*$t);
   $Y1 += 0.00000024020*cos(4.95060362012 + 63.9797157869*$t);
   $Y1 += 0.00000023780*cos(5.91699417045 + 105.76971804189*$t);
   $Y1 += 0.00000023110*cos(4.08428537053 + 23.87457247379*$t);
   $Y1 += 0.00000022233*cos(2.78662410030 + 174.9222423167*$t);
   $Y1 += 0.00000021377*cos(2.17060095397 + 316.6356871401*$t);
   $Y1 += 0.00000025400*cos(6.09781709877 + 106.73292588839*$t);
   $Y1 += 0.00000020754*cos(5.65712726150 + 5.6604434549*$t);
   $Y1 += 0.00000025572*cos(0.74829738831 + 529.44714761109*$t);
   $Y1 += 0.00000019878*cos(5.73044838456 + 32.9602271499*$t);
   $Y1 += 0.00000019754*cos(2.91920492275 + 49.42255338521*$t);
   $Y1 += 0.00000019241*cos(4.44333892046 + 7.14491616321*$t);
   $Y1 += 0.00000017979*cos(6.19717030924 + 62.4952430786*$t);
   $Y1 += 0.00000019513*cos(0.93528726944 + 68.5998902506*$t);
   $Y1 += 0.00000018273*cos(3.63050723326 + 227.77000692311*$t);
   $Y1 += 0.00000017552*cos(4.23270606709 + 69.0875252176*$t);
   $Y1 += 0.00000016704*cos(5.51562885485 + 40.8581635709*$t);
   $Y1 += 0.00000016996*cos(2.67528896312 + 91.54262404029*$t);
   $Y1 += 0.00000016800*cos(2.08712613778 + 30.4668546128*$t);
   $Y1 += 0.00000016800*cos(5.22871879137 + 30.95448957981*$t);
   $Y1 += 0.00000016400*cos(3.45346576095 + 33.26904369061*$t);
   $Y1 += 0.00000017242*cos(4.89590986485 + 11.55015017831*$t);
   $Y1 += 0.00000015590*cos(0.42181314281 + 37.1048287341*$t);
   $Y1 += 0.00000015590*cos(3.91877412353 + 39.6488775085*$t);
   $Y1 += 0.00000015469*cos(4.91170489358 + 43.79347909271*$t);
   $Y1 += 0.00000016590*cos(1.19757876004 + 33.71098667531*$t);
   $Y1 += 0.00000019347*cos(4.06418655235 + 152.77596003471*$t);
   $Y1 += 0.00000014994*cos(4.29075263091 + 319.06881347989*$t);
   $Y1 += 0.00000014395*cos(5.67189517492 + 110.45013870291*$t);
   $Y1 += 0.00000015528*cos(5.87587490674 + 79.43065006591*$t);
   $Y1 += 0.00000013727*cos(0.88731617093 + 43.484662552*$t);
   $Y1 += 0.00000013988*cos(5.54059308769 + 4.2096006414*$t);
   $Y1 += 0.00000014467*cos(5.13403607047 + 108.70503356371*$t);
   $Y1 += 0.00000016652*cos(4.74696813612 + 304.84171947829*$t);
   $Y1 += 0.00000015153*cos(1.64704158732 + 72.31710306511*$t);
   $Y1 += 0.00000012810*cos(0.80784638784 + 11.2895177474*$t);
   $Y1 += 0.00000012751*cos(5.32663860873 + 45.7992166628*$t);
   $Y1 += 0.00000013293*cos(3.14432194523 + 43.0427195673*$t);
   $Y1 += 0.00000012751*cos(0.98606109283 + 515.70768857651*$t);
   $Y1 += 0.00000011616*cos(4.07265201948 + 97.17169833279*$t);
   $Y1 += 0.00000011538*cos(4.63247506911 + 633.0275567967*$t);
   $Y1 += 0.00000011046*cos(5.97427560684 + 25.8466801491*$t);
   $Y1 += 0.00000011032*cos(5.39646944302 + 4.8639919472*$t);
   $Y1 += 0.00000011189*cos(2.37859784397 + 83.1021708981*$t);
   $Y1 += 0.00000010860*cos(5.09978655023 + 9.8050450391*$t);
   $Y1 += 0.00000010958*cos(3.05455531642 + 415.04804069769*$t);
   $Y1 += 0.00000010244*cos(4.97854342755 + 71.09326278771*$t);
   $Y1 += 0.00000011427*cos(3.07758676009 + 129.6756596781*$t);
   $Y1 += 0.00000009895*cos(4.05388510292 + 251.6759485593*$t);
   $Y1 += 0.00000009802*cos(3.40894474212 + 44.48150029329*$t);
   $Y1 += 0.00000011029*cos(6.26821027792 + 143.38148881789*$t);
   $Y1 += 0.00000009235*cos(4.42290386641 + 199.3158189199*$t);
   $Y1 += 0.00000008899*cos(1.97879285736 + 7.3573644843*$t);
   $Y1 += 0.00000007746*cos(4.32608949084 + 103.3365917021*$t);
   $Y1 += 0.00000008691*cos(2.29051174612 + 32.7477788288*$t);
   $Y1 += 0.00000007714*cos(3.51056446926 + 65.46418849521*$t);
   $Y1 += 0.00000008007*cos(0.23872922784 + 544.1618765797*$t);
   $Y1 += 0.00000007513*cos(6.18736050552 + 69.6087900794*$t);
   $Y1 += 0.00000007336*cos(3.43409422317 + 15.7429358723*$t);
   $Y1 += 0.00000007195*cos(4.56950200257 + 949.4194264533*$t);
   $Y1 += 0.00000009601*cos(5.68191403081 + 80.963306884*$t);
   $Y1 += 0.00000008094*cos(1.70304241092 + 526.7533888404*$t);
   $Y1 += 0.00000008109*cos(5.77532188995 + 533.1161763158*$t);
   $Y1 += 0.00000006906*cos(3.70672232078 + 137.2768416459*$t);
   $Y1 += 0.00000007455*cos(1.11362695292 + 105.2484531801*$t);
   $Y1 += 0.00000007826*cos(2.45321405406 + 77.0311536209*$t);
   $Y1 += 0.00000006529*cos(5.57837212493 + 65.2035560643*$t);
   $Y1 += 0.00000007134*cos(2.05010386093 + 44.00592741381*$t);
   $Y1 += 0.00000006186*cos(0.85023811841 + 31.4757544416*$t);
   $Y1 += 0.00000006186*cos(3.99183077200 + 30.9881194746*$t);
   $Y1 += 0.00000007698*cos(4.89115030216 + 14.47091148511*$t);
   $Y1 += 0.00000007434*cos(3.96333556733 + 146.8380692015*$t);
   $Y1 += 0.00000006317*cos(5.24777799313 + 66.9486612035*$t);
   $Y1 += 0.00000006903*cos(4.63739310514 + 75.98862389731*$t);
   $Y1 += 0.00000005591*cos(3.47781120117 + 448.98829064149*$t);
   $Y1 += 0.00000006425*cos(3.47626562775 + 678.27413943531*$t);
   $Y1 += 0.00000005483*cos(1.61247704205 + 34.44469985821*$t);
   $Y1 += 0.00000005483*cos(2.72811022429 + 42.3090063844*$t);
   $Y1 += 0.00000005519*cos(1.27116075236 + 853.4401992355*$t);
   $Y1 += 0.00000005483*cos(5.10869779974 + 100.14064374939*$t);
   $Y1 += 0.00000005483*cos(1.96710514615 + 100.6282787164*$t);
   $Y1 += 0.00000006288*cos(2.60319684406 + 143.9027536797*$t);
   $Y1 += 0.00000006239*cos(4.20987077870 + 17.76992530181*$t);
   $Y1 += 0.00000005246*cos(3.52035332490 + 209.6107596584*$t);
   $Y1 += 0.00000005331*cos(4.83550697489 + 45.9659730016*$t);
   $Y1 += 0.00000005131*cos(4.53503564274 + 217.4750661846*$t);
   $Y1 += 0.00000005325*cos(2.82680123889 + 19.2543980101*$t);
   $Y1 += 0.00000005172*cos(2.44008575183 + 25.3590451821*$t);
   $Y1 += 0.00000005139*cos(4.17507085285 + 6.86972951729*$t);
   $Y1 += 0.00000005992*cos(2.76367557670 + 9.3174100721*$t);
   $Y1 += 0.00000005011*cos(4.91884286875 + 38.85242600079*$t);
   $Y1 += 0.00000004975*cos(3.01044533436 + 525.2543619171*$t);
   $Y1 += 0.00000004910*cos(3.47707407879 + 45.277951801*$t);
   $Y1 += 0.00000005250*cos(0.16559612363 + 0.719390363*$t);
   $Y1 += 0.00000004731*cos(6.27469301850 + 40.3825906914*$t);
   $Y1 += 0.00000004731*cos(1.20748690143 + 36.3711155512*$t);
   $Y1 += 0.00000005910*cos(1.40566081690 + 6168.43292559449*$t);
   $Y1 += 0.00000004700*cos(4.66314397827 + 50.9070260935*$t);
   $Y1 += 0.00000005127*cos(1.64029328726 + 140.9338082631*$t);
   $Y1 += 0.00000005321*cos(2.09939112611 + 1104.87233031131*$t);
   $Y1 += 0.00000006339*cos(1.02786059939 + 10175.3963280567*$t);
   $Y1 += 0.00000004983*cos(1.46113982673 + 1090.6452363097*$t);
   $Y1 += 0.00000005487*cos(0.13979521980 + 180.03005174739*$t);
   $Y1 += 0.00000004560*cos(2.38015606975 + 323.74923414091*$t);
   $Y1 += 0.00000004689*cos(5.95510153546 + 1068.22376738181*$t);
   $Y1 += 0.00000005562*cos(2.83481631972 + 10098.64262181409*$t);
   $Y1 += 0.00000004432*cos(0.83559275468 + 415.7963080956*$t);
   $Y1 += 0.00000004456*cos(1.46246408589 + 235.68919520349*$t);
   $Y1 += 0.00000004289*cos(4.40449246840 + 1051.0277279636*$t);
   $Y1 += 0.00000004145*cos(4.70457869197 + 33.6964324603*$t);
   $Y1 += 0.00000004167*cos(3.29886964345 + 416.532513406*$t);
   $Y1 += 0.00000004107*cos(0.91956436736 + 61.01077037031*$t);
   $Y1 += 0.00000004088*cos(3.88660175347 + 423.66061462181*$t);
   $Y1 += 0.00000005027*cos(2.86873904525 + 21.7020785649*$t);
   $Y1 += 0.00000004030*cos(3.44189647415 + 216.72430665921*$t);
   $Y1 += 0.00000004278*cos(6.22413352457 + 310.4707937708*$t);
   $Y1 += 0.00000004013*cos(2.96769071148 + 104275.10267753768*$t);
   $Y1 += 0.00000004505*cos(5.93746161630 + 291.9478482112*$t);
   $Y1 += 0.00000003959*cos(4.60954974650 + 210.36151918381*$t);
   $Y1 += 0.00000003962*cos(5.59162611271 + 978.93988816699*$t);
   $Y1 += 0.00000005561*cos(3.31923216598 + 1409.47023230609*$t);
   $Y1 += 0.00000005073*cos(5.15285057233 + 1498.3359125231*$t);
   $Y1 += 0.00000004227*cos(6.19954210169 + 534.38820070301*$t);
   $Y1 += 0.00000004054*cos(2.45804475947 + 430.02340209721*$t);
   $Y1 += 0.00000003863*cos(0.67184399240 + 1127.50624756031*$t);
   $Y1 += 0.00000004367*cos(0.14073726901 + 58.9837809408*$t);
   $Y1 += 0.00000004694*cos(4.91041582057 + 77.5067265004*$t);
   $Y1 += 0.00000004144*cos(5.16137286617 + 518.1408149163*$t);
   $Y1 += 0.00000004289*cos(1.72696806473 + 921.3206991231*$t);
   $Y1 += 0.00000004039*cos(5.37067473153 + 1622.76932774409*$t);
   $Y1 += 0.00000005180*cos(3.80035699018 + 99.1438060081*$t);
   $Y1 += 0.00000004845*cos(1.33083083566 + 136.78920667889*$t);
   $Y1 += 0.00000004827*cos(1.21379713661 + 418.2439886504*$t);
   $Y1 += 0.00000003722*cos(4.94171351364 + 1065.2548219652*$t);
   $Y1 += 0.00000004729*cos(2.19682691364 + 421.212934067*$t);
   $Y1 += 0.00000003490*cos(0.54756448610 + 986.8041946932*$t);
   $Y1 += 0.00000003715*cos(1.30912268012 + 254.10907489909*$t);
   $Y1 += 0.00000003488*cos(5.95100195908 + 187.9400502559*$t);
   $Y1 += 0.00000003989*cos(5.37041318514 + 95.7354097343*$t);
   $Y1 += 0.00000003603*cos(2.22310220083 + 67.1154175423*$t);
   $Y1 += 0.00000003530*cos(0.93986174870 + 24.36220744081*$t);
   $Y1 += 0.00000003538*cos(1.51952328076 + 57.4993082325*$t);
   $Y1 += 0.00000003838*cos(3.56895316428 + 979.90309601349*$t);
   $Y1 += 0.00000003615*cos(1.60474010406 + 493.2862196486*$t);
   $Y1 += 0.00000003457*cos(1.79944886939 + 807.70598162989*$t);
   $Y1 += 0.00000003648*cos(1.43920595596 + 647.25465079831*$t);
   $Y1 += 0.00000004048*cos(6.25251011272 + 979.69064769239*$t);
   $Y1 += 0.00000004414*cos(2.00415973362 + 1062.59469308931*$t);
   $Y1 += 0.00000003631*cos(0.74841494891 + 486.1726726478*$t);
   $Y1 += 0.00000003347*cos(4.13560148025 + 151.2914873264*$t);
   $Y1 += 0.00000003305*cos(5.23397852699 + 1544.07013012871*$t);
   $Y1 += 0.00000003428*cos(0.11713176717 + 107.2205608554*$t);
   $Y1 += 0.00000003286*cos(3.55869926238 + 1131.6990332543*$t);
   $Y1 += 0.00000003389*cos(3.22644735392 + 28.98238190449*$t);
   $Y1 += 0.00000003353*cos(2.30309048870 + 10289.7954349701*$t);
   $Y1 += 0.00000003214*cos(0.83720162261 + 569.5522909242*$t);
   $Y1 += 0.00000003210*cos(1.05449812296 + 114.1552894299*$t);
   $Y1 += 0.00000003353*cos(1.62613341505 + 157.8837694654*$t);
   $Y1 += 0.00000003339*cos(5.26712406495 + 443.0985839181*$t);
   $Y1 += 0.00000003188*cos(2.62887165071 + 361.13400238079*$t);
   $Y1 += 0.00000003390*cos(5.53564544873 + 1558.2972241303*$t);
   $Y1 += 0.00000003933*cos(2.08622660372 + 313.43973918739*$t);
   $Y1 += 0.00000003131*cos(0.52572989907 + 275.3067035496*$t);
   $Y1 += 0.00000003156*cos(6.23565991208 + 431.8404353331*$t);
   $Y1 += 0.00000003993*cos(4.90080803105 + 67.6366824041*$t);
   $Y1 += 0.00000003708*cos(0.24836934654 + 500.39976664941*$t);
   $Y1 += 0.00000004051*cos(4.41826493037 + 59.038662695*$t);
   $Y1 += 0.00000003757*cos(2.02838234929 + 296.4012663361*$t);
   $Y1 += 0.00000003138*cos(0.63906969040 + 347.1193567003*$t);
   $Y1 += 0.00000003086*cos(1.67235466145 + 392.9017584157*$t);
   $Y1 += 0.00000003466*cos(1.60020779124 + 215.1941419686*$t);
   $Y1 += 0.00000003139*cos(3.09999506971 + 159.36824217371*$t);
   $Y1 += 0.00000003466*cos(3.47361825954 + 2145.34674583789*$t);
   $Y1 += 0.00000003737*cos(3.53018898305 + 449.0364747513*$t);
   $Y1 += 0.00000003286*cos(1.82620986507 + 435.44002806861*$t);
   $Y1 += 0.00000003043*cos(5.02988988519 + 2.20386307129*$t);
   $Y1 += 0.00000003999*cos(5.93005561135 + 6245.1866318371*$t);
   $Y1 += 0.00000003999*cos(5.93005561135 + 6244.69899687009*$t);
   $Y1 += 0.00000002999*cos(0.07518657231 + 526.00262931501*$t);
   $Y1 += 0.00000003014*cos(5.52171912448 + 1054.94532701169*$t);
   $Y1 += 0.00000003091*cos(4.52477390940 + 42.997027585*$t);
   $Y1 += 0.00000003274*cos(5.81401559586 + 736.1203310153*$t);
   $Y1 += 0.00000002965*cos(1.12065249261 + 533.8669358412*$t);
   $Y1 += 0.00000003149*cos(2.34844411589 + 103.7639804718*$t);
   $Y1 += 0.00000003610*cos(1.47397387042 + 55.05162767771*$t);
   $Y1 += 0.00000002937*cos(5.93931708618 + 385.2523923381*$t);
   $Y1 += 0.00000002903*cos(4.35235911504 + 117.5636857037*$t);
   $Y1 += 0.00000002968*cos(1.28091906944 + 613.31440085451*$t);
   $Y1 += 0.00000003097*cos(4.42120029558 + 1395.24313830449*$t);
   $Y1 += 0.00000002931*cos(3.60795663266 + 202.4972126576*$t);
   $Y1 += 0.00000003013*cos(1.49526296600 + 121.2352065359*$t);
   $Y1 += 0.00000003206*cos(2.86107032756 + 53.40958840249*$t);
   $Y1 += 0.00000003269*cos(0.45608619325 + 480.00777927849*$t);
   $Y1 += 0.00000003948*cos(5.43052261409 + 112.8832650427*$t);
   $Y1 += 0.00000002824*cos(3.14926129801 + 176.406715025*$t);
   $Y1 += 0.00000002827*cos(0.36860696411 + 429.81095377611*$t);
   $Y1 += 0.00000003348*cos(3.55163976673 + 6284.8041401832*$t);
   $Y1 += 0.00000002862*cos(2.43356518574 + 384.02855206069*$t);
   $Y1 += 0.00000003228*cos(5.13696496058 + 52.6039471229*$t);
   $Y1 += 0.00000003446*cos(5.32686217736 + 62.0076081116*$t);
   $Y1 += 0.00000003096*cos(4.83839993614 + 71.82946809809*$t);
   $Y1 += 0.00000003031*cos(6.24076040166 + 494.2348732801*$t);
   $Y1 += 0.00000003021*cos(6.10531658530 + 328.5964111407*$t);
   $Y1 += 0.00000002731*cos(0.79873177065 + 432.471082652*$t);
   $Y1 += 0.00000003171*cos(4.97187934370 + 10215.0138364028*$t);
   $Y1 += 0.00000002674*cos(2.29257372574 + 158.12984768129*$t);
   $Y1 += 0.00000002901*cos(4.22947732371 + 559.4697985068*$t);
   $Y1 += 0.00000002631*cos(4.21066619701 + 2008.8013566425*$t);
   $Y1 += 0.00000002695*cos(3.54636234855 + 81.61769818981*$t);
   $Y1 += 0.00000002695*cos(3.54636234855 + 81.13006322279*$t);
   $Y1 += 0.00000002721*cos(4.26045579509 + 326.1823604807*$t);
   $Y1 += 0.00000002775*cos(4.27616320157 + 457.8614969965*$t);
   $Y1 += 0.00000003054*cos(6.23455983590 + 6281.8351947666*$t);
   $Y1 += 0.00000002852*cos(2.90626399353 + 186.71620997851*$t);
   $Y1 += 0.00000002538*cos(1.73224718947 + 111.18634401329*$t);
   $Y1 += 0.00000002835*cos(6.07135630955 + 419.50145882259*$t);
   $Y1 += 0.00000002868*cos(3.66893253825 + 844.56699288049*$t);
   $Y1 += 0.00000002530*cos(2.61093052560 + 1050.7525413177*$t);
   $Y1 += 0.00000002843*cos(4.15972261299 + 830.3398988789*$t);
   $Y1 += 0.00000002848*cos(4.69330398359 + 659.36662477269*$t);
   $Y1 += 0.00000003031*cos(2.55942970028 + 406.3469551246*$t);
   $Y1 += 0.00000002907*cos(3.71503751053 + 573.6968925084*$t);
   $Y1 += 0.00000002536*cos(5.01251643852 + 82.6145359311*$t);
   $Y1 += 0.00000002957*cos(2.02121290773 + 947.70795120889*$t);
   $Y1 += 0.00000003321*cos(3.87615887284 + 449.9996825978*$t);
   $Y1 += 0.00000003117*cos(4.74251772899 + 457.32567791969*$t);
   $Y1 += 0.00000002902*cos(1.37682148855 + 10212.0448909862*$t);
   $Y1 += 0.00000002459*cos(3.74222344492 + 450.73339578069*$t);
   $Y1 += 0.00000002557*cos(1.32711393852 + 525.4813644532*$t);
   $Y1 += 0.00000002624*cos(3.35106775051 + 946.2234785006*$t);
   $Y1 += 0.00000002417*cos(0.09697452811 + 351.5727748252*$t);
   $Y1 += 0.00000002454*cos(3.27912412212 + 196.01680510321*$t);
   $Y1 += 0.00000002585*cos(5.70826849733 + 248.70700314271*$t);
   $Y1 += 0.00000002549*cos(0.23244817308 + 1062.80714141041*$t);
   $Y1 += 0.00000002615*cos(4.06090316067 + 425.13053311509*$t);
   $Y1 += 0.00000002387*cos(2.04191008078 + 654.3681977991*$t);
   $Y1 += 0.00000002439*cos(1.45718218253 + 462.74230389109*$t);
   $Y1 += 0.00000002367*cos(2.75159024078 + 107.52937739611*$t);
   $Y1 += 0.00000002538*cos(4.19012282298 + 481.2316195559*$t);
   $Y1 += 0.00000002479*cos(3.56223236298 + 205.9417309537*$t);
   $Y1 += 0.00000002791*cos(5.44719714506 + 24.14975911971*$t);
   $Y1 += 0.00000002626*cos(2.73743077295 + 213.0552779545*$t);
   $Y1 += 0.00000002445*cos(0.13750022894 + 146.87169909629*$t);
   $Y1 += 0.00000002575*cos(0.32351821119 + 86.07111631471*$t);
   $Y1 += 0.00000003120*cos(1.20503303199 + 456.36247007319*$t);
   $Y1 += 0.00000002587*cos(1.59304506140 + 400.8209466961*$t);
   $Y1 += 0.00000002261*cos(3.24987212470 + 644.33388949151*$t);
   $Y1 += 0.00000002796*cos(0.30156280343 + 216.67861467689*$t);
   $Y1 += 0.00000002896*cos(0.71993168447 + 1685.2959399851*$t);
   $Y1 += 0.00000002453*cos(4.81368306062 + 109.9625037359*$t);
   $Y1 += 0.00000002325*cos(0.25394919776 + 442.886135597*$t);
   $Y1 += 0.00000002387*cos(3.75345095238 + 599.0873068529*$t);
   $Y1 += 0.00000002873*cos(5.13430840850 + 834.5326845729*$t);
   $Y1 += 0.00000002963*cos(5.48260613029 + 2119.00767786191*$t);
   $Y1 += 0.00000002233*cos(4.37346978315 + 709.29362807231*$t);
   $Y1 += 0.00000002337*cos(2.73478761543 + 210.5739675049*$t);
   $Y1 += 0.00000002259*cos(5.24608284286 + 29.5036467663*$t);
   $Y1 += 0.00000002300*cos(2.19835177792 + 986.0534351678*$t);
   $Y1 += 0.00000002199*cos(1.21359358990 + 606.2008538537*$t);
   $Y1 += 0.00000002325*cos(4.84070679976 + 109.701871305*$t);
   return $Y1*$t;
}



   function Neptune_Y2($t) // 113 terms of order 2
{
   $Y2  = 0.01620002167*cos(5.31277371181 + 38.3768531213*$t);
   $Y2 += 0.00028138323*cos(4.01361134771 + 0.2438174835*$t);
   $Y2 += 0.00012318619*cos(1.01433481938 + 39.86132582961*$t);
   $Y2 += 0.00008346956*cos(0.42201817445 + 37.88921815429*$t);
   $Y2 += 0.00005131003*cos(3.55894443240 + 76.50988875911*$t);
   $Y2 += 0.00004109792*cos(6.17733924169 + 36.892380413*$t);
   $Y2 += 0.00001369663*cos(1.98683082370 + 1.7282901918*$t);
   $Y2 += 0.00000633706*cos(0.81055475696 + 3.21276290011*$t);
   $Y2 += 0.00000583006*cos(6.25831267359 + 41.3457985379*$t);
   $Y2 += 0.00000546517*cos(5.42211492491 + 75.0254160508*$t);
   $Y2 += 0.00000246224*cos(0.87539145895 + 213.5429129215*$t);
   $Y2 += 0.00000159773*cos(5.97653264005 + 206.42936592071*$t);
   $Y2 += 0.00000156619*cos(2.04577076492 + 220.6564599223*$t);
   $Y2 += 0.00000191674*cos(0.60086490402 + 529.9347825781*$t);
   $Y2 += 0.00000188212*cos(2.86105100061 + 35.40790770471*$t);
   $Y2 += 0.00000117788*cos(2.55450585422 + 522.8212355773*$t);
   $Y2 += 0.00000114488*cos(4.76320074833 + 35.9291725665*$t);
   $Y2 += 0.00000112666*cos(4.92459292590 + 537.0483295789*$t);
   $Y2 += 0.00000105949*cos(5.84319366771 + 40.8245336761*$t);
   $Y2 += 0.00000077696*cos(5.55872082952 + 77.9943614674*$t);
   $Y2 += 0.00000090798*cos(0.48400254359 + 73.5409433425*$t);
   $Y2 += 0.00000067696*cos(0.87599797871 + 426.8420083595*$t);
   $Y2 += 0.00000074860*cos(6.15585546499 + 4.6972356084*$t);
   $Y2 += 0.00000064717*cos(1.34762573111 + 34.9202727377*$t);
   $Y2 += 0.00000051378*cos(1.41763897935 + 36.404745446*$t);
   $Y2 += 0.00000050205*cos(5.38246230326 + 42.83027124621*$t);
   $Y2 += 0.00000040929*cos(4.64969715335 + 33.9234349964*$t);
   $Y2 += 0.00000036136*cos(1.44221344970 + 98.6561710411*$t);
   $Y2 += 0.00000033953*cos(3.45488669371 + 1059.6257476727*$t);
   $Y2 += 0.00000034603*cos(4.83781708761 + 76.0222537921*$t);
   $Y2 += 0.00000035441*cos(0.92439194787 + 31.2633061205*$t);
   $Y2 += 0.00000029614*cos(1.77735061850 + 28.81562556571*$t);
   $Y2 += 0.00000031027*cos(3.40007815913 + 45.49040012211*$t);
   $Y2 += 0.00000035521*cos(2.70107635202 + 39.3736908626*$t);
   $Y2 += 0.00000025488*cos(2.47241259934 + 47.9380806769*$t);
   $Y2 += 0.00000020115*cos(5.50307482336 + 1.24065522479*$t);
   $Y2 += 0.00000014328*cos(1.16675266548 + 433.9555553603*$t);
   $Y2 += 0.00000015503*cos(1.56080925316 + 114.6429243969*$t);
   $Y2 += 0.00000016998*cos(2.50473507501 + 33.43580002939*$t);
   $Y2 += 0.00000013166*cos(5.10795715214 + 419.72846135871*$t);
   $Y2 += 0.00000013053*cos(1.40065469605 + 60.52313540329*$t);
   $Y2 += 0.00000010637*cos(4.37252543304 + 34.1840674273*$t);
   $Y2 += 0.00000009610*cos(0.08619380662 + 640.1411037975*$t);
   $Y2 += 0.00000009354*cos(6.12654852334 + 42.5696388153*$t);
   $Y2 += 0.00000011447*cos(1.48554252527 + 71.5688356672*$t);
   $Y2 += 0.00000008454*cos(4.32641802480 + 2.7251279331*$t);
   $Y2 += 0.00000009012*cos(2.87032368668 + 72.05647063421*$t);
   $Y2 += 0.00000009594*cos(4.22403656438 + 69.3963417583*$t);
   $Y2 += 0.00000007419*cos(1.92565712551 + 227.77000692311*$t);
   $Y2 += 0.00000006800*cos(3.57170452455 + 113.15845168861*$t);
   $Y2 += 0.00000006267*cos(5.50825416463 + 1066.7392946735*$t);
   $Y2 += 0.00000006895*cos(2.74011142877 + 111.67397898031*$t);
   $Y2 += 0.00000005770*cos(5.94492182042 + 32.4389622881*$t);
   $Y2 += 0.00000005686*cos(0.66726291170 + 30.300098274*$t);
   $Y2 += 0.00000006679*cos(3.28449699734 + 258.78949556011*$t);
   $Y2 += 0.00000007799*cos(0.01316502615 + 7.3573644843*$t);
   $Y2 += 0.00000005906*cos(4.35406299044 + 44.31474395451*$t);
   $Y2 += 0.00000005606*cos(3.60862172739 + 46.4536079686*$t);
   $Y2 += 0.00000005525*cos(2.04832143671 + 1052.51220067191*$t);
   $Y2 += 0.00000007257*cos(4.88554087166 + 1097.7587833105*$t);
   $Y2 += 0.00000005427*cos(3.37665889417 + 105.76971804189*$t);
   $Y2 += 0.00000005179*cos(2.68906561571 + 515.70768857651*$t);
   $Y2 += 0.00000005163*cos(1.56680359144 + 7.83293736379*$t);
   $Y2 += 0.00000004688*cos(0.95059580199 + 222.14093263061*$t);
   $Y2 += 0.00000005379*cos(1.15102731522 + 22.3900997655*$t);
   $Y2 += 0.00000004607*cos(0.17861908533 + 549.1603035533*$t);
   $Y2 += 0.00000004101*cos(1.86095686008 + 213.0552779545*$t);
   $Y2 += 0.00000004262*cos(3.94315605774 + 204.9448932124*$t);
   $Y2 += 0.00000003916*cos(4.92658442131 + 207.913838629*$t);
   $Y2 += 0.00000004089*cos(0.26445229364 + 304.84171947829*$t);
   $Y2 += 0.00000003729*cos(6.12087852262 + 199.3158189199*$t);
   $Y2 += 0.00000003680*cos(3.97729685951 + 1589.3167127673*$t);
   $Y2 += 0.00000003702*cos(2.58942752453 + 319.06881347989*$t);
   $Y2 += 0.00000004832*cos(5.97662492227 + 215.0273856298*$t);
   $Y2 += 0.00000003474*cos(5.88640441483 + 103.3365917021*$t);
   $Y2 += 0.00000003298*cos(4.81858024415 + 544.1618765797*$t);
   $Y2 += 0.00000004521*cos(1.64991198460 + 108.2173985967*$t);
   $Y2 += 0.00000003967*cos(4.24856395374 + 944.7390057923*$t);
   $Y2 += 0.00000004059*cos(1.44024718167 + 149.8070146181*$t);
   $Y2 += 0.00000004009*cos(4.04772901629 + 533.1161763158*$t);
   $Y2 += 0.00000003288*cos(3.02037527521 + 407.9344936969*$t);
   $Y2 += 0.00000003976*cos(3.43142225420 + 526.7533888404*$t);
   $Y2 += 0.00000003343*cos(5.37024544109 + 531.4192552864*$t);
   $Y2 += 0.00000003932*cos(5.23324378146 + 91.54262404029*$t);
   $Y2 += 0.00000003478*cos(4.62796796973 + 6.1817083167*$t);
   $Y2 += 0.00000002967*cos(5.75717546362 + 860.55374623631*$t);
   $Y2 += 0.00000003058*cos(1.59562573237 + 342.9747551161*$t);
   $Y2 += 0.00000003974*cos(3.61989902199 + 335.8612081153*$t);
   $Y2 += 0.00000002849*cos(2.43690877786 + 666.4801717735*$t);
   $Y2 += 0.00000002999*cos(2.84954389869 + 937.62545879149*$t);
   $Y2 += 0.00000003008*cos(0.45545092573 + 74.53778108379*$t);
   $Y2 += 0.00000003080*cos(4.61982032828 + 129.6756596781*$t);
   $Y2 += 0.00000003346*cos(3.07224007183 + 1162.7185218913*$t);
   $Y2 += 0.00000002625*cos(3.26539092131 + 273.8222308413*$t);
   $Y2 += 0.00000002931*cos(3.14888688193 + 235.68919520349*$t);
   $Y2 += 0.00000002579*cos(5.19712816213 + 1073.85284167431*$t);
   $Y2 += 0.00000002550*cos(1.43127384605 + 26.58288545949*$t);
   $Y2 += 0.00000002542*cos(2.65218049337 + 1265.81129610991*$t);
   $Y2 += 0.00000002483*cos(3.30358671055 + 453.1810763355*$t);
   $Y2 += 0.00000002732*cos(3.33706438099 + 563.38739755489*$t);
   $Y2 += 0.00000002508*cos(0.10584642422 + 37.8555882595*$t);
   $Y2 += 0.00000002508*cos(5.05315792539 + 425.35753565121*$t);
   $Y2 += 0.00000002680*cos(1.03370719327 + 454.6655490438*$t);
   $Y2 += 0.00000002511*cos(1.57939297348 + 209.6107596584*$t);
   $Y2 += 0.00000002512*cos(0.17397391459 + 217.4750661846*$t);
   $Y2 += 0.00000002552*cos(4.09952672426 + 79.47883417571*$t);
   $Y2 += 0.00000002457*cos(1.09953412303 + 38.89811798311*$t);
   $Y2 += 0.00000002343*cos(3.50679449028 + 981.3875687218*$t);
   $Y2 += 0.00000002501*cos(3.24491806395 + 669.4009330803*$t);
   $Y2 += 0.00000002330*cos(2.37985529884 + 38.32866901151*$t);
   $Y2 += 0.00000002327*cos(5.10713891298 + 38.4250372311*$t);
   $Y2 += 0.00000002481*cos(0.85514029866 + 655.1738390787*$t);
   $Y2 += 0.00000002569*cos(2.65544269508 + 464.97504399731*$t);
   return $Y2*$t*$t;
}



   function Neptune_Y3($t) // 37 terms of order 3
{
   $Y3  = 0.00000985355*cos(5.40479271994 + 38.3768531213*$t);
   $Y3 += 0.00000482798*cos(2.40351592403 + 37.88921815429*$t);
   $Y3 += 0.00000416447*cos(5.08276459732 + 0.2438174835*$t);
   $Y3 += 0.00000303825*cos(5.25036318156 + 39.86132582961*$t);
   $Y3 += 0.00000089203*cos(6.23576998030 + 36.892380413*$t);
   $Y3 += 0.00000070862*cos(4.26820111330 + 76.50988875911*$t);
   $Y3 += 0.00000028900*cos(4.07922314280 + 41.3457985379*$t);
   $Y3 += 0.00000022279*cos(1.38807052555 + 206.42936592071*$t);
   $Y3 += 0.00000021480*cos(0.30279640762 + 220.6564599223*$t);
   $Y3 += 0.00000016157*cos(4.26502283154 + 522.8212355773*$t);
   $Y3 += 0.00000015714*cos(3.19639937559 + 537.0483295789*$t);
   $Y3 += 0.00000011404*cos(0.68881522230 + 35.40790770471*$t);
   $Y3 += 0.00000013199*cos(4.77296321336 + 7.3573644843*$t);
   $Y3 += 0.00000007024*cos(5.41129077346 + 3.21276290011*$t);
   $Y3 += 0.00000006772*cos(5.90918041474 + 69.3963417583*$t);
   $Y3 += 0.00000004517*cos(1.71813394760 + 45.49040012211*$t);
   $Y3 += 0.00000004523*cos(2.61625996387 + 31.2633061205*$t);
   $Y3 += 0.00000003682*cos(3.04341607939 + 98.6561710411*$t);
   $Y3 += 0.00000003656*cos(2.17226292493 + 968.64494742849*$t);
   $Y3 += 0.00000003927*cos(5.25979459691 + 426.8420083595*$t);
   $Y3 += 0.00000003199*cos(3.24406648940 + 1519.6765535255*$t);
   $Y3 += 0.00000003498*cos(4.84556329465 + 407.9344936969*$t);
   $Y3 += 0.00000003304*cos(3.81825313228 + 422.1615876985*$t);
   $Y3 += 0.00000003331*cos(3.54124873059 + 36.404745446*$t);
   $Y3 += 0.00000003244*cos(4.42247914038 + 484.2005649725*$t);
   $Y3 += 0.00000002689*cos(5.61171743826 + 441.06910236111*$t);
   $Y3 += 0.00000003247*cos(3.33592493083 + 498.42765897409*$t);
   $Y3 += 0.00000002651*cos(2.02749548795 + 304.84171947829*$t);
   $Y3 += 0.00000002645*cos(0.90433895865 + 461.77909604459*$t);
   $Y3 += 0.00000002542*cos(1.05108120438 + 444.5830566264*$t);
   $Y3 += 0.00000002524*cos(5.46978523129 + 433.9555553603*$t);
   $Y3 += 0.00000002472*cos(0.92177286185 + 319.06881347989*$t);
   $Y3 += 0.00000002355*cos(2.03272387563 + 447.552002043*$t);
   $Y3 += 0.00000002876*cos(3.65433810175 + 853.4401992355*$t);
   $Y3 += 0.00000002279*cos(6.20789133449 + 458.810150628*$t);
   $Y3 += 0.00000002147*cos(1.06531556689 + 175.40987728371*$t);
   $Y3 += 0.00000002637*cos(2.06613866653 + 73.5409433425*$t);
   return $Y3*$t*$t*$t;
}



   function Neptune_Y4($t) // 14 terms of order 4
{
   $Y4  = 0.00003455306*cos(2.04385259535 + 38.3768531213*$t);
   $Y4 += 0.00000047405*cos(0.64311364094 + 0.2438174835*$t);
   $Y4 += 0.00000021936*cos(4.30052120876 + 37.88921815429*$t);
   $Y4 += 0.00000015596*cos(0.30774488881 + 76.50988875911*$t);
   $Y4 += 0.00000017186*cos(3.96705739007 + 39.86132582961*$t);
   $Y4 += 0.00000017459*cos(3.25820107685 + 36.892380413*$t);
   $Y4 += 0.00000004229*cos(6.14484758916 + 515.70768857651*$t);
   $Y4 += 0.00000004334*cos(3.84568484898 + 433.9555553603*$t);
   $Y4 += 0.00000003547*cos(1.04322259069 + 989.98558843089*$t);
   $Y4 += 0.00000003155*cos(0.14083942013 + 467.40817033709*$t);
   $Y4 += 0.00000003017*cos(4.77718347184 + 227.77000692311*$t);
   $Y4 += 0.00000002981*cos(5.01159762849 + 1.7282901918*$t);
   $Y4 += 0.00000002295*cos(4.84988240730 + 220.6564599223*$t);
   $Y4 += 0.00000002296*cos(3.13566627364 + 206.42936592071*$t);
   return $Y4*$t*$t*$t*$t;
}



   function Neptune_Y5($t) // 1 term of order 5
{
   $Y5  = 0.00000026291*cos(2.14645097520 + 38.3768531213*$t);
   return $Y5*$t*$t*$t*$t*$t;
}



   function Neptune_Z0($t) // 133 terms of order 0
{
   $Z0  = 0.92866054405*cos(1.44103930278 + 38.1330356378*$t);
   $Z0 += 0.01245978462;
   $Z0 += 0.00474333567*cos(2.52218774238 + 36.6485629295*$t);
   $Z0 += 0.00451987936*cos(3.50949720541 + 39.6175083461*$t);
   $Z0 += 0.00417558068*cos(5.91310695421 + 76.2660712756*$t);
   $Z0 += 0.00084104329*cos(4.38928900096 + 1.4844727083*$t);
   $Z0 += 0.00032704958*cos(1.52048692001 + 74.7815985673*$t);
   $Z0 += 0.00030873335*cos(3.29017611456 + 35.1640902212*$t);
   $Z0 += 0.00025812584*cos(3.19303128782 + 2.9689454166*$t);
   $Z0 += 0.00016865319*cos(2.13251104425 + 41.1019810544*$t);
   $Z0 += 0.00011789909*cos(3.60001877675 + 213.299095438*$t);
   $Z0 += 0.00009770125*cos(2.80133971586 + 73.297125859*$t);
   $Z0 += 0.00011279680*cos(3.55816676334 + 529.6909650946*$t);
   $Z0 += 0.00004119873*cos(1.67934316836 + 77.7505439839*$t);
   $Z0 += 0.00002818034*cos(4.10661077794 + 114.3991069134*$t);
   $Z0 += 0.00002868677*cos(4.27011526203 + 33.6796175129*$t);
   $Z0 += 0.00002213464*cos(1.96045135168 + 4.4534181249*$t);
   $Z0 += 0.00001865650*cos(5.05540709577 + 71.8126531507*$t);
   $Z0 += 0.00000840177*cos(0.94268885160 + 42.5864537627*$t);
   $Z0 += 0.00000457516*cos(5.71650412080 + 108.4612160802*$t);
   $Z0 += 0.00000530252*cos(0.85800267793 + 111.4301614968*$t);
   $Z0 += 0.00000490859*cos(6.07827301209 + 112.9146342051*$t);
   $Z0 += 0.00000331254*cos(0.29304964526 + 70.3281804424*$t);
   $Z0 += 0.00000330045*cos(2.83839676215 + 426.598190876*$t);
   $Z0 += 0.00000273589*cos(3.91013681794 + 1059.3819301892*$t);
   $Z0 += 0.00000277586*cos(1.45092010545 + 148.0787244263*$t);
   $Z0 += 0.00000274474*cos(5.42657022437 + 32.1951448046*$t);
   $Z0 += 0.00000205306*cos(0.75818737085 + 5.9378908332*$t);
   $Z0 += 0.00000173516*cos(5.85498030099 + 145.1097790097*$t);
   $Z0 += 0.00000141275*cos(1.73147597657 + 28.5718080822*$t);
   $Z0 += 0.00000139093*cos(1.67466701191 + 184.7272873558*$t);
   $Z0 += 0.00000143647*cos(2.51620047812 + 37.611770776*$t);
   $Z0 += 0.00000136955*cos(0.20339778664 + 79.2350166922*$t);
   $Z0 += 0.00000126296*cos(4.40661385040 + 37.1698277913*$t);
   $Z0 += 0.00000120906*cos(1.61767636602 + 39.0962434843*$t);
   $Z0 += 0.00000111761*cos(6.20948230785 + 98.8999885246*$t);
   $Z0 += 0.00000140758*cos(3.50944989694 + 38.6543004996*$t);
   $Z0 += 0.00000111589*cos(4.18561395578 + 47.6942631934*$t);
   $Z0 += 0.00000133509*cos(4.78977105547 + 38.084851528*$t);
   $Z0 += 0.00000102622*cos(0.81673762159 + 4.192785694*$t);
   $Z0 += 0.00000133292*cos(1.23386935925 + 38.1812197476*$t);
   $Z0 += 0.00000098771*cos(0.72335005782 + 106.9767433719*$t);
   $Z0 += 0.00000093919*cos(0.56607810948 + 206.1855484372*$t);
   $Z0 += 0.00000081727*cos(3.47861315258 + 220.4126424388*$t);
   $Z0 += 0.00000074559*cos(2.31518880439 + 312.1990839626*$t);
   $Z0 += 0.00000074401*cos(5.99935727164 + 181.7583419392*$t);
   $Z0 += 0.00000073141*cos(1.80069951634 + 137.0330241624*$t);
   $Z0 += 0.00000066838*cos(1.87185330904 + 221.3758502853*$t);
   $Z0 += 0.00000058303*cos(5.61662561548 + 35.685355083*$t);
   $Z0 += 0.00000051685*cos(6.02831347649 + 44.070926471*$t);
   $Z0 += 0.00000051928*cos(0.40473854286 + 40.5807161926*$t);
   $Z0 += 0.00000048182*cos(2.97141991737 + 37.8724032069*$t);
   $Z0 += 0.00000049439*cos(1.66178905717 + 68.8437077341*$t);
   $Z0 += 0.00000047742*cos(3.05261105371 + 38.3936680687*$t);
   $Z0 += 0.00000046428*cos(2.66596739242 + 146.594251718*$t);
   $Z0 += 0.00000050936*cos(0.19994012329 + 30.0562807905*$t);
   $Z0 += 0.00000041127*cos(6.05239303825 + 115.8835796217*$t);
   $Z0 += 0.00000055537*cos(2.11977296055 + 109.9456887885*$t);
   $Z0 += 0.00000041357*cos(0.86667380713 + 143.6253063014*$t);
   $Z0 += 0.00000044492*cos(6.00613878606 + 149.5631971346*$t);
   $Z0 += 0.00000037856*cos(5.19945796177 + 72.0732855816*$t);
   $Z0 += 0.00000047361*cos(3.58964541604 + 38.0211610532*$t);
   $Z0 += 0.00000034690*cos(1.47398766326 + 8.0767548473*$t);
   $Z0 += 0.00000037349*cos(5.15067903040 + 33.9402499438*$t);
   $Z0 += 0.00000034386*cos(6.15246630929 + 218.4069048687*$t);
   $Z0 += 0.00000047180*cos(2.43405967107 + 38.2449102224*$t);
   $Z0 += 0.00000033382*cos(0.88396990078 + 42.3258213318*$t);
   $Z0 += 0.00000040753*cos(3.59668759304 + 522.5774180938*$t);
   $Z0 += 0.00000033071*cos(2.02572550598 + 258.0244132148*$t);
   $Z0 += 0.00000038849*cos(5.79294381756 + 46.2097904851*$t);
   $Z0 += 0.00000031716*cos(0.30412624027 + 536.8045120954*$t);
   $Z0 += 0.00000027605*cos(2.81540405940 + 183.2428146475*$t);
   $Z0 += 0.00000024616*cos(0.40597272412 + 30.7106720963*$t);
   $Z0 += 0.00000021716*cos(0.90792314747 + 175.1660598002*$t);
   $Z0 += 0.00000021634*cos(3.25469228647 + 388.4651552382*$t);
   $Z0 += 0.00000020384*cos(5.80954414865 + 7.4223635415*$t);
   $Z0 += 0.00000018640*cos(1.06424642993 + 180.2738692309*$t);
   $Z0 += 0.00000016716*cos(0.02332590259 + 255.0554677982*$t);
   $Z0 += 0.00000018790*cos(0.62408059806 + 35.212274331*$t);
   $Z0 += 0.00000016990*cos(2.19726523790 + 294.6729761443*$t);
   $Z0 += 0.00000016083*cos(4.20629091415 + 0.9632078465*$t);
   $Z0 += 0.00000021571*cos(2.39337706760 + 152.5321425512*$t);
   $Z0 += 0.00000017102*cos(5.39964889794 + 41.0537969446*$t);
   $Z0 += 0.00000014503*cos(4.66614523797 + 110.2063212194*$t);
   $Z0 += 0.00000015218*cos(2.93182248771 + 219.891377577*$t);
   $Z0 += 0.00000014757*cos(2.02029526083 + 105.4922706636*$t);
   $Z0 += 0.00000013303*cos(2.09362099250 + 639.897286314*$t);
   $Z0 += 0.00000013582*cos(0.99222619680 + 44.7253177768*$t);
   $Z0 += 0.00000011309*cos(4.15253392707 + 487.3651437628*$t);
   $Z0 += 0.00000012521*cos(0.41449986025 + 186.2117600641*$t);
   $Z0 += 0.00000012363*cos(3.07599476497 + 6.592282139*$t);
   $Z0 += 0.00000010825*cos(4.13817476053 + 0.5212648618*$t);
   $Z0 += 0.00000014304*cos(5.15644933777 + 31.5407534988*$t);
   $Z0 += 0.00000010056*cos(4.27077049743 + 1589.0728952838*$t);
   $Z0 += 0.00000009355*cos(1.23360360711 + 216.9224321604*$t);
   $Z0 += 0.00000008774*cos(5.77195684843 + 12.5301729722*$t);
   $Z0 += 0.00000008445*cos(0.17584724644 + 291.7040307277*$t);
   $Z0 += 0.00000008927*cos(2.36869187243 + 331.3215390738*$t);
   $Z0 += 0.00000009613*cos(0.28151591238 + 60.7669528868*$t);
   $Z0 += 0.00000008279*cos(5.72084525545 + 36.7604375141*$t);
   $Z0 += 0.00000009111*cos(3.49027191661 + 45.2465826386*$t);
   $Z0 += 0.00000008178*cos(0.25637861075 + 39.5056337615*$t);
   $Z0 += 0.00000008598*cos(3.10287346009 + 256.5399405065*$t);
   $Z0 += 0.00000009489*cos(4.94205919676 + 151.0476698429*$t);
   $Z0 += 0.00000008564*cos(2.15904622462 + 274.0660483248*$t);
   $Z0 += 0.00000007474*cos(2.93279436008 + 27.0873353739*$t);
   $Z0 += 0.00000007944*cos(0.38277699900 + 10213.285546211*$t);
   $Z0 += 0.00000007132*cos(1.50971234331 + 944.9828232758*$t);
   $Z0 += 0.00000009005*cos(0.07284074730 + 419.4846438752*$t);
   $Z0 += 0.00000007642*cos(5.56097006597 + 187.6962327724*$t);
   $Z0 += 0.00000007705*cos(1.54152595157 + 84.3428261229*$t);
   $Z0 += 0.00000006896*cos(4.71453324740 + 406.1031376411*$t);
   $Z0 += 0.00000007282*cos(5.81348163927 + 316.3918696566*$t);
   $Z0 += 0.00000006215*cos(5.27967153537 + 7.1135470008*$t);
   $Z0 += 0.00000006090*cos(4.48506819561 + 415.2918581812*$t);
   $Z0 += 0.00000006316*cos(0.59502514374 + 453.424893819*$t);
   $Z0 += 0.00000006177*cos(5.20115334051 + 80.7194894005*$t);
   $Z0 += 0.00000006324*cos(2.18406254461 + 142.1408335931*$t);
   $Z0 += 0.00000005646*cos(0.76840537906 + 11.0457002639*$t);
   $Z0 += 0.00000006102*cos(5.58764378724 + 662.531203563*$t);
   $Z0 += 0.00000005334*cos(4.52703538458 + 103.0927742186*$t);
   $Z0 += 0.00000006269*cos(1.95162790177 + 605.9570363702*$t);
   $Z0 += 0.00000005591*cos(5.20631788297 + 14.0146456805*$t);
   $Z0 += 0.00000004914*cos(1.39906038110 + 253.5709950899*$t);
   $Z0 += 0.00000004519*cos(2.07610590431 + 2042.4977891028*$t);
   $Z0 += 0.00000005681*cos(4.80791039970 + 641.1211265914*$t);
   $Z0 += 0.00000006294*cos(0.56936923702 + 31.019488637*$t);
   $Z0 += 0.00000004758*cos(2.54312258712 + 367.9701020033*$t);
   $Z0 += 0.00000004406*cos(0.33696669222 + 328.3525936572*$t);
   $Z0 += 0.00000004390*cos(5.08949604858 + 286.596221297*$t);
   $Z0 += 0.00000004678*cos(4.87546696295 + 442.7517005706*$t);
   $Z0 += 0.00000004407*cos(5.58110402011 + 252.0865223816*$t);
   $Z0 += 0.00000004305*cos(1.31724140028 + 493.0424021651*$t);
   return $Z0;
}



   function Neptune_Z1($t) // 61 terms of order 1
{
   $Z1  = 0.06832633707*cos(3.80782656293 + 38.1330356378*$t);
   $Z1 -= 0.00064598028;
   $Z1 += 0.00042738331*cos(4.82540335637 + 36.6485629295*$t);
   $Z1 += 0.00031421638*cos(6.08083255385 + 39.6175083461*$t);
   $Z1 += 0.00027088623*cos(1.97557659098 + 76.2660712756*$t);
   $Z1 += 0.00005924197*cos(0.48500737803 + 1.4844727083*$t);
   $Z1 += 0.00002429056*cos(3.86784381378 + 74.7815985673*$t);
   $Z1 += 0.00002107258*cos(6.19720726581 + 35.1640902212*$t);
   $Z1 += 0.00001644542*cos(5.76041185818 + 2.9689454166*$t);
   $Z1 += 0.00001059588*cos(4.89687990866 + 41.1019810544*$t);
   $Z1 += 0.00001084464*cos(5.33722455731 + 213.299095438*$t);
   $Z1 += 0.00000880611*cos(5.70150456912 + 529.6909650946*$t);
   $Z1 += 0.00000824125*cos(5.04137560987 + 73.297125859*$t);
   $Z1 += 0.00000250821*cos(4.25953295692 + 77.7505439839*$t);
   $Z1 += 0.00000158517*cos(0.13500997625 + 114.3991069134*$t);
   $Z1 += 0.00000129390*cos(4.76999039957 + 4.4534181249*$t);
   $Z1 += 0.00000105033*cos(0.99234583035 + 33.6796175129*$t);
   $Z1 += 0.00000054734*cos(3.96812588022 + 42.5864537627*$t);
   $Z1 += 0.00000034799*cos(4.30403521625 + 37.611770776*$t);
   $Z1 += 0.00000041340*cos(2.29314729799 + 206.1855484372*$t);
   $Z1 += 0.00000028374*cos(1.67853213747 + 111.4301614968*$t);
   $Z1 += 0.00000025340*cos(1.70015942799 + 220.4126424388*$t);
   $Z1 += 0.00000026021*cos(6.09040669128 + 426.598190876*$t);
   $Z1 += 0.00000027198*cos(5.95188476775 + 71.8126531507*$t);
   $Z1 += 0.00000021598*cos(2.17619854748 + 112.9146342051*$t);
   $Z1 += 0.00000025154*cos(4.13631230281 + 28.5718080822*$t);
   $Z1 += 0.00000020543*cos(1.56946393801 + 38.6543004996*$t);
   $Z1 += 0.00000017216*cos(2.81703507859 + 98.8999885246*$t);
   $Z1 += 0.00000019926*cos(3.15301554161 + 108.4612160802*$t);
   $Z1 += 0.00000015544*cos(2.07364839388 + 40.5807161926*$t);
   $Z1 += 0.00000015357*cos(5.45891321516 + 522.5774180938*$t);
   $Z1 += 0.00000012266*cos(3.82427247378 + 5.9378908332*$t);
   $Z1 += 0.00000013587*cos(1.34795861192 + 47.6942631934*$t);
   $Z1 += 0.00000010839*cos(4.75461825384 + 536.8045120954*$t);
   $Z1 += 0.00000010785*cos(2.61566414257 + 79.2350166922*$t);
   $Z1 += 0.00000010916*cos(3.88744647444 + 35.685355083*$t);
   $Z1 += 0.00000009833*cos(3.62341506247 + 38.1812197476*$t);
   $Z1 += 0.00000009849*cos(0.89613145346 + 38.084851528*$t);
   $Z1 += 0.00000009317*cos(0.51297445145 + 37.1698277913*$t);
   $Z1 += 0.00000008955*cos(4.00532631258 + 39.0962434843*$t);
   $Z1 += 0.00000007089*cos(2.29610703652 + 137.0330241624*$t);
   $Z1 += 0.00000007573*cos(3.20619266484 + 4.192785694*$t);
   $Z1 += 0.00000008063*cos(5.86511590361 + 1059.3819301892*$t);
   $Z1 += 0.00000007655*cos(3.39616255650 + 145.1097790097*$t);
   $Z1 += 0.00000006061*cos(2.31235275416 + 109.9456887885*$t);
   $Z1 += 0.00000005726*cos(6.23400745185 + 312.1990839626*$t);
   $Z1 += 0.00000003739*cos(2.50010254963 + 30.0562807905*$t);
   $Z1 += 0.00000004145*cos(2.00938305966 + 44.070926471*$t);
   $Z1 += 0.00000003480*cos(5.88971113590 + 38.0211610532*$t);
   $Z1 += 0.00000003467*cos(4.73412534395 + 38.2449102224*$t);
   $Z1 += 0.00000004736*cos(6.28313624461 + 149.5631971346*$t);
   $Z1 += 0.00000003905*cos(4.49400805134 + 106.9767433719*$t);
   $Z1 += 0.00000002982*cos(1.80386443362 + 46.2097904851*$t);
   $Z1 += 0.00000003538*cos(5.27114846878 + 37.8724032069*$t);
   $Z1 += 0.00000003508*cos(5.35267669439 + 38.3936680687*$t);
   $Z1 += 0.00000002821*cos(1.10242173566 + 33.9402499438*$t);
   $Z1 += 0.00000003150*cos(2.14792830412 + 115.8835796217*$t);
   $Z1 += 0.00000003329*cos(3.56226463770 + 181.7583419392*$t);
   $Z1 += 0.00000002787*cos(1.21334651843 + 72.0732855816*$t);
   $Z1 += 0.00000002453*cos(3.18401661435 + 42.3258213318*$t);
   $Z1 += 0.00000002523*cos(5.51669920239 + 8.0767548473*$t);
   return $Z1*$t;
}



   function Neptune_Z2($t) // 20 terms of order 2
{
   $Z2  = 0.00291361164*cos(5.57085222635 + 38.1330356378*$t);
   $Z2 += 0.00002207820*cos(0.45423510946 + 36.6485629295*$t);
   $Z2 -= 0.00002644401;
   $Z2 += 0.00001184984*cos(3.62696666572 + 76.2660712756*$t);
   $Z2 += 0.00000875873*cos(1.60783110298 + 39.6175083461*$t);
   $Z2 += 0.00000253280*cos(2.25499665308 + 1.4844727083*$t);
   $Z2 += 0.00000139875*cos(1.66224942942 + 35.1640902212*$t);
   $Z2 += 0.00000105837*cos(5.61746558118 + 74.7815985673*$t);
   $Z2 += 0.00000055479*cos(0.51417309302 + 213.299095438*$t);
   $Z2 += 0.00000051858*cos(1.20450519900 + 2.9689454166*$t);
   $Z2 += 0.00000040183*cos(1.45604293605 + 529.6909650946*$t);
   $Z2 += 0.00000041153*cos(0.64158589676 + 73.297125859*$t);
   $Z2 += 0.00000013931*cos(0.27428875486 + 41.1019810544*$t);
   $Z2 += 0.00000009181*cos(2.83312722213 + 33.6796175129*$t);
   $Z2 += 0.00000007421*cos(4.32019600438 + 206.1855484372*$t);
   $Z2 += 0.00000006998*cos(5.87666052849 + 77.7505439839*$t);
   $Z2 += 0.00000007085*cos(1.66037085233 + 71.8126531507*$t);
   $Z2 += 0.00000006818*cos(1.56386946094 + 114.3991069134*$t);
   $Z2 += 0.00000004838*cos(0.83470875824 + 220.4126424388*$t);
   $Z2 += 0.00000002545*cos(0.43712705655 + 4.4534181249*$t);
   return $Z2*$t*$t;
}



   function Neptune_Z3($t) // 8 terms of order 3
{
   $Z3  = 0.00008221290*cos(1.01632472042 + 38.1330356378*$t);
   $Z3 += 0.00000103933;
   $Z3 += 0.00000070154*cos(2.36502685986 + 36.6485629295*$t);
   $Z3 += 0.00000031617*cos(5.35266161292 + 76.2660712756*$t);
   $Z3 += 0.00000015470*cos(3.21170859085 + 39.6175083461*$t);
   $Z3 += 0.00000007111*cos(3.99067059016 + 1.4844727083*$t);
   $Z3 += 0.00000004656*cos(3.62376309338 + 35.1640902212*$t);
   $Z3 += 0.00000002988*cos(1.03727330540 + 74.7815985673*$t);
   return $Z3*$t*$t*$t;
}



   function Neptune_Z4($t) // 1 term of order 4
{
   $Z4  = 0.00000172227*cos(2.66872693322 + 38.1330356378*$t);
   return $Z4*$t*$t*$t*$t;
}



   function Neptune_Z5($t) // 1 term of order 5
{
   $Z5  = 0.00000003394*cos(4.70646877989 + 38.1330356378*$t);
   return $Z5*$t*$t*$t*$t*$t;
}


?>