<?PHP

/*

   ******************************************************
   MERCURY

   Heliocentric Coords Module - VSOP 87 Theory - Series C3

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

   Module Range: 2000 BC  to  6000 AD

   Written in PHP v5.2.5

   This source code is released to the public domain.

   Jay Tanner
   VSOP87@NeoProgrammics.com

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

*/


   function Mercury_hXYZR($JDArg)
{

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

// Compute the heliocentric coordinates for time ($t).
   $hX = Mercury_X0($t) + Mercury_X1($t) + Mercury_X2($t)
       + Mercury_X3($t) + Mercury_X4($t) + Mercury_X5($t);

   $hY = Mercury_Y0($t) + Mercury_Y1($t) + Mercury_Y2($t)
       + Mercury_Y3($t) + Mercury_Y4($t) + Mercury_Y5($t);

   $hZ = Mercury_Z0($t) + Mercury_Z1($t) + Mercury_Z2($t)
       + Mercury_Z3($t) + Mercury_Z4($t) + Mercury_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";

}





/*

   Mercury - VSOP87 Series Version C3 - Rectangular (X,Y,Z) Coordinates

   X = X-Coordinate in AU (Astronomical Units)
   Y = Y-Coordinate in AU
   Z = Z-Coordinate in AU

   R*R = (X*X + Y*Y + Z*Z)

   HELIOCENTRIC DYNAMICAL ECLIPTIC AND EQUINOX OF THE DATE

   PHP Language
   VSOP87 Functions Source Code
   Generated By NeoProgrammics VSOP87 Code Generator
   (c) Jay Tanner 2008

   Ref:
   Astronomy & Astrophysics
   vol. 202, p309-p315
   Pierre Bretagnon, Gerard Francou
   1988

*/


   function Mercury_X0($t) // 1853 terms of order 0
{
   $X0  = 0.37749277893*cos(4.40259139579 + 26088.1469590577*$t);
   $X0 += 0.11918926148*cos(4.49027758439 + 0.2438174835*$t);
   $X0 += 0.03840153904*cos(1.17015646101 + 52176.0501006319*$t);
   $X0 += 0.00585979278*cos(4.22090402969 + 78263.95324220609*$t);
   $X0 += 0.00305833424*cos(2.10298673336 + 26087.65932409069*$t);
   $X0 += 0.00105974941*cos(0.98846517420 + 104351.85638378029*$t);
   $X0 += 0.00024906132*cos(5.26305668971 + 52175.56246566489*$t);
   $X0 += 0.00021056065*cos(4.03921104994 + 130439.75952535449*$t);
   $X0 += 0.00004441671*cos(0.80677167456 + 156527.66266692868*$t);
   $X0 += 0.00003347442*cos(2.10873209401 + 78263.46560723908*$t);
   $X0 += 0.00000976617*cos(3.85751708019 + 182615.56580850288*$t);
   $X0 += 0.00000703903*cos(4.46040321768 + 24978.7684069643*$t);
   $X0 += 0.00000640528*cos(1.20142454428 + 27197.5255111511*$t);
   $X0 += 0.00000558149*cos(5.21749759764 + 104351.36874881329*$t);
   $X0 += 0.00000447775*cos(2.97591075236 + 1059.6257476727*$t);
   $X0 += 0.00000400281*cos(1.86944903196 + 20426.8149099055*$t);
   $X0 += 0.00000283882*cos(3.79350724209 + 31749.4790082099*$t);
   $X0 += 0.00000191007*cos(4.27537754512 + 53285.4286527253*$t);
   $X0 += 0.00000181454*cos(4.95018365158 + 1109.1347346099*$t);
   $X0 += 0.00000193895*cos(0.67633415224 + 4552.1973145423*$t);
   $X0 += 0.00000221371*cos(0.62507677073 + 208703.46895007708*$t);
   $X0 += 0.00000139001*cos(1.22954955274 + 51066.6715485385*$t);
   $X0 += 0.00000183933*cos(1.19500306041 + 5661.0882316687*$t);
   $X0 += 0.00000153303*cos(2.68451868547 + 51116.6681704427*$t);
   $X0 += 0.00000104855*cos(2.02959651352 + 130439.27189038748*$t);
   $X0 += 0.00000115202*cos(0.56691147306 + 57837.3821497841*$t);
   $X0 += 0.00000090628*cos(0.25792152823 + 529.9347825781*$t);
   $X0 += 0.00000075318*cos(6.07215712399 + 27147.5288892469*$t);
   $X0 += 0.00000072957*cos(5.00412566043 + 21536.1934619989*$t);
   $X0 += 0.00000074803*cos(4.92914440147 + 46514.7180514797*$t);
   $X0 += 0.00000068710*cos(0.20379815554 + 25132.5472174491*$t);
   $X0 += 0.00000083504*cos(3.17939445535 + 10213.5293636945*$t);
   $X0 += 0.00000060985*cos(5.45128332631 + 27043.7467006663*$t);
   $X0 += 0.00000057987*cos(5.70479654236 + 14765.48286075331*$t);
   $X0 += 0.00000060953*cos(5.00244327341 + 47624.0966035731*$t);
   $X0 += 0.00000053356*cos(2.29756051926 + 26617.8379241523*$t);
   $X0 += 0.00000054964*cos(5.31144278536 + 12566.3955174663*$t);
   $X0 += 0.00000047881*cos(1.04626983477 + 79373.33179429949*$t);
   $X0 += 0.00000051263*cos(3.53744966658 + 426.8420083595*$t);
   $X0 += 0.00000051361*cos(3.67582188055 + 234791.37209165128*$t);
   $X0 += 0.00000050374*cos(3.60286953784 + 25558.4559939631*$t);
   $X0 += 0.00000048449*cos(3.51993896091 + 1589.3167127673*$t);
   $X0 += 0.00000048867*cos(5.73548681205 + 77204.57131201689*$t);
   $X0 += 0.00000034739*cos(5.68510489030 + 51646.3591355373*$t);
   $X0 += 0.00000032851*cos(2.99883640297 + 955.3559241251*$t);
   $X0 += 0.00000044998*cos(2.48247314947 + 41962.7645544209*$t);
   $X0 += 0.00000031618*cos(6.23993881626 + 37410.8110573621*$t);
   $X0 += 0.00000028634*cos(0.71509820566 + 30640.1004561165*$t);
   $X0 += 0.00000031480*cos(4.28075443320 + 77154.57469011268*$t);
   $X0 += 0.00000032102*cos(3.61877734434 + 83925.28529135829*$t);
   $X0 += 0.00000027670*cos(0.34889366405 + 39609.8984006491*$t);
   $X0 += 0.00000026872*cos(6.26000952694 + 36301.4325052687*$t);
   $X0 += 0.00000023054*cos(2.29052909388 + 53131.6498422405*$t);
   $X0 += 0.00000026193*cos(3.69823179514 + 11322.42028082089*$t);
   $X0 += 0.00000021235*cos(5.11548231564 + 156527.17503196168*$t);
   $X0 += 0.00000026946*cos(1.76252593609 + 6283.3196674749*$t);
   $X0 += 0.00000020875*cos(5.66887296875 + 15874.8614128467*$t);
   $X0 += 0.00000016454*cos(1.69895735267 + 72602.62119305388*$t);
   $X0 += 0.00000016101*cos(3.22620073160 + 9104.1508116011*$t);
   $X0 += 0.00000022241*cos(4.03643224642 + 13521.50762410789*$t);
   $X0 += 0.00000021188*cos(1.77076461428 + 73711.99974514729*$t);
   $X0 += 0.00000015123*cos(2.81544648697 + 18849.4713674577*$t);
   $X0 += 0.00000017255*cos(4.95346284309 + 27197.03787618409*$t);
   $X0 += 0.00000017287*cos(2.12451701243 + 51749.45190975589*$t);
   $X0 += 0.00000013862*cos(2.86403540216 + 53235.43203082109*$t);
   $X0 += 0.00000015239*cos(0.39591934360 + 7238.4317741165*$t);
   $X0 += 0.00000016863*cos(2.14228359969 + 50586.97720534809*$t);
   $X0 += 0.00000013546*cos(5.21986559185 + 52705.7410657265*$t);
   $X0 += 0.00000013134*cos(5.78471170881 + 25028.7650288685*$t);
   $X0 += 0.00000014145*cos(3.03635370573 + 63498.71419893629*$t);
   $X0 += 0.00000013081*cos(1.77889761864 + 26068.47719815791*$t);
   $X0 += 0.00000013058*cos(3.88464356096 + 26107.81671995749*$t);
   $X0 += 0.00000013609*cos(3.25855054515 + 51220.4503590233*$t);
   $X0 += 0.00000013539*cos(2.50293964820 + 103292.47445359109*$t);
   $X0 += 0.00000012138*cos(0.44338161953 + 260879.27523322542*$t);
   $X0 += 0.00000011433*cos(1.98105303514 + 19317.43635781211*$t);
   $X0 += 0.00000010174*cos(2.39402085953 + 77734.26227711148*$t);
   $X0 += 0.00000012016*cos(5.53519559373 + 68050.66769599509*$t);
   $X0 += 0.00000012094*cos(4.09914561799 + 105461.23493587368*$t);
   $X0 += 0.00000009215*cos(2.48225447254 + 40853.3860023275*$t);
   $X0 += 0.00000009157*cos(2.82670347755 + 33326.8225506577*$t);
   $X0 += 0.00000009552*cos(2.11034031277 + 38654.2986590405*$t);
   $X0 += 0.00000012500*cos(3.89244437690 + 45892.9742506405*$t);
   $X0 += 0.00000008978*cos(0.47617343198 + 26084.2656236997*$t);
   $X0 += 0.00000008975*cos(5.18743195952 + 26092.0282944157*$t);
   $X0 += 0.00000012160*cos(3.40664771625 + 65697.80154222329*$t);
   $X0 += 0.00000008880*cos(0.33806954264 + 26514.7451499337*$t);
   $X0 += 0.00000008892*cos(0.74770854519 + 3442.81876244891*$t);
   $X0 += 0.00000008503*cos(0.38676770328 + 110013.18843293248*$t);
   $X0 += 0.00000010244*cos(2.50326457964 + 21535.70582703189*$t);
   $X0 += 0.00000008816*cos(4.86930066154 + 32371.2228090491*$t);
   $X0 += 0.00000009705*cos(5.44815918458 + 529.44714761109*$t);
   $X0 += 0.00000007663*cos(3.73484444482 + 56728.0035976907*$t);
   $X0 += 0.00000007852*cos(0.65554683317 + 5661.5758666357*$t);
   $X0 += 0.00000008166*cos(0.32786623322 + 27677.2198543415*$t);
   $X0 += 0.00000007299*cos(1.14994821071 + 6770.46678376209*$t);
   $X0 += 0.00000007437*cos(3.67894554888 + 32858.8575603033*$t);
   $X0 += 0.00000007796*cos(1.18993742629 + 31748.99137324289*$t);
   $X0 += 0.00000006786*cos(2.43978460253 + 43072.1431065143*$t);
   $X0 += 0.00000007408*cos(4.54789639858 + 23869.3898548709*$t);
   $X0 += 0.00000005938*cos(5.34593352715 + 79219.55298381469*$t);
   $X0 += 0.00000007553*cos(1.04863475066 + 103242.47783168689*$t);
   $X0 += 0.00000005988*cos(3.04417882527 + 62389.33564684289*$t);
   $X0 += 0.00000006154*cos(5.99522472277 + 59414.7256922319*$t);
   $X0 += 0.00000006213*cos(0.75145729813 + 19805.0711090663*$t);
   $X0 += 0.00000006507*cos(1.06344526474 + 213.5429129215*$t);
   $X0 += 0.00000006284*cos(4.91987886888 + 22645.57201409229*$t);
   $X0 += 0.00000006068*cos(4.82277476434 + 99799.90288672148*$t);
   $X0 += 0.00000006276*cos(2.74748364541 + 640.1411037975*$t);
   $X0 += 0.00000006192*cos(1.11265105508 + 28306.90406324449*$t);
   $X0 += 0.00000006081*cos(5.23278439947 + 25874.8478636197*$t);
   $X0 += 0.00000004693*cos(6.19313162709 + 16983.75232997309*$t);
   $X0 += 0.00000004527*cos(1.91140424398 + 182615.07817353586*$t);
   $X0 += 0.00000005085*cos(0.33812112463 + 26301.4460544957*$t);
   $X0 += 0.00000004658*cos(4.11167846402 + 26095.2605060585*$t);
   $X0 += 0.00000005323*cos(2.15023457135 + 24978.28077199729*$t);
   $X0 += 0.00000004497*cos(1.59603827995 + 26081.03341205689*$t);
   $X0 += 0.00000005479*cos(5.17786692376 + 76674.88034692229*$t);
   $X0 += 0.00000003898*cos(4.75161525594 + 98690.52433462809*$t);
   $X0 += 0.00000005352*cos(5.17556723587 + 77837.35505133009*$t);
   $X0 += 0.00000003694*cos(0.48936321493 + 58946.76070187749*$t);
   $X0 += 0.00000003631*cos(5.55357343180 + 129380.37759516528*$t);
   $X0 += 0.00000004821*cos(3.64928863412 + 37410.32342239509*$t);
   $X0 += 0.00000003323*cos(1.95435021777 + 78793.64420730069*$t);
   $X0 += 0.00000003932*cos(0.76247078505 + 29530.7219040231*$t);
   $X0 += 0.00000004022*cos(4.06373546409 + 2119.00767786191*$t);
   $X0 += 0.00000003208*cos(5.89844713322 + 25557.96835899609*$t);
   $X0 += 0.00000003611*cos(0.17577280462 + 91785.70468379749*$t);
   $X0 += 0.00000003062*cos(5.92483558903 + 79323.33517239528*$t);
   $X0 += 0.00000003480*cos(0.66265476262 + 71980.87739221469*$t);
   $X0 += 0.00000003093*cos(2.30327965785 + 94138.57083756929*$t);
   $X0 += 0.00000003172*cos(3.00172025362 + 27043.2590656993*$t);
   $X0 += 0.00000002912*cos(3.49412631679 + 286967.17837479962*$t);
   $X0 += 0.00000003746*cos(6.08415745758 + 89586.61734051049*$t);
   $X0 += 0.00000002870*cos(5.51397391523 + 69160.04624808849*$t);
   $X0 += 0.00000002730*cos(5.88663339742 + 44937.3745090319*$t);
   $X0 += 0.00000002725*cos(5.42457603553 + 103822.16541868569*$t);
   $X0 += 0.00000003214*cos(4.87298940652 + 2218.51328670329*$t);
   $X0 += 0.00000002660*cos(4.82966654366 + 52156.38033973211*$t);
   $X0 += 0.00000003257*cos(2.71278189877 + 25934.3681485729*$t);
   $X0 += 0.00000002620*cos(5.77949301476 + 20426.32727493849*$t);
   $X0 += 0.00000003227*cos(2.95128548648 + 26241.9257695425*$t);
   $X0 += 0.00000003086*cos(0.02730531846 + 77308.35350059748*$t);
   $X0 += 0.00000003099*cos(0.86870364149 + 131549.13807744789*$t);
   $X0 += 0.00000002731*cos(0.19114675485 + 149.8070146181*$t);
   $X0 += 0.00000002486*cos(3.12136440583 + 1052.51220067191*$t);
   $X0 += 0.00000003167*cos(0.38944502659 + 33326.33491569069*$t);
   $X0 += 0.00000002680*cos(0.65295917827 + 52195.71986153169*$t);
   $X0 += 0.00000002231*cos(3.43792316659 + 136101.09157450669*$t);
   $X0 += 0.00000002653*cos(1.68316051523 + 7.3573644843*$t);
   $X0 += 0.00000002074*cos(4.96316067320 + 48733.47515566649*$t);
   $X0 += 0.00000001974*cos(5.16962188890 + 64742.2018006147*$t);
   $X0 += 0.00000002064*cos(0.21494181057 + 51116.18053547569*$t);
   $X0 += 0.00000002533*cos(6.02031593619 + 1066.7392946735*$t);
   $X0 += 0.00000001949*cos(1.68714181050 + 58459.1259506233*$t);
   $X0 += 0.00000002010*cos(2.44539246304 + 16984.2399649401*$t);
   $X0 += 0.00000001876*cos(0.49249036640 + 82815.90673926489*$t);
   $X0 += 0.00000001832*cos(1.95461512625 + 52179.9314359899*$t);
   $X0 += 0.00000002306*cos(4.20103483106 + 54394.80720481869*$t);
   $X0 += 0.00000001837*cos(5.53329054515 + 66941.2891439017*$t);
   $X0 += 0.00000001783*cos(1.94386918249 + 25620.1819687033*$t);
   $X0 += 0.00000001826*cos(3.52694014247 + 52172.1687652739*$t);
   $X0 += 0.00000001791*cos(5.32229718021 + 25661.5487681817*$t);
   $X0 += 0.00000002126*cos(2.91445652095 + 51536.15281431789*$t);
   $X0 += 0.00000001714*cos(3.72047839107 + 26556.11194941211*$t);
   $X0 += 0.00000001972*cos(5.03869626311 + 45405.3394993863*$t);
   $X0 += 0.00000001711*cos(1.11320004200 + 32858.36992533629*$t);
   $X0 += 0.00000001643*cos(3.40283361772 + 52602.6482915079*$t);
   $X0 += 0.00000001665*cos(3.83085129266 + 5327.7199258663*$t);
   $X0 += 0.00000001930*cos(5.78785787875 + 13656.10430865991*$t);
   $X0 += 0.00000001655*cos(1.59098456165 + 125887.80602829569*$t);
   $X0 += 0.00000001554*cos(3.40019334049 + 13521.9952590749*$t);
   $X0 += 0.00000001517*cos(3.39842653971 + 53765.1229959157*$t);
   $X0 += 0.00000001870*cos(4.09951350071 + 129330.38097326108*$t);
   $X0 += 0.00000001705*cos(6.14540598785 + 43071.65547154729*$t);
   $X0 += 0.00000001683*cos(4.32584442162 + 52168.93655363109*$t);
   $X0 += 0.00000001449*cos(6.10448204410 + 88477.23878841709*$t);
   $X0 += 0.00000001466*cos(5.27211735766 + 24499.0740637739*$t);
   $X0 += 0.00000001655*cos(6.12815645892 + 76.50988875911*$t);
   $X0 += 0.00000001539*cos(2.12176953420 + 105307.45612538888*$t);
   $X0 += 0.00000001542*cos(1.96595530367 + 102762.78348849648*$t);
   $X0 += 0.00000001400*cos(1.26185265808 + 26081.51840015769*$t);
   $X0 += 0.00000001400*cos(4.40173881619 + 26094.77551795771*$t);
   $X0 += 0.00000001415*cos(1.31785110641 + 49957.2929964451*$t);
   $X0 += 0.00000001545*cos(2.74460517130 + 85502.6288338061*$t);
   $X0 += 0.00000001259*cos(4.06949140437 + 51962.7510051939*$t);
   $X0 += 0.00000001464*cos(1.94328769190 + 103925.25819290428*$t);
   $X0 += 0.00000001265*cos(6.23687279994 + 35192.0539531753*$t);
   $X0 += 0.00000001563*cos(1.53248979312 + 6681.46867088311*$t);
   $X0 += 0.00000001517*cos(4.14158249910 + 213.0552779545*$t);
   $X0 += 0.00000001171*cos(4.44560816323 + 57836.89451481709*$t);
   $X0 += 0.00000001547*cos(3.43699337530 + 52389.3491960699*$t);
   $X0 += 0.00000001423*cos(1.60092130514 + 50057.2862402535*$t);
   $X0 += 0.00000001238*cos(0.84389836177 + 52183.1636476327*$t);
   $X0 += 0.00000001070*cos(5.82812348558 + 26728.0442453717*$t);
   $X0 += 0.00000001020*cos(3.63373915432 + 12431.79883291429*$t);
   $X0 += 0.00000000965*cos(2.32109036696 + 155468.28073673949*$t);
   $X0 += 0.00000001018*cos(5.37034692069 + 24498.58642880689*$t);
   $X0 += 0.00000000994*cos(3.22732624356 + 117873.60782537168*$t);
   $X0 += 0.00000001002*cos(4.98556762896 + 208702.98131511007*$t);
   $X0 += 0.00000001214*cos(2.58462840069 + 25661.06113321469*$t);
   $X0 += 0.00000000958*cos(1.52001998159 + 124778.42747620228*$t);
   $X0 += 0.00000000893*cos(3.52720868596 + 85034.66384345168*$t);
   $X0 += 0.00000000875*cos(1.72393184919 + 74821.37829724069*$t);
   $X0 += 0.00000000871*cos(0.27938200831 + 1059.1381127057*$t);
   $X0 += 0.00000000910*cos(3.71329662418 + 98068.78053378889*$t);
   $X0 += 0.00000000827*cos(2.44624289116 + 22645.08437912529*$t);
   $X0 += 0.00000000829*cos(4.98909621401 + 104881.54734887488*$t);
   $X0 += 0.00000000870*cos(5.31437509457 + 51066.18391357149*$t);
   $X0 += 0.00000000978*cos(6.15736380216 + 38520.1896094555*$t);
   $X0 += 0.00000000915*cos(1.34262350391 + 6.86972951729*$t);
   $X0 += 0.00000000855*cos(2.53346806421 + 51123.7817174435*$t);
   $X0 += 0.00000000795*cos(5.35307581508 + 120226.47397914348*$t);
   $X0 += 0.00000000778*cos(6.26214759185 + 11322.9079157879*$t);
   $X0 += 0.00000000913*cos(5.46819895663 + 52026.4869034973*$t);
   $X0 += 0.00000000930*cos(2.84523614939 + 115674.52048208468*$t);
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   $X0 += 0.00000000002*cos(1.72941826067 + 158745.93213614845*$t);
   $X0 += 0.00000000002*cos(5.48576882408 + 52367.49836674349*$t);
   $X0 += 0.00000000002*cos(6.20502032580 + 41520.61024889929*$t);
   $X0 += 0.00000000002*cos(4.14056597313 + 51950.2208322217*$t);
   $X0 += 0.00000000002*cos(2.55940503302 + 28133.4554918599*$t);
   $X0 += 0.00000000002*cos(3.10421999819 + 24042.8384262555*$t);
   $X0 += 0.00000000003*cos(2.17160326158 + 51753.38406301899*$t);
   $X0 += 0.00000000003*cos(6.15199422925 + 25633.23759253039*$t);
   $X0 += 0.00000000003*cos(5.79481610914 + 26543.05632558499*$t);
   $X0 += 0.00000000002*cos(3.97512757833 + 24999.54380245671*$t);
   $X0 += 0.00000000002*cos(1.68849745288 + 27176.75011565869*$t);
   $X0 += 0.00000000002*cos(0.30844272162 + 309.0345051723*$t);
   $X0 += 0.00000000002*cos(2.40438367720 + 1155.6049748905*$t);
   $X0 += 0.00000000002*cos(0.34200603730 + 236702.57157486846*$t);
   $X0 += 0.00000000002*cos(3.00390396144 + 76887.69180739328*$t);
   $X0 += 0.00000000002*cos(0.98682277986 + 4084.2323241879*$t);
   $X0 += 0.00000000002*cos(1.59074157843 + 24601.67920302549*$t);
   $X0 += 0.00000000002*cos(2.80906034932 + 27818.78167702329*$t);
   $X0 += 0.00000000002*cos(2.26687572256 + 2198.8435258035*$t);
   $X0 += 0.00000000002*cos(4.53134788435 + 24292.8885153367*$t);
   $X0 += 0.00000000002*cos(1.58580178730 + 22759.5236678105*$t);
   $X0 += 0.00000000002*cos(2.91202347140 + 27143.5967359838*$t);
   $X0 += 0.00000000002*cos(1.70541081745 + 25973.22003540546*$t);
   $X0 += 0.00000000002*cos(0.14177660173 + 10021.5934626159*$t);
   $X0 += 0.00000000002*cos(1.51917223670 + 20618.2631760171*$t);
   $X0 += 0.00000000002*cos(4.14445279451 + 31558.0307420983*$t);
   $X0 += 0.00000000002*cos(2.33949764052 + 2854.8841913937*$t);
   $X0 += 0.00000000002*cos(1.98831285254 + 51953.18977763829*$t);
   $X0 += 0.00000000002*cos(0.41604857841 + 51951.21766996299*$t);
   $X0 += 0.00000000002*cos(1.57183044674 + 52249.34722649089*$t);
   $X0 += 0.00000000002*cos(1.70818461045 + 138633.54722359608*$t);
   $X0 += 0.00000000002*cos(5.13575806013 + 225687.46509753366*$t);
   $X0 += 0.00000000002*cos(1.56258965853 + 138319.36104372646*$t);
   $X0 += 0.00000000002*cos(2.18966503711 + 32768.88417749029*$t);
   $X0 += 0.00000000002*cos(0.33098015159 + 24079.5894198987*$t);
   $X0 += 0.00000000002*cos(4.71436622522 + 52202.3484204317*$t);
   $X0 += 0.00000000002*cos(4.96992436419 + 28206.42318446909*$t);
   $X0 += 0.00000000002*cos(4.96216423435 + 180496.80194812448*$t);
   $X0 += 0.00000000002*cos(4.73660629226 + 78259.58427188109*$t);
   $X0 += 0.00000000002*cos(2.28401532959 + 26624.46383618609*$t);
   $X0 += 0.00000000002*cos(0.07960474111 + 23549.8984548041*$t);
   $X0 += 0.00000000002*cos(0.37327493336 + 26293.84487252789*$t);
   $X0 += 0.00000000002*cos(5.83913193896 + 4601.70630147949*$t);
   $X0 += 0.00000000002*cos(6.23015270329 + 21716.2705922835*$t);
   $X0 += 0.00000000002*cos(3.66936461651 + 330.8627811417*$t);
   $X0 += 0.00000000002*cos(1.51579465920 + 51219.27330969429*$t);
   $X0 += 0.00000000002*cos(5.05016618926 + 78256.35206023828*$t);
   $X0 += 0.00000000002*cos(3.58281342347 + 50063.91215228729*$t);
   $X0 += 0.00000000002*cos(1.42199745004 + 132658.02899457427*$t);
   $X0 += 0.00000000002*cos(3.28152370063 + 96.2230447013*$t);
   $X0 += 0.00000000002*cos(4.38858567715 + 1265.32366114289*$t);
   $X0 += 0.00000000002*cos(2.49109566786 + 52823.0609339467*$t);
   $X0 += 0.00000000002*cos(1.26800894276 + 78270.57915423988*$t);
   $X0 += 0.00000000002*cos(5.41071683840 + 7392.21058460129*$t);
   $X0 += 0.00000000002*cos(1.10270458425 + 61165.03017109729*$t);
   $X0 += 0.00000000002*cos(2.14950038663 + 2544.4288194089*$t);
   $X0 += 0.00000000002*cos(1.97162097641 + 26421.5152648601*$t);
   $X0 += 0.00000000002*cos(1.33257889355 + 2655.8121899573*$t);
   $X0 += 0.00000000002*cos(0.79025165001 + 24705.9490265731*$t);
   $X0 += 0.00000000002*cos(4.87337338120 + 27470.3448915423*$t);
   $X0 += 0.00000000002*cos(6.14740336072 + 1353.5049275333*$t);
   $X0 += 0.00000000002*cos(0.11906484226 + 1603.5438067689*$t);
   $X0 += 0.00000000002*cos(3.46701006002 + 40738.45907867528*$t);
   $X0 += 0.00000000002*cos(5.71504799272 + 30460.0233258319*$t);
   $X0 += 0.00000000002*cos(1.16042497962 + 4578.4956343421*$t);
   $X0 += 0.00000000002*cos(0.14527391572 + 78113.90241010448*$t);
   $X0 += 0.00000000002*cos(4.19897532608 + 32839.1877994035*$t);
   $X0 += 0.00000000002*cos(0.13374340654 + 14297.5178703989*$t);
   $X0 += 0.00000000002*cos(5.52988162467 + 37878.7760477165*$t);
   $X0 += 0.00000000002*cos(6.20542886765 + 104501.41958091488*$t);
   $X0 += 0.00000000002*cos(2.61097814223 + 25138.48371512089*$t);
   $X0 += 0.00000000002*cos(1.06395351693 + 44131.52503670349*$t);
   $X0 += 0.00000000002*cos(4.10426443523 + 104358.48229581409*$t);
   $X0 += 0.00000000002*cos(5.39518200455 + 23336.5993593661*$t);
   $X0 += 0.00000000002*cos(5.39518200455 + 23336.11172439909*$t);
   $X0 += 0.00000000002*cos(6.04499536111 + 224.1009782184*$t);
   $X0 += 0.00000000002*cos(3.63958668308 + 51547.19851458179*$t);
   $X0 += 0.00000000002*cos(3.16690823789 + 202.0095776906*$t);
   $X0 += 0.00000000002*cos(3.16690823789 + 202.4972126576*$t);
   $X0 += 0.00000000002*cos(6.25775046727 + 31108.06544647091*$t);
   $X0 += 0.00000000002*cos(5.68905987112 + 21068.2284716445*$t);
   $X0 += 0.00000000002*cos(2.96587029379 + 117076.82218358829*$t);
   $X0 += 0.00000000002*cos(6.10746294738 + 117077.30981855528*$t);
   $X0 += 0.00000000002*cos(5.38291113550 + 24814.97829846349*$t);
   $X0 += 0.00000000002*cos(1.98570847468 + 27299.4880294167*$t);
   $X0 += 0.00000000002*cos(3.67791655653 + 24876.8058886987*$t);
   $X0 += 0.00000000002*cos(2.83769263825 + 26086.17485138239*$t);
   $X0 += 0.00000000002*cos(5.74298703182 + 105418.35186097029*$t);
   $X0 += 0.00000000002*cos(2.69099617398 + 49534.7088221597*$t);
   $X0 += 0.00000000002*cos(4.25460776712 + 107679.99204006046*$t);
   $X0 += 0.00000000002*cos(1.43038533012 + 19337.1061187119*$t);
   $X0 += 0.00000000002*cos(1.80708255079 + 24957.9930114719*$t);
   $X0 += 0.00000000002*cos(3.85654248042 + 27218.3009066435*$t);
   $X0 += 0.00000000002*cos(3.46898572008 + 66826.36222024946*$t);
   $X0 += 0.00000000002*cos(3.11677200697 + 27257.7352104663*$t);
   $X0 += 0.00000000002*cos(1.54813681705 + 26197.86564531009*$t);
   $X0 += 0.00000000002*cos(2.26084282341 + 151199.69892357888*$t);
   $X0 += 0.00000000002*cos(2.41505887981 + 426.1525939975*$t);
   $X0 += 0.00000000002*cos(2.05501019547 + 76784.59903317469*$t);
   $X0 += 0.00000000002*cos(5.17891248404 + 179172.50322857044*$t);
   $X0 += 0.00000000002*cos(3.03839569379 + 168959.21768235945*$t);
   $X0 += 0.00000000002*cos(3.03839569378 + 168959.70531732646*$t);
   $X0 += 0.00000000002*cos(6.05144227865 + 7829.84871395129*$t);
   $X0 += 0.00000000002*cos(2.93845777192 + 151975.22153490288*$t);
   $X0 += 0.00000000002*cos(5.56610117919 + 20235.36664379391*$t);
   $X0 += 0.00000000002*cos(0.09752385202 + 31940.9272743215*$t);
   $X0 += 0.00000000002*cos(0.34264055281 + 1585.38455950421*$t);
   $X0 += 0.00000000002*cos(3.25664376155 + 76.0222537921*$t);
   $X0 += 0.00000000002*cos(4.50673995632 + 1581.7155307995*$t);
   $X0 += 0.00000000002*cos(4.26102899883 + 52643.5274560193*$t);
   $X0 += 0.00000000002*cos(0.89847733804 + 130433.13096645445*$t);
   $X0 += 0.00000000002*cos(5.35295047368 + 79956.11891170849*$t);
   $X0 += 0.00000000002*cos(1.38123247936 + 190809.35350674443*$t);
   $X0 += 0.00000000002*cos(5.22748899717 + 155417.79647986828*$t);
   $X0 += 0.00000000002*cos(2.25472465461 + 58219.79104704029*$t);
   $X0 += 0.00000000002*cos(5.67352931908 + 299399.22102519739*$t);
   $X0 += 0.00000000002*cos(0.82971507937 + 51738.40620949199*$t);
   $X0 += 0.00000000002*cos(2.97072309926 + 2045.5523502857*$t);
   $X0 += 0.00000000002*cos(4.40886857181 + 27953.3783615753*$t);
   $X0 += 0.00000000002*cos(1.25475645940 + 24222.9155565401*$t);
   $X0 += 0.00000000002*cos(4.61765528518 + 164721.45036517028*$t);
   $X0 += 0.00000000002*cos(0.02963994293 + 28441.0131128295*$t);
   $X0 += 0.00000000002*cos(5.63398508828 + 23735.2808052859*$t);
   $X0 += 0.00000000002*cos(4.94052786966 + 26948.4568878105*$t);
   $X0 += 0.00000000002*cos(0.72309716155 + 25227.83703030489*$t);
   $X0 += 0.00000000002*cos(2.26852923431 + 148532.64658993746*$t);
   $X0 += 0.00000000002*cos(2.26852923431 + 148533.13422490445*$t);
   $X0 += 0.00000000002*cos(1.51852948979 + 77307.17645126847*$t);
   $X0 += 0.00000000002*cos(6.10588157940 + 191.6920835951*$t);
   $X0 += 0.00000000002*cos(0.34186830904 + 23976.00901071309*$t);
   $X0 += 0.00000000002*cos(4.08150026692 + 206370.27255720507*$t);
   $X0 += 0.00000000002*cos(5.05627960945 + 4268.3379956771*$t);
   $X0 += 0.00000000002*cos(1.84151604889 + 23962.2695516785*$t);
   $X0 += 0.00000000002*cos(1.84151604889 + 23961.78191671149*$t);
   $X0 += 0.00000000002*cos(4.35044814692 + 3776.6747032183*$t);
   $X0 += 0.00000000002*cos(2.20524904392 + 24918.55870764909*$t);
   $X0 += 0.00000000002*cos(3.21408526505 + 102769.40940053028*$t);
   $X0 += 0.00000000002*cos(2.12858110666 + 25889.0749576213*$t);
   $X0 += 0.00000000002*cos(3.53504392455 + 26287.21896049409*$t);
   $X0 += 0.00000000002*cos(1.66367572246 + 2648.2110079895*$t);
   $X0 += 0.00000000002*cos(5.71672028658 + 80432.71372448868*$t);
   $X0 += 0.00000000002*cos(2.91629438354 + 13989.9602494293*$t);
   $X0 += 0.00000000002*cos(2.74733064767 + 38186.3336686861*$t);
   $X0 += 0.00000000002*cos(3.61656667123 + 8194.5191506921*$t);
   $X0 += 0.00000000002*cos(4.13822438475 + 237009.64156087102*$t);
   $X0 += 0.00000000002*cos(2.25489644524 + 24863.84148331209*$t);
   $X0 += 0.00000000002*cos(0.79435355035 + 76064.86589891909*$t);
   $X0 += 0.00000000002*cos(6.11153635623 + 71492.75500599349*$t);
   $X0 += 0.00000000002*cos(1.47457311729 + 30831.5487222281*$t);
   $X0 += 0.00000000002*cos(4.18905191391 + 21344.7451958873*$t);
   $X0 += 0.00000000002*cos(2.64103330733 + 124663.98818751707*$t);
   $X0 += 0.00000000001*cos(4.41626377495 + 101702.91392334028*$t);
   $X0 += 0.00000000002*cos(2.92553614920 + 105404.12476696869*$t);
   $X0 += 0.00000000002*cos(1.90962776233 + 307.31380348609*$t);
   $X0 += 0.00000000002*cos(1.20163121188 + 184834.32291268966*$t);
   $X0 += 0.00000000002*cos(4.34322386547 + 184833.83527772261*$t);
   $X0 += 0.00000000001*cos(5.20673509792 + 124156.19604039608*$t);
   $X0 += 0.00000000001*cos(3.29097711242 + 22909.51353352309*$t);
   $X0 += 0.00000000001*cos(3.29097711242 + 22910.0011684901*$t);
   $X0 += 0.00000000001*cos(4.22627101320 + 958.87904247409*$t);
   $X0 += 0.00000000002*cos(0.74624553136 + 77196.97013004909*$t);
   $X0 += 0.00000000002*cos(2.61684173604 + 9591.29792788829*$t);
   $X0 += 0.00000000002*cos(1.03105335724 + 189385.78877478145*$t);
   $X0 += 0.00000000001*cos(0.57809610749 + 24919.2481220111*$t);
   $X0 += 0.00000000001*cos(5.08552892372 + 27257.0457961043*$t);
   $X0 += 0.00000000002*cos(3.46440981619 + 25440.64849077589*$t);
   $X0 += 0.00000000001*cos(0.45556161499 + 26010.3964150738*$t);
   $X0 += 0.00000000002*cos(0.42518108376 + 43693.8869073535*$t);
   $X0 += 0.00000000002*cos(3.47315264300 + 25014.05029989989*$t);
   $X0 += 0.00000000001*cos(5.34981963981 + 9385.0848255587*$t);
   $X0 += 0.00000000002*cos(4.60292662632 + 26202.09861277591*$t);
   $X0 += 0.00000000001*cos(4.92214692877 + 52499.55551728929*$t);
   $X0 += 0.00000000002*cos(3.46155131960 + 14650.55593710108*$t);
   $X0 += 0.00000000002*cos(5.08759156576 + 78690.06379811508*$t);
   $X0 += 0.00000000001*cos(0.08764164508 + 5039.34443082949*$t);
   $X0 += 0.00000000002*cos(4.10611692906 + 2214.98690507971*$t);
   $X0 += 0.00000000001*cos(3.50305053765 + 77211.19722405069*$t);
   $X0 += 0.00000000001*cos(5.68985540916 + 233202.29919636747*$t);
   $X0 += 0.00000000002*cos(5.49174220323 + 21516.52370109911*$t);
   $X0 += 0.00000000002*cos(0.17188282798 + 30659.77021701629*$t);
   $X0 += 0.00000000002*cos(5.30439852095 + 621.49998335569*$t);
   $X0 += 0.00000000002*cos(1.13720629039 + 25764.15390743329*$t);
   $X0 += 0.00000000001*cos(5.32131294248 + 26.5421372833*$t);
   $X0 += 0.00000000001*cos(2.30545913825 + 226796.35601466001*$t);
   $X0 += 0.00000000001*cos(5.44705179184 + 226796.84364962706*$t);
   $X0 += 0.00000000002*cos(0.33446329498 + 28839.69455874929*$t);
   $X0 += 0.00000000002*cos(5.50347633955 + 102225.97897640108*$t);
   $X0 += 0.00000000002*cos(1.56059892812 + 129971.79453500008*$t);
   $X0 += 0.00000000002*cos(4.06465171282 + 27139.92770727909*$t);
   $X0 += 0.00000000001*cos(2.62468643294 + 50807.38984778689*$t);
   $X0 += 0.00000000001*cos(6.16306543539 + 78187.19953596349*$t);
   $X0 += 0.00000000002*cos(5.06371993416 + 51472.41691601449*$t);
   return $X0;
}



   function Mercury_X1($t) // 1023 terms of order 1
{
   $X1  = 0.00328639517*cos(6.04028758995 + 0.2438174835*$t);
   $X1 += 0.00106107047*cos(5.91538469937 + 52176.0501006319*$t);
   $X1 += 0.00032448440*cos(2.68404164136 + 78263.95324220609*$t);
   $X1 += 0.00009699418*cos(5.42935843059 + 26087.65932409069*$t);
   $X1 += 0.00008808490*cos(5.73515025839 + 104351.85638378029*$t);
   $X1 += 0.00004833058*cos(0.21935428474 + 26088.1469590577*$t);
   $X1 += 0.00002334329*cos(2.50289115433 + 130439.75952535449*$t);
   $X1 += 0.00000890250*cos(2.61758665086 + 52175.56246566489*$t);
   $X1 += 0.00000615643*cos(5.55374456387 + 156527.66266692868*$t);
   $X1 += 0.00000147225*cos(6.09730240676 + 78263.46560723908*$t);
   $X1 += 0.00000162460*cos(2.32137690587 + 182615.56580850288*$t);
   $X1 += 0.00000069502*cos(2.91939587909 + 24978.7684069643*$t);
   $X1 += 0.00000063529*cos(2.74219954754 + 27197.5255111511*$t);
   $X1 += 0.00000042967*cos(5.37217235288 + 208703.46895007708*$t);
   $X1 += 0.00000032514*cos(3.18436046111 + 104351.36874881329*$t);
   $X1 += 0.00000017597*cos(5.97213886087 + 51066.6715485385*$t);
   $X1 += 0.00000013287*cos(5.79146748296 + 53285.4286527253*$t);
   $X1 += 0.00000011758*cos(0.18693736842 + 1109.1347346099*$t);
   $X1 += 0.00000012502*cos(1.40596439354 + 1059.6257476727*$t);
   $X1 += 0.00000011468*cos(0.35008608561 + 20426.8149099055*$t);
   $X1 += 0.00000011394*cos(2.13977164486 + 234791.37209165128*$t);
   $X1 += 0.00000008221*cos(5.31229385932 + 31749.4790082099*$t);
   $X1 += 0.00000008067*cos(0.15951495713 + 130439.27189038748*$t);
   $X1 += 0.00000006176*cos(5.46098436501 + 4552.1973145423*$t);
   $X1 += 0.00000004784*cos(0.26415468148 + 21536.1934619989*$t);
   $X1 += 0.00000004858*cos(2.74077664990 + 77154.57469011268*$t);
   $X1 += 0.00000004269*cos(3.39637722107 + 46514.7180514797*$t);
   $X1 += 0.00000004412*cos(5.10134190424 + 25132.5472174491*$t);
   $X1 += 0.00000003922*cos(2.37978972370 + 1589.3167127673*$t);
   $X1 += 0.00000004017*cos(4.41672907758 + 27147.5288892469*$t);
   $X1 += 0.00000003763*cos(4.17909693196 + 14765.48286075331*$t);
   $X1 += 0.00000004285*cos(4.27106878562 + 51116.6681704427*$t);
   $X1 += 0.00000003901*cos(0.54893072973 + 27043.7467006663*$t);
   $X1 += 0.00000003221*cos(1.09802577229 + 26617.8379241523*$t);
   $X1 += 0.00000003080*cos(4.68247133566 + 25558.4559939631*$t);
   $X1 += 0.00000003030*cos(5.19056049817 + 260879.27523322542*$t);
   $X1 += 0.00000002907*cos(0.23044150312 + 26068.47719815791*$t);
   $X1 += 0.00000002906*cos(5.43307929185 + 26107.81671995749*$t);
   $X1 += 0.00000002383*cos(2.07830748691 + 26084.2656236997*$t);
   $X1 += 0.00000002381*cos(3.58525530417 + 26092.0282944157*$t);
   $X1 += 0.00000002069*cos(1.48127323869 + 37410.8110573621*$t);
   $X1 += 0.00000002028*cos(5.44501246598 + 30640.1004561165*$t);
   $X1 += 0.00000002088*cos(3.34536117513 + 156527.17503196168*$t);
   $X1 += 0.00000001998*cos(2.50305248201 + 79373.33179429949*$t);
   $X1 += 0.00000001880*cos(0.22580120983 + 47624.0966035731*$t);
   $X1 += 0.00000001580*cos(1.69158612681 + 9104.1508116011*$t);
   $X1 += 0.00000001575*cos(4.31668154619 + 955.3559241251*$t);
   $X1 += 0.00000001508*cos(0.43559873501 + 19317.43635781211*$t);
   $X1 += 0.00000001397*cos(0.16380111329 + 72602.62119305388*$t);
   $X1 += 0.00000001363*cos(3.28693470602 + 50586.97720534809*$t);
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   $X1 += 0.00000000001*cos(4.14165011369 + 94138.08320260228*$t);
   $X1 += 0.00000000001*cos(5.17339556279 + 24602.8562523545*$t);
   $X1 += 0.00000000001*cos(0.49022946842 + 27573.4376657609*$t);
   $X1 += 0.00000000001*cos(4.40553516948 + 121335.36489626988*$t);
   $X1 += 0.00000000001*cos(0.40614537067 + 198490.18340386607*$t);
   $X1 += 0.00000000001*cos(0.84588819348 + 181555.69624334667*$t);
   $X1 += 0.00000000001*cos(5.13509102157 + 156534.77621392948*$t);
   $X1 += 0.00000000001*cos(1.73614423183 + 12725.6972522585*$t);
   $X1 += 0.00000000001*cos(0.52115552294 + 130006.04778747768*$t);
   $X1 += 0.00000000001*cos(1.59903474540 + 89586.12970554348*$t);
   $X1 += 0.00000000001*cos(3.74413194011 + 131394.87163199608*$t);
   $X1 += 0.00000000001*cos(0.61669479944 + 77039.64776646046*$t);
   return $X1*$t;
}



   function Mercury_X2($t) // 413 terms of order 2
{
   $X2  = 0.00020000263*cos(5.96893489541 + 26088.1469590577*$t);
   $X2 += 0.00008268782*cos(0.41593027178 + 0.2438174835*$t);
   $X2 += 0.00002498175*cos(3.38864668295 + 52176.0501006319*$t);
   $X2 += 0.00000949347*cos(0.79533142414 + 78263.95324220609*$t);
   $X2 += 0.00000776108*cos(5.52747825416 + 26087.65932409069*$t);
   $X2 += 0.00000371109*cos(4.03419264198 + 104351.85638378029*$t);
   $X2 += 0.00000130259*cos(0.87132938107 + 130439.75952535449*$t);
   $X2 += 0.00000069902*cos(2.02066051600 + 52175.56246566489*$t);
   $X2 += 0.00000042865*cos(3.95497707255 + 156527.66266692868*$t);
   $X2 += 0.00000013564*cos(0.74070016642 + 182615.56580850288*$t);
   $X2 += 0.00000011344*cos(4.89785767709 + 78263.46560723908*$t);
   $X2 += 0.00000004184*cos(3.80256859065 + 208703.46895007708*$t);
   $X2 += 0.00000002952*cos(1.21119140823 + 24978.7684069643*$t);
   $X2 += 0.00000002715*cos(4.19935661957 + 27197.5255111511*$t);
   $X2 += 0.00000002412*cos(1.63037150116 + 104351.36874881329*$t);
   $X2 += 0.00000001268*cos(0.57748866225 + 234791.37209165128*$t);
   $X2 += 0.00000001017*cos(4.33432055001 + 51066.6715485385*$t);
   $X2 += 0.00000000591*cos(4.73978384246 + 130439.27189038748*$t);
   $X2 += 0.00000000372*cos(0.82364022383 + 53285.4286527253*$t);
   $X2 += 0.00000000379*cos(3.63308186625 + 260879.27523322542*$t);
   $X2 += 0.00000000353*cos(1.13633330939 + 77154.57469011268*$t);
   $X2 += 0.00000000353*cos(2.07182576415 + 1109.1347346099*$t);
   $X2 += 0.00000000259*cos(4.03007203572 + 20426.8149099055*$t);
   $X2 += 0.00000000259*cos(5.19867290786 + 1059.6257476727*$t);
   $X2 += 0.00000000198*cos(1.36980571393 + 27043.7467006663*$t);
   $X2 += 0.00000000178*cos(5.96725527175 + 31749.4790082099*$t);
   $X2 += 0.00000000161*cos(1.00641443984 + 1589.3167127673*$t);
   $X2 += 0.00000000148*cos(2.97453779319 + 4552.1973145423*$t);
   $X2 += 0.00000000145*cos(1.59448029290 + 21536.1934619989*$t);
   $X2 += 0.00000000158*cos(1.60582346371 + 156527.17503196168*$t);
   $X2 += 0.00000000169*cos(4.00782299083 + 25132.5472174491*$t);
   $X2 += 0.00000000134*cos(5.93157203334 + 25558.4559939631*$t);
   $X2 += 0.00000000112*cos(0.40462785686 + 286967.17837479962*$t);
   $X2 += 0.00000000111*cos(5.65704047760 + 26617.8379241523*$t);
   $X2 += 0.00000000122*cos(1.49577379421 + 46514.7180514797*$t);
   $X2 += 0.00000000125*cos(1.39636100360 + 23869.3898548709*$t);
   $X2 += 0.00000000111*cos(2.28972892610 + 14765.48286075331*$t);
   $X2 += 0.00000000106*cos(4.77037689879 + 51116.6681704427*$t);
   $X2 += 0.00000000120*cos(4.20635563605 + 103242.47783168689*$t);
   $X2 += 0.00000000113*cos(2.57148364836 + 27147.5288892469*$t);
   $X2 += 0.00000000105*cos(4.19895688280 + 28306.90406324449*$t);
   $X2 += 0.00000000086*cos(5.07571410391 + 19317.43635781211*$t);
   $X2 += 0.00000000103*cos(5.90310312996 + 5661.0882316687*$t);
   $X2 += 0.00000000067*cos(6.26109568890 + 9104.1508116011*$t);
   $X2 += 0.00000000076*cos(1.89488008069 + 529.9347825781*$t);
   $X2 += 0.00000000066*cos(4.44479405797 + 50586.97720534809*$t);
   $X2 += 0.00000000066*cos(3.84543572024 + 3442.81876244891*$t);
   $X2 += 0.00000000061*cos(2.83683010519 + 37410.8110573621*$t);
   $X2 += 0.00000000059*cos(4.74002403670 + 72602.62119305388*$t);
   $X2 += 0.00000000074*cos(1.71392170541 + 22645.57201409229*$t);
   $X2 += 0.00000000056*cos(2.44778877932 + 52705.7410657265*$t);
   $X2 += 0.00000000061*cos(3.55810846013 + 30640.1004561165*$t);
   $X2 += 0.00000000053*cos(5.29509726913 + 640.1411037975*$t);
   $X2 += 0.00000000056*cos(0.44039665586 + 32858.8575603033*$t);
   $X2 += 0.00000000062*cos(0.55305609443 + 51220.4503590233*$t);
   $X2 += 0.00000000050*cos(4.18169929034 + 53131.6498422405*$t);
   $X2 += 0.00000000046*cos(3.94824823145 + 27677.2198543415*$t);
   $X2 += 0.00000000045*cos(1.59652029747 + 25973.70767037247*$t);
   $X2 += 0.00000000045*cos(4.05512833234 + 26202.58624774291*$t);
   $X2 += 0.00000000044*cos(4.75905220926 + 182615.07817353586*$t);
   $X2 += 0.00000000046*cos(2.53699777188 + 27197.03787618409*$t);
   $X2 += 0.00000000046*cos(5.78816990516 + 53235.43203082109*$t);
   $X2 += 0.00000000058*cos(2.08536631307 + 57837.3821497841*$t);
   $X2 += 0.00000000043*cos(3.15018018958 + 529.44714761109*$t);
   $X2 += 0.00000000042*cos(1.10095861133 + 47624.0966035731*$t);
   $X2 += 0.00000000041*cos(2.92440512287 + 26301.4460544957*$t);
   $X2 += 0.00000000039*cos(5.52297144186 + 40853.3860023275*$t);
   $X2 += 0.00000000038*cos(2.59002993610 + 25874.8478636197*$t);
   $X2 += 0.00000000045*cos(3.87761344478 + 29530.7219040231*$t);
   $X2 += 0.00000000045*cos(4.83071642182 + 10213.5293636945*$t);
   $X2 += 0.00000000035*cos(1.77114967266 + 2119.00767786191*$t);
   $X2 += 0.00000000034*cos(0.50537233993 + 56728.0035976907*$t);
   $X2 += 0.00000000040*cos(4.99855315823 + 24978.28077199729*$t);
   $X2 += 0.00000000040*cos(0.98737142456 + 129330.38097326108*$t);
   $X2 += 0.00000000033*cos(3.45515093268 + 313055.08151637383*$t);
   $X2 += 0.00000000039*cos(5.42516034342 + 955.3559241251*$t);
   $X2 += 0.00000000031*cos(4.38256920252 + 6770.46678376209*$t);
   $X2 += 0.00000000038*cos(1.73621782583 + 2218.51328670329*$t);
   $X2 += 0.00000000031*cos(1.18390533268 + 12566.3955174663*$t);
   $X2 += 0.00000000032*cos(4.46582914668 + 49957.2929964451*$t);
   $X2 += 0.00000000029*cos(5.65827133315 + 426.8420083595*$t);
   $X2 += 0.00000000028*cos(5.46107883558 + 43072.1431065143*$t);
   $X2 += 0.00000000025*cos(1.58123453631 + 98690.52433462809*$t);
   $X2 += 0.00000000030*cos(3.15402941421 + 79373.33179429949*$t);
   $X2 += 0.00000000023*cos(5.44646488235 + 78793.64420730069*$t);
   $X2 += 0.00000000030*cos(0.97936081436 + 77204.57131201689*$t);
   $X2 += 0.00000000020*cos(1.34579383399 + 11322.42028082089*$t);
   $X2 += 0.00000000027*cos(0.95498900102 + 54394.80720481869*$t);
   $X2 += 0.00000000023*cos(3.49479332748 + 77308.35350059748*$t);
   $X2 += 0.00000000019*cos(5.90875785254 + 83925.28529135829*$t);
   $X2 += 0.00000000022*cos(1.88106368245 + 45405.3394993863*$t);
   $X2 += 0.00000000020*cos(2.33312866023 + 36301.4325052687*$t);
   $X2 += 0.00000000018*cos(2.63764225914 + 79323.33517239528*$t);
   $X2 += 0.00000000021*cos(2.63713620085 + 13656.10430865991*$t);
   $X2 += 0.00000000020*cos(4.83742385337 + 33326.8225506577*$t);
   $X2 += 0.00000000018*cos(1.65998530501 + 52156.38033973211*$t);
   $X2 += 0.00000000023*cos(4.13597342584 + 41962.7645544209*$t);
   $X2 += 0.00000000018*cos(6.07003180743 + 52389.3491960699*$t);
   $X2 += 0.00000000017*cos(3.47243675916 + 58946.76070187749*$t);
   $X2 += 0.00000000016*cos(1.64800690653 + 23754.95056618569*$t);
   $X2 += 0.00000000019*cos(2.36847359761 + 39609.8984006491*$t);
   $X2 += 0.00000000017*cos(0.25513432917 + 51536.15281431789*$t);
   $X2 += 0.00000000018*cos(0.34702974356 + 18849.4713674577*$t);
   $X2 += 0.00000000015*cos(0.95866304490 + 76674.88034692229*$t);
   $X2 += 0.00000000015*cos(1.75514605179 + 48733.47515566649*$t);
   $X2 += 0.00000000015*cos(4.34995902728 + 853.4401992355*$t);
   $X2 += 0.00000000014*cos(3.61473044000 + 82815.90673926489*$t);
   $X2 += 0.00000000014*cos(5.02500731242 + 52179.9314359899*$t);
   $X2 += 0.00000000014*cos(1.69891784853 + 15874.8614128467*$t);
   $X2 += 0.00000000014*cos(2.36729572184 + 66941.2891439017*$t);
   $X2 += 0.00000000015*cos(5.49473150242 + 16984.2399649401*$t);
   $X2 += 0.00000000015*cos(5.05704278229 + 38654.2986590405*$t);
   $X2 += 0.00000000013*cos(0.64687702919 + 53765.1229959157*$t);
   $X2 += 0.00000000013*cos(1.62167132693 + 208702.98131511007*$t);
   $X2 += 0.00000000013*cos(3.82178316362 + 50057.2862402535*$t);
   $X2 += 0.00000000016*cos(2.05228361219 + 51646.3591355373*$t);
   $X2 += 0.00000000012*cos(3.97912977913 + 28421.3433519297*$t);
   $X2 += 0.00000000013*cos(4.04493324307 + 155418.28411483529*$t);
   $X2 += 0.00000000016*cos(0.65996554595 + 55618.6250455973*$t);
   $X2 += 0.00000000012*cos(3.62569930460 + 5661.5758666357*$t);
   $X2 += 0.00000000015*cos(0.75515577986 + 52195.71986153169*$t);
   $X2 += 0.00000000014*cos(2.81046707561 + 26514.7451499337*$t);
   $X2 += 0.00000000014*cos(3.30095837282 + 110013.18843293248*$t);
   $X2 += 0.00000000013*cos(0.56442607871 + 213.0552779545*$t);
   $X2 += 0.00000000014*cos(2.10561918260 + 26728.0442453717*$t);
   $X2 += 0.00000000013*cos(3.66951257967 + 52172.1687652739*$t);
   $X2 += 0.00000000011*cos(5.46295418561 + 63498.71419893629*$t);
   $X2 += 0.00000000011*cos(0.61230507574 + 79219.55298381469*$t);
   $X2 += 0.00000000010*cos(4.66712610746 + 103292.47445359109*$t);
   $X2 += 0.00000000011*cos(5.20556952105 + 31748.99137324289*$t);
   $X2 += 0.00000000014*cos(3.33453776277 + 6283.3196674749*$t);
   $X2 += 0.00000000010*cos(0.83705988710 + 52290.48938931711*$t);
   $X2 += 0.00000000012*cos(2.60449391926 + 13521.50762410789*$t);
   $X2 += 0.00000000009*cos(3.03188275218 + 35192.0539531753*$t);
   $X2 += 0.00000000009*cos(1.24305000805 + 76045.1961380193*$t);
   $X2 += 0.00000000011*cos(5.89042281055 + 62389.33564684289*$t);
   $X2 += 0.00000000010*cos(4.16418363493 + 51749.45190975589*$t);
   $X2 += 0.00000000009*cos(4.66321261687 + 124778.42747620228*$t);
   $X2 += 0.00000000009*cos(0.22808750229 + 339142.98465794802*$t);
   $X2 += 0.00000000009*cos(4.75513146544 + 78244.28348130629*$t);
   $X2 += 0.00000000009*cos(2.64262688750 + 20426.32727493849*$t);
   $X2 += 0.00000000011*cos(2.92721365751 + 38520.1896094555*$t);
   $X2 += 0.00000000010*cos(3.30244477369 + 16983.75232997309*$t);
   $X2 += 0.00000000009*cos(1.16009282528 + 1109.6223695769*$t);
   $X2 += 0.00000000009*cos(4.65609022876 + 52061.61081194667*$t);
   $X2 += 0.00000000009*cos(2.15470374859 + 104881.54734887488*$t);
   $X2 += 0.00000000008*cos(1.58129311338 + 68050.66769599509*$t);
   $X2 += 0.00000000008*cos(4.01456932062 + 2333.44021035551*$t);
   $X2 += 0.00000000008*cos(0.50473636519 + 12431.79883291429*$t);
   $X2 += 0.00000000008*cos(4.71148146957 + 28206.9108194361*$t);
   $X2 += 0.00000000008*cos(0.22428318331 + 136101.09157450669*$t);
   $X2 += 0.00000000008*cos(5.13855904986 + 213.5429129215*$t);
   $X2 += 0.00000000008*cos(1.53446312549 + 24499.0740637739*$t);
   $X2 += 0.00000000008*cos(0.19632874417 + 103396.25664217169*$t);
   $X2 += 0.00000000007*cos(4.83084149979 + 52168.93655363109*$t);
   $X2 += 0.00000000009*cos(0.68229010552 + 21535.70582703189*$t);
   $X2 += 0.00000000007*cos(5.67305147777 + 53284.94101775829*$t);
   $X2 += 0.00000000007*cos(4.91493686906 + 105461.23493587368*$t);
   $X2 += 0.00000000007*cos(2.13257749573 + 69160.04624808849*$t);
   $X2 += 0.00000000009*cos(0.17767669866 + 7994.77225950771*$t);
   $X2 += 0.00000000009*cos(3.44284310428 + 73711.99974514729*$t);
   $X2 += 0.00000000008*cos(1.40334354171 + 59414.7256922319*$t);
   $X2 += 0.00000000008*cos(3.92015227538 + 52183.1636476327*$t);
   $X2 += 0.00000000007*cos(1.95913527567 + 64742.2018006147*$t);
   $X2 += 0.00000000007*cos(1.83770637593 + 78267.83457756409*$t);
   $X2 += 0.00000000007*cos(5.50637575808 + 26107.81671995749*$t);
   $X2 += 0.00000000007*cos(3.29290677599 + 26068.47719815791*$t);
   $X2 += 0.00000000006*cos(2.48089512320 + 25028.7650288685*$t);
   $X2 += 0.00000000007*cos(6.10010912620 + 51962.7510051939*$t);
   $X2 += 0.00000000007*cos(5.20852269117 + 18208.05780571871*$t);
   $X2 += 0.00000000008*cos(3.20036201627 + 44937.3745090319*$t);
   $X2 += 0.00000000008*cos(1.81720177562 + 51066.18391357149*$t);
   $X2 += 0.00000000006*cos(5.72654755255 + 105411.23831396949*$t);
   $X2 += 0.00000000007*cos(4.86085983191 + 65697.80154222329*$t);
   $X2 += 0.00000000006*cos(2.84309765149 + 88477.23878841709*$t);
   $X2 += 0.00000000006*cos(2.90025697766 + 78477.25233764409*$t);
   $X2 += 0.00000000006*cos(6.10721529063 + 52602.6482915079*$t);
   $X2 += 0.00000000007*cos(3.76564310534 + 78283.62300310588*$t);
   $X2 += 0.00000000006*cos(2.54939515992 + 19805.0711090663*$t);
   $X2 += 0.00000000005*cos(0.40790961084 + 108903.80988083909*$t);
   $X2 += 0.00000000006*cos(2.08187740275 + 129380.37759516528*$t);
   $X2 += 0.00000000005*cos(4.74517813371 + 74821.37829724069*$t);
   $X2 += 0.00000000007*cos(5.47163902652 + 45892.9742506405*$t);
   $X2 += 0.00000000005*cos(3.96385649366 + 1059.1381127057*$t);
   $X2 += 0.00000000005*cos(2.11024903764 + 26084.2656236997*$t);
   $X2 += 0.00000000005*cos(0.40769424239 + 26092.0282944157*$t);
   $X2 += 0.00000000007*cos(4.95181465375 + 71493.2426409605*$t);
   $X2 += 0.00000000005*cos(3.72498845601 + 81706.5281871715*$t);
   $X2 += 0.00000000005*cos(1.28192740378 + 51322.85371887989*$t);
   $X2 += 0.00000000005*cos(0.38902168011 + 33968.23611239669*$t);
   $X2 += 0.00000000005*cos(1.36259031496 + 78256.83969520529*$t);
   $X2 += 0.00000000005*cos(2.94315074391 + 26617.35028918529*$t);
   $X2 += 0.00000000006*cos(0.40666986327 + 78260.07190684808*$t);
   $X2 += 0.00000000004*cos(3.59234736829 + 25661.5487681817*$t);
   $X2 += 0.00000000005*cos(5.20687247513 + 94138.57083756929*$t);
   $X2 += 0.00000000004*cos(5.73436372945 + 22645.08437912529*$t);
   $X2 += 0.00000000005*cos(5.43911125012 + 93029.19228547589*$t);
   $X2 += 0.00000000004*cos(1.51966869369 + 22760.01130277751*$t);
   $X2 += 0.00000000004*cos(4.11367481672 + 29416.28261533789*$t);
   $X2 += 0.00000000004*cos(0.33419603419 + 76145.18938182769*$t);
   $X2 += 0.00000000004*cos(0.81789657863 + 181506.18725640948*$t);
   $X2 += 0.00000000004*cos(5.87548494754 + 13521.9952590749*$t);
   $X2 += 0.00000000004*cos(0.98530676575 + 99799.90288672148*$t);
   $X2 += 0.00000000004*cos(3.64991710996 + 79853.02613748988*$t);
   $X2 += 0.00000000005*cos(5.51168134551 + 44181.52165860769*$t);
   $X2 += 0.00000000004*cos(4.17969593700 + 4551.7096795753*$t);
   $X2 += 0.00000000004*cos(1.07013306418 + 32371.2228090491*$t);
   $X2 += 0.00000000004*cos(4.56317466224 + 32858.36992533629*$t);
   $X2 += 0.00000000004*cos(0.76064444657 + 54509.2464935039*$t);
   $X2 += 0.00000000004*cos(5.34376558738 + 155468.28073673949*$t);
   $X2 += 0.00000000003*cos(3.33102397097 + 162188.99471608088*$t);
   $X2 += 0.00000000003*cos(1.90784099869 + 24498.58642880689*$t);
   $X2 += 0.00000000005*cos(0.70628118340 + 78271.06678920689*$t);
   $X2 += 0.00000000004*cos(4.75154050928 + 234790.88445668427*$t);
   $X2 += 0.00000000003*cos(5.20128667447 + 77734.26227711148*$t);
   $X2 += 0.00000000004*cos(4.16379409199 + 7879.84533585549*$t);
   $X2 += 0.00000000004*cos(5.89383677298 + 64608.09275102969*$t);
   $X2 += 0.00000000004*cos(4.51512332677 + 51116.18053547569*$t);
   $X2 += 0.00000000003*cos(1.82486201671 + 28306.41642827749*$t);
   $X2 += 0.00000000004*cos(5.71282679191 + 39744.0074502341*$t);
   $X2 += 0.00000000003*cos(1.53805667122 + 104332.1866228805*$t);
   $X2 += 0.00000000004*cos(3.89140851351 + 80482.71034639288*$t);
   $X2 += 0.00000000003*cos(1.85783050998 + 37410.32342239509*$t);
   $X2 += 0.00000000004*cos(1.55416627058 + 24864.32911827909*$t);
   $X2 += 0.00000000003*cos(2.39011669525 + 103822.16541868569*$t);
   $X2 += 0.00000000004*cos(4.09022608915 + 27311.96479983631*$t);
   $X2 += 0.00000000003*cos(2.12318372488 + 120226.47397914348*$t);
   $X2 += 0.00000000003*cos(4.30318589016 + 102133.09927959349*$t);
   $X2 += 0.00000000003*cos(1.44971105205 + 150866.33061777649*$t);
   $X2 += 0.00000000003*cos(5.04167948013 + 90830.10494218889*$t);
   $X2 += 0.00000000003*cos(3.27662875658 + 77624.05595589208*$t);
   $X2 += 0.00000000003*cos(3.21324303917 + 129484.15978374588*$t);
   $X2 += 0.00000000003*cos(4.58517957507 + 125887.80602829569*$t);
   $X2 += 0.00000000003*cos(5.16830743449 + 130969.45049044909*$t);
   $X2 += 0.00000000003*cos(4.95343110449 + 58459.1259506233*$t);
   $X2 += 0.00000000002*cos(0.76903109719 + 6282.83203250789*$t);
   $X2 += 0.00000000003*cos(1.18091352454 + 26941.3433408097*$t);
   $X2 += 0.00000000002*cos(1.64968376160 + 3327.89183879669*$t);
   $X2 += 0.00000000003*cos(2.92429834126 + 18093.13088206649*$t);
   $X2 += 0.00000000002*cos(1.24139720028 + 25132.0595824821*$t);
   $X2 += 0.00000000003*cos(0.05117365042 + 26095.2605060585*$t);
   $X2 += 0.00000000003*cos(6.12547181968 + 71025.27765060609*$t);
   $X2 += 0.00000000003*cos(3.14802602217 + 43071.65547154729*$t);
   $X2 += 0.00000000002*cos(5.96655122637 + 114565.14192999128*$t);
   $X2 += 0.00000000002*cos(2.80186013990 + 71980.87739221469*$t);
   $X2 += 0.00000000002*cos(2.32214550421 + 91785.70468379749*$t);
   $X2 += 0.00000000002*cos(2.48797331613 + 2648.6986429565*$t);
   $X2 += 0.00000000002*cos(3.89856574340 + 78378.3925308913*$t);
   $X2 += 0.00000000003*cos(4.90084849261 + 104355.73771913828*$t);
   $X2 += 0.00000000002*cos(2.45748414015 + 26081.03341205689*$t);
   $X2 += 0.00000000002*cos(2.90684371055 + 77197.45776501608*$t);
   $X2 += 0.00000000002*cos(3.27787980454 + 365230.88779952223*$t);
   $X2 += 0.00000000002*cos(2.96609297657 + 78690.55143308209*$t);
   $X2 += 0.00000000003*cos(5.20911364004 + 52815.9473869459*$t);
   $X2 += 0.00000000002*cos(3.65607552967 + 25448.2496727437*$t);
   $X2 += 0.00000000003*cos(0.46560289429 + 77837.35505133009*$t);
   $X2 += 0.00000000002*cos(0.51377942249 + 104371.52614468009*$t);
   $X2 += 0.00000000002*cos(1.04438989611 + 25028.27739390149*$t);
   $X2 += 0.00000000002*cos(2.95995089299 + 11322.9079157879*$t);
   $X2 += 0.00000000002*cos(2.29166292494 + 77211.68485901768*$t);
   $X2 += 0.00000000002*cos(3.65747965646 + 105307.45612538888*$t);
   $X2 += 0.00000000002*cos(3.59068071614 + 78050.65414676809*$t);
   $X2 += 0.00000000002*cos(0.09837196170 + 27043.2590656993*$t);
   $X2 += 0.00000000002*cos(4.33096627724 + 104344.74283677948*$t);
   $X2 += 0.00000000002*cos(5.54465700187 + 46514.23041651269*$t);
   $X2 += 0.00000000002*cos(4.94013298829 + 77154.08705514569*$t);
   $X2 += 0.00000000002*cos(3.18110797568 + 25451.1506870335*$t);
   $X2 += 0.00000000002*cos(2.48251705553 + 26725.1432310819*$t);
   $X2 += 0.00000000002*cos(2.52179042190 + 131499.14145554368*$t);
   $X2 += 0.00000000002*cos(6.07056602539 + 61279.9570947495*$t);
   $X2 += 0.00000000002*cos(1.27106707156 + 89586.61734051049*$t);
   $X2 += 0.00000000002*cos(1.28866377354 + 30639.61282114949*$t);
   $X2 += 0.00000000002*cos(1.72917997527 + 97581.14578253469*$t);
   $X2 += 0.00000000002*cos(1.43340926720 + 78149.51395352086*$t);
   $X2 += 0.00000000002*cos(4.01850243495 + 7238.4317741165*$t);
   $X2 += 0.00000000002*cos(5.54249111609 + 426.3543733925*$t);
   $X2 += 0.00000000002*cos(0.49218153901 + 107794.43132874569*$t);
   $X2 += 0.00000000002*cos(0.34191520237 + 47623.60896860609*$t);
   $X2 += 0.00000000002*cos(5.99315014021 + 104565.15547921829*$t);
   $X2 += 0.00000000002*cos(1.99101623607 + 44295.9609472929*$t);
   $X2 += 0.00000000002*cos(5.47567807736 + 18093.6185170335*$t);
   $X2 += 0.00000000002*cos(5.22941762292 + 10213.0417287275*$t);
   $X2 += 0.00000000002*cos(3.76589759239 + 104358.96993078108*$t);
   $X2 += 0.00000000002*cos(3.44277374163 + 104347.97504842229*$t);
   $X2 += 0.00000000002*cos(3.46735728702 + 134991.71302241329*$t);
   $X2 += 0.00000000002*cos(5.38147823295 + 129910.06856025988*$t);
   $X2 += 0.00000000002*cos(1.91253822385 + 57836.89451481709*$t);
   $X2 += 0.00000000002*cos(3.81440405932 + 25557.96835899609*$t);
   $X2 += 0.00000000002*cos(1.41016954122 + 54294.81396101029*$t);
   $X2 += 0.00000000002*cos(3.48149032535 + 102762.78348849648*$t);
   $X2 += 0.00000000001*cos(1.23200675306 + 7238.9194090835*$t);
   $X2 += 0.00000000002*cos(4.28600144274 + 25934.3681485729*$t);
   $X2 += 0.00000000001*cos(1.40803647408 + 151975.70916986988*$t);
   $X2 += 0.00000000002*cos(4.52450590998 + 26241.9257695425*$t);
   $X2 += 0.00000000001*cos(1.50678411527 + 131549.13807744789*$t);
   $X2 += 0.00000000001*cos(1.06085484841 + 23968.89546371229*$t);
   $X2 += 0.00000000002*cos(2.95379110730 + 25021.6514818677*$t);
   $X2 += 0.00000000002*cos(5.72041106584 + 27154.6424362477*$t);
   $X2 += 0.00000000001*cos(2.16358753423 + 181556.18387831368*$t);
   $X2 += 0.00000000001*cos(0.24053830744 + 27140.41534224609*$t);
   $X2 += 0.00000000001*cos(1.76435464195 + 149.8070146181*$t);
   $X2 += 0.00000000001*cos(3.46637889336 + 50586.48957038109*$t);
   $X2 += 0.00000000001*cos(4.03245836538 + 85502.6288338061*$t);
   $X2 += 0.00000000001*cos(4.69456883146 + 1052.51220067191*$t);
   $X2 += 0.00000000001*cos(1.69300525500 + 84547.0290921975*$t);
   $X2 += 0.00000000001*cos(3.42418885871 + 41962.27691945389*$t);
   $X2 += 0.00000000002*cos(1.10596292069 + 1066.7392946735*$t);
   $X2 += 0.00000000001*cos(4.90928501927 + 33326.33491569069*$t);
   $X2 += 0.00000000001*cos(5.93281924072 + 103285.36090659029*$t);
   $X2 += 0.00000000001*cos(0.91877297183 + 55504.18575691209*$t);
   $X2 += 0.00000000001*cos(6.04736307912 + 117873.60782537168*$t);
   $X2 += 0.00000000001*cos(2.53958781081 + 25035.8785758693*$t);
   $X2 += 0.00000000001*cos(4.09517185988 + 58946.27306691049*$t);
   $X2 += 0.00000000001*cos(0.11578152669 + 188276.89785765509*$t);
   $X2 += 0.00000000001*cos(1.73884599121 + 49842.85370775989*$t);
   $X2 += 0.00000000001*cos(4.77533799776 + 29428.7593857575*$t);
   $X2 += 0.00000000001*cos(5.22199381468 + 146314.37712071768*$t);
   $X2 += 0.00000000001*cos(2.12230022464 + 119117.0954270501*$t);
   $X2 += 0.00000000001*cos(2.86720953628 + 39629.56816154889*$t);
   $X2 += 0.00000000001*cos(2.74763511093 + 12546.72575656651*$t);
   $X2 += 0.00000000001*cos(0.25887140846 + 64607.60511606269*$t);
   $X2 += 0.00000000001*cos(5.22258225356 + 23868.9022199039*$t);
   $X2 += 0.00000000001*cos(4.58859350492 + 48847.9144443517*$t);
   $X2 += 0.00000000001*cos(1.51099098110 + 260878.78759825832*$t);
   $X2 += 0.00000000001*cos(3.51708181436 + 25620.1819687033*$t);
   $X2 += 0.00000000001*cos(0.18832551491 + 98068.78053378889*$t);
   $X2 += 0.00000000001*cos(0.48744281934 + 22747.5345323579*$t);
   $X2 += 0.00000000001*cos(5.29369767440 + 26556.11194941211*$t);
   $X2 += 0.00000000001*cos(5.89974555271 + 85034.66384345168*$t);
   $X2 += 0.00000000001*cos(5.40405552306 + 5327.7199258663*$t);
   $X2 += 0.00000000001*cos(3.99805833912 + 63498.22656396929*$t);
   $X2 += 0.00000000001*cos(0.48047428009 + 26300.95841952869*$t);
   $X2 += 0.00000000001*cos(0.36034529603 + 105940.92927906409*$t);
   $X2 += 0.00000000001*cos(2.48936428540 + 65831.91059180829*$t);
   $X2 += 0.00000000001*cos(2.46490999297 + 79372.84415933248*$t);
   $X2 += 0.00000000001*cos(3.19576682217 + 7.3573644843*$t);
   $X2 += 0.00000000001*cos(0.86957384492 + 53399.86794141051*$t);
   $X2 += 0.00000000001*cos(3.82636106300 + 80597.14963507809*$t);
   $X2 += 0.00000000001*cos(3.10426657434 + 49527.59527515889*$t);
   $X2 += 0.00000000001*cos(0.58848037656 + 36300.94487030169*$t);
   $X2 += 0.00000000001*cos(1.70956045888 + 116918.00808376308*$t);
   $X2 += 0.00000000001*cos(4.85073507517 + 26080.54577708989*$t);
   $X2 += 0.00000000001*cos(3.44422946655 + 60056.13925397089*$t);
   $X2 += 0.00000000001*cos(4.81916140005 + 10022.0810975829*$t);
   $X2 += 0.00000000001*cos(5.11488921531 + 51123.7817174435*$t);
   $X2 += 0.00000000001*cos(0.47588667079 + 51645.87150057029*$t);
   $X2 += 0.00000000001*cos(1.41817736905 + 76.50988875911*$t);
   $X2 += 0.00000000001*cos(0.99594891808 + 106570.61348796709*$t);
   $X2 += 0.00000000001*cos(0.28396033479 + 25021.16384690069*$t);
   $X2 += 0.00000000001*cos(1.51089793343 + 15874.37377787969*$t);
   $X2 += 0.00000000001*cos(0.30377336401 + 86144.04239554508*$t);
   $X2 += 0.00000000001*cos(3.39681294015 + 52644.0150909863*$t);
   $X2 += 0.00000000001*cos(5.97495759877 + 26094.77551795771*$t);
   $X2 += 0.00000000001*cos(2.83507136702 + 26081.51840015769*$t);
   $X2 += 0.00000000001*cos(5.89040270497 + 6.86972951729*$t);
   $X2 += 0.00000000001*cos(0.29019267678 + 16703.3059509825*$t);
   $X2 += 0.00000000001*cos(5.32811862019 + 35472.9879671329*$t);
   $X2 += 0.00000000001*cos(0.32321972304 + 42154.2128205325*$t);
   $X2 += 0.00000000001*cos(4.39149562944 + 77410.75686045409*$t);
   $X2 += 0.00000000001*cos(3.51650331906 + 103925.25819290428*$t);
   $X2 += 0.00000000001*cos(2.00607418956 + 52329.8289111167*$t);
   $X2 += 0.00000000001*cos(3.10569882865 + 6681.46867088311*$t);
   $X2 += 0.00000000001*cos(0.56719469804 + 6770.9544187291*$t);
   $X2 += 0.00000000001*cos(4.66201946613 + 955.8435590921*$t);
   $X2 += 0.00000000001*cos(0.75784126065 + 51109.55462344189*$t);
   $X2 += 0.00000000001*cos(1.25573296054 + 29530.2342690561*$t);
   $X2 += 0.00000000001*cos(1.77919762464 + 26067.9895631909*$t);
   $X2 += 0.00000000001*cos(4.03762558727 + 25447.76203777669*$t);
   $X2 += 0.00000000001*cos(5.95598082912 + 52705.25343075949*$t);
   $X2 += 0.00000000001*cos(1.01747250713 + 33967.74847742969*$t);
   $X2 += 0.00000000001*cos(0.01664299877 + 25035.39094090229*$t);
   $X2 += 0.00000000001*cos(6.20560095721 + 26107.32908499049*$t);
   $X2 += 0.00000000001*cos(0.93578815320 + 23969.3830986793*$t);
   $X2 += 0.00000000001*cos(2.52616943216 + 19316.9487228451*$t);
   $X2 += 0.00000000001*cos(5.09896744500 + 26091.5406594487*$t);
   $X2 += 0.00000000001*cos(2.39439324238 + 53131.16220727349*$t);
   $X2 += 0.00000000001*cos(2.74115190658 + 95247.94938966268*$t);
   $X2 += 0.00000000001*cos(5.36396008776 + 103299.58800059189*$t);
   $X2 += 0.00000000001*cos(4.59387367112 + 26094.77287109149*$t);
   $X2 += 0.00000000001*cos(3.12740178962 + 102233.09252340188*$t);
   $X2 += 0.00000000001*cos(2.15814286033 + 25668.17468021549*$t);
   $X2 += 0.00000000000*cos(6.02426301935 + 12565.9078824993*$t);
   $X2 += 0.00000000000*cos(5.08027895309 + 54394.31956985169*$t);
   $X2 += 0.00000000000*cos(2.97863205244 + 111122.56698502589*$t);
   $X2 += 0.00000000001*cos(3.29290475293 + 12432.2864678813*$t);
   $X2 += 0.00000000001*cos(4.11678654325 + 115674.52048208468*$t);
   $X2 += 0.00000000000*cos(1.52900740701 + 25234.46294233869*$t);
   $X2 += 0.00000000001*cos(0.81921278001 + 25661.06113321469*$t);
   $X2 += 0.00000000001*cos(1.94160256445 + 39609.41076568209*$t);
   $X2 += 0.00000000000*cos(4.43222686144 + 45892.48661567349*$t);
   $X2 += 0.00000000000*cos(5.52190845642 + 77830.24150432929*$t);
   $X2 += 0.00000000000*cos(5.87054542331 + 116783.89903417809*$t);
   $X2 += 0.00000000000*cos(0.73723465850 + 28420.8557169627*$t);
   $X2 += 0.00000000000*cos(1.91678340872 + 103241.99019671988*$t);
   $X2 += 0.00000000000*cos(0.75824711372 + 52026.4869034973*$t);
   $X2 += 0.00000000000*cos(1.73983373880 + 19804.5834740993*$t);
   $X2 += 0.00000000001*cos(2.85651249975 + 26083.7779887327*$t);
   $X2 += 0.00000000000*cos(2.54986446702 + 53242.5455778219*$t);
   $X2 += 0.00000000000*cos(4.12464845193 + 1588.82907780029*$t);
   $X2 += 0.00000000000*cos(4.10463489089 + 51219.96272405629*$t);
   $X2 += 0.00000000000*cos(5.49428153801 + 157637.04121902208*$t);
   $X2 += 0.00000000000*cos(2.31218688576 + 72602.13355808688*$t);
   $X2 += 0.00000000000*cos(4.67530659291 + 83924.79765639128*$t);
   $X2 += 0.00000000000*cos(4.56610835896 + 130420.08976445469*$t);
   $X2 += 0.00000000000*cos(5.25102871130 + 25668.6623151825*$t);
   $X2 += 0.00000000000*cos(1.26830048676 + 3340.8562441833*$t);
   $X2 += 0.00000000000*cos(1.02801034430 + 77204.08367704989*$t);
   $X2 += 0.00000000000*cos(3.83991637789 + 207594.09039798369*$t);
   $X2 += 0.00000000000*cos(2.19144576095 + 419.72846135871*$t);
   $X2 += 0.00000000000*cos(5.62747197310 + 32370.73517408209*$t);
   $X2 += 0.00000000000*cos(1.99592158964 + 78903.8505285201*$t);
   $X2 += 0.00000000000*cos(0.06549387620 + 44936.88687406489*$t);
   $X2 += 0.00000000000*cos(4.55067254270 + 286966.69073983253*$t);
   return $X2*$t*$t;
}



   function Mercury_X3($t) // 135 terms of order 3
{
   $X3  = 0.00000180660*cos(1.53524873089 + 0.2438174835*$t);
   $X3 += 0.00000056109*cos(1.50368825372 + 52176.0501006319*$t);
   $X3 += 0.00000023909*cos(5.09285389011 + 78263.95324220609*$t);
   $X3 += 0.00000011317*cos(2.22514154728 + 104351.85638378029*$t);
   $X3 += 0.00000011202*cos(6.20552374893 + 26088.1469590577*$t);
   $X3 += 0.00000007321*cos(1.49034347852 + 26087.65932409069*$t);
   $X3 += 0.00000005011*cos(5.45015928644 + 130439.75952535449*$t);
   $X3 += 0.00000002025*cos(2.30601224164 + 156527.66266692868*$t);
   $X3 += 0.00000001152*cos(0.12743555397 + 52175.56246566489*$t);
   $X3 += 0.00000000763*cos(5.40668920792 + 182615.56580850288*$t);
   $X3 += 0.00000000387*cos(3.30772457389 + 78263.46560723908*$t);
   $X3 += 0.00000000274*cos(2.20509049018 + 208703.46895007708*$t);
   $X3 += 0.00000000112*cos(0.07801111545 + 104351.36874881329*$t);
   $X3 += 0.00000000095*cos(5.27592058522 + 234791.37209165128*$t);
   $X3 += 0.00000000037*cos(4.50900105290 + 24978.7684069643*$t);
   $X3 += 0.00000000034*cos(4.28000177876 + 27197.5255111511*$t);
   $X3 += 0.00000000032*cos(2.05675254224 + 260879.27523322542*$t);
   $X3 += 0.00000000024*cos(2.45956768858 + 51066.6715485385*$t);
   $X3 += 0.00000000032*cos(3.14716159333 + 130439.27189038748*$t);
   $X3 += 0.00000000013*cos(5.72061024737 + 77154.57469011268*$t);
   $X3 += 0.00000000010*cos(5.11454206540 + 286967.17837479962*$t);
   $X3 += 0.00000000013*cos(0.11908599274 + 53285.4286527253*$t);
   $X3 += 0.00000000010*cos(6.24570451816 + 156527.17503196168*$t);
   $X3 += 0.00000000006*cos(4.82972887929 + 1109.1347346099*$t);
   $X3 += 0.00000000007*cos(2.99175820133 + 1059.6257476727*$t);
   $X3 += 0.00000000006*cos(1.93767779760 + 20426.8149099055*$t);
   $X3 += 0.00000000006*cos(2.56259446748 + 103242.47783168689*$t);
   $X3 += 0.00000000004*cos(0.57540517960 + 31749.4790082099*$t);
   $X3 += 0.00000000004*cos(2.89306042580 + 79373.33179429949*$t);
   $X3 += 0.00000000003*cos(1.89223297598 + 313055.08151637383*$t);
   $X3 += 0.00000000003*cos(0.79688696210 + 4552.1973145423*$t);
   $X3 += 0.00000000003*cos(3.08934162665 + 182615.07817353586*$t);
   $X3 += 0.00000000003*cos(5.67790423166 + 46514.7180514797*$t);
   $X3 += 0.00000000003*cos(1.82353994272 + 21536.1934619989*$t);
   $X3 += 0.00000000002*cos(0.08756125776 + 27147.5288892469*$t);
   $X3 += 0.00000000002*cos(3.96079675679 + 1589.3167127673*$t);
   $X3 += 0.00000000002*cos(0.44816937719 + 25132.5472174491*$t);
   $X3 += 0.00000000002*cos(5.80684121758 + 14765.48286075331*$t);
   $X3 += 0.00000000002*cos(5.81670079373 + 51116.6681704427*$t);
   $X3 += 0.00000000002*cos(5.64942685187 + 129330.38097326108*$t);
   $X3 += 0.00000000002*cos(4.47727329739 + 27197.03787618409*$t);
   $X3 += 0.00000000002*cos(2.76458797335 + 26617.8379241523*$t);
   $X3 += 0.00000000002*cos(2.01320187052 + 27043.7467006663*$t);
   $X3 += 0.00000000002*cos(6.24606226113 + 25558.4559939631*$t);
   $X3 += 0.00000000002*cos(2.88488990350 + 72602.62119305388*$t);
   $X3 += 0.00000000002*cos(1.80402690775 + 26068.47719815791*$t);
   $X3 += 0.00000000002*cos(0.72272570426 + 26107.81671995749*$t);
   $X3 += 0.00000000001*cos(5.15880419190 + 26092.0282944157*$t);
   $X3 += 0.00000000001*cos(3.65122349702 + 26084.2656236997*$t);
   $X3 += 0.00000000001*cos(3.47204379646 + 24978.28077199729*$t);
   $X3 += 0.00000000001*cos(3.04599592472 + 37410.8110573621*$t);
   $X3 += 0.00000000001*cos(0.31369621903 + 30640.1004561165*$t);
   $X3 += 0.00000000001*cos(0.38979376906 + 52705.7410657265*$t);
   $X3 += 0.00000000001*cos(5.01792294793 + 51220.4503590233*$t);
   $X3 += 0.00000000001*cos(1.77400727778 + 47624.0966035731*$t);
   $X3 += 0.00000000001*cos(6.21364236354 + 208702.98131511007*$t);
   $X3 += 0.00000000001*cos(3.26982842147 + 9104.1508116011*$t);
   $X3 += 0.00000000001*cos(6.10085930771 + 98690.52433462809*$t);
   $X3 += 0.00000000001*cos(2.72881790021 + 955.3559241251*$t);
   $X3 += 0.00000000001*cos(2.74013903592 + 1109.6223695769*$t);
   $X3 += 0.00000000001*cos(2.00927169251 + 19317.43635781211*$t);
   $X3 += 0.00000000001*cos(4.85871407247 + 50586.97720534809*$t);
   $X3 += 0.00000000001*cos(5.37897907969 + 12566.3955174663*$t);
   $X3 += 0.00000000001*cos(3.51249866668 + 40853.3860023275*$t);
   $X3 += 0.00000000001*cos(3.74067924304 + 53235.43203082109*$t);
   $X3 += 0.00000000001*cos(4.93930525226 + 339142.98465794802*$t);
   $X3 += 0.00000000001*cos(3.64879489376 + 426.8420083595*$t);
   $X3 += 0.00000000001*cos(2.70663061614 + 49957.2929964451*$t);
   $X3 += 0.00000000001*cos(4.05940415323 + 26095.2605060585*$t);
   $X3 += 0.00000000001*cos(4.79523771458 + 26081.03341205689*$t);
   $X3 += 0.00000000001*cos(4.56727257443 + 23869.3898548709*$t);
   $X3 += 0.00000000001*cos(1.91316161387 + 77308.35350059748*$t);
   $X3 += 0.00000000001*cos(5.81582715174 + 105461.23493587368*$t);
   $X3 += 0.00000000001*cos(1.67826436610 + 51646.3591355373*$t);
   $X3 += 0.00000000001*cos(2.42681597375 + 155418.28411483529*$t);
   $X3 += 0.00000000001*cos(4.76066610745 + 56728.0035976907*$t);
   $X3 += 0.00000000001*cos(3.51433188972 + 53131.6498422405*$t);
   $X3 += 0.00000000001*cos(0.78156168692 + 3442.81876244891*$t);
   $X3 += 0.00000000001*cos(3.65095652022 + 78793.64420730069*$t);
   $X3 += 0.00000000001*cos(6.11514198482 + 54394.80720481869*$t);
   $X3 += 0.00000000001*cos(0.70996446104 + 79323.33517239528*$t);
   $X3 += 0.00000000001*cos(4.23955129941 + 28306.90406324449*$t);
   $X3 += 0.00000000001*cos(0.04814737416 + 45405.3394993863*$t);
   $X3 += 0.00000000001*cos(0.51322200896 + 32858.8575603033*$t);
   $X3 += 0.00000000000*cos(2.70568366640 + 529.44714761109*$t);
   $X3 += 0.00000000001*cos(1.65918694650 + 25028.7650288685*$t);
   $X3 += 0.00000000000*cos(2.60942411635 + 25874.8478636197*$t);
   $X3 += 0.00000000001*cos(1.76282246473 + 22645.57201409229*$t);
   $X3 += 0.00000000000*cos(2.31611990566 + 640.1411037975*$t);
   $X3 += 0.00000000000*cos(0.89355979270 + 529.9347825781*$t);
   $X3 += 0.00000000000*cos(6.21531765450 + 26301.4460544957*$t);
   $X3 += 0.00000000000*cos(3.72335130305 + 83925.28529135829*$t);
   $X3 += 0.00000000000*cos(1.81919615354 + 82815.90673926489*$t);
   $X3 += 0.00000000001*cos(1.59769152646 + 27677.2198543415*$t);
   $X3 += 0.00000000000*cos(3.60725162991 + 11322.42028082089*$t);
   $X3 += 0.00000000000*cos(0.07486495309 + 36301.4325052687*$t);
   $X3 += 0.00000000000*cos(4.52680880738 + 5661.5758666357*$t);
   $X3 += 0.00000000000*cos(3.07463170530 + 18849.4713674577*$t);
   $X3 += 0.00000000000*cos(1.10484790510 + 6770.46678376209*$t);
   $X3 += 0.00000000000*cos(5.54664261005 + 43072.1431065143*$t);
   $X3 += 0.00000000000*cos(4.85626455897 + 52156.38033973211*$t);
   $X3 += 0.00000000000*cos(3.44123385645 + 39609.8984006491*$t);
   $X3 += 0.00000000000*cos(0.10298074121 + 1052.51220067191*$t);
   $X3 += 0.00000000000*cos(2.42274340940 + 15874.8614128467*$t);
   $X3 += 0.00000000000*cos(5.90990701318 + 1066.7392946735*$t);
   $X3 += 0.00000000000*cos(0.47240363594 + 24499.0740637739*$t);
   $X3 += 0.00000000000*cos(4.58808593083 + 2119.00767786191*$t);
   $X3 += 0.00000000000*cos(1.93271006548 + 52179.9314359899*$t);
   $X3 += 0.00000000000*cos(2.71699794579 + 27043.2590656993*$t);
   $X3 += 0.00000000000*cos(0.78321130217 + 29530.7219040231*$t);
   $X3 += 0.00000000000*cos(0.87395244120 + 20426.32727493849*$t);
   $X3 += 0.00000000000*cos(0.22412464998 + 26514.7451499337*$t);
   $X3 += 0.00000000000*cos(2.09910746178 + 38654.2986590405*$t);
   $X3 += 0.00000000000*cos(0.37782872130 + 51066.18391357149*$t);
   $X3 += 0.00000000000*cos(6.08588015961 + 63498.71419893629*$t);
   $X3 += 0.00000000000*cos(3.06180705468 + 234790.88445668427*$t);
   $X3 += 0.00000000000*cos(0.44816354598 + 110013.18843293248*$t);
   $X3 += 0.00000000000*cos(3.76757290021 + 52195.71986153169*$t);
   $X3 += 0.00000000000*cos(0.26388289924 + 76674.88034692229*$t);
   $X3 += 0.00000000000*cos(3.06411835882 + 4551.7096795753*$t);
   $X3 += 0.00000000000*cos(1.55289005756 + 7.3573644843*$t);
   $X3 += 0.00000000000*cos(5.69100090266 + 33326.8225506577*$t);
   $X3 += 0.00000000000*cos(4.84238249166 + 2218.51328670329*$t);
   $X3 += 0.00000000000*cos(5.21804461989 + 51749.45190975589*$t);
   $X3 += 0.00000000000*cos(0.07928724753 + 7238.4317741165*$t);
   $X3 += 0.00000000000*cos(0.41819802690 + 52172.1687652739*$t);
   $X3 += 0.00000000000*cos(1.04835331170 + 53284.94101775829*$t);
   $X3 += 0.00000000000*cos(0.31150101949 + 66941.2891439017*$t);
   $X3 += 0.00000000000*cos(1.30179196383 + 52168.93655363109*$t);
   $X3 += 0.00000000000*cos(3.59073128026 + 58946.76070187749*$t);
   $X3 += 0.00000000000*cos(5.69460606394 + 30639.61282114949*$t);
   $X3 += 0.00000000000*cos(3.09211354360 + 62389.33564684289*$t);
   $X3 += 0.00000000000*cos(3.64742441695 + 105411.23831396949*$t);
   $X3 += 0.00000000000*cos(2.56174511433 + 103292.47445359109*$t);
   $X3 += 0.00000000000*cos(3.50117859238 + 23868.9022199039*$t);
   return $X3*$t*$t*$t;
}



   function Mercury_X4($t) // 42 terms of order 4
{
   $X4  = 0.00000043303*cos(2.70854317703 + 26088.1469590577*$t);
   $X4 += 0.00000016746*cos(2.85109602051 + 0.2438174835*$t);
   $X4 += 0.00000005097*cos(5.82035608585 + 52176.0501006319*$t);
   $X4 += 0.00000001110*cos(2.85416500039 + 78263.95324220609*$t);
   $X4 += 0.00000000968*cos(3.18837996543 + 26087.65932409069*$t);
   $X4 += 0.00000000362*cos(0.10660634045 + 104351.85638378029*$t);
   $X4 += 0.00000000161*cos(3.56341896847 + 130439.75952535449*$t);
   $X4 += 0.00000000075*cos(0.55603774289 + 156527.66266692868*$t);
   $X4 += 0.00000000076*cos(6.07252064875 + 52175.56246566489*$t);
   $X4 += 0.00000000033*cos(3.72826875982 + 182615.56580850288*$t);
   $X4 += 0.00000000014*cos(2.40716156772 + 78263.46560723908*$t);
   $X4 += 0.00000000014*cos(0.56399976721 + 208703.46895007708*$t);
   $X4 += 0.00000000005*cos(3.66056233199 + 234791.37209165128*$t);
   $X4 += 0.00000000004*cos(5.13174489459 + 104351.36874881329*$t);
   $X4 += 0.00000000002*cos(2.87490875788 + 24978.7684069643*$t);
   $X4 += 0.00000000002*cos(5.84989349950 + 27197.5255111511*$t);
   $X4 += 0.00000000002*cos(0.45146054812 + 260879.27523322542*$t);
   $X4 += 0.00000000001*cos(1.74376603369 + 130439.27189038748*$t);
   $X4 += 0.00000000001*cos(3.51635178690 + 286967.17837479962*$t);
   $X4 += 0.00000000001*cos(0.06797049294 + 51066.6715485385*$t);
   $X4 += 0.00000000001*cos(1.33488273309 + 1059.6257476727*$t);
   $X4 += 0.00000000001*cos(0.19743580633 + 20426.8149099055*$t);
   $X4 += 0.00000000000*cos(4.73344633686 + 156527.17503196168*$t);
   $X4 += 0.00000000000*cos(3.03361722015 + 53285.4286527253*$t);
   $X4 += 0.00000000000*cos(0.28697199826 + 1109.1347346099*$t);
   $X4 += 0.00000000000*cos(2.12246327493 + 31749.4790082099*$t);
   $X4 += 0.00000000000*cos(3.62335756262 + 77154.57469011268*$t);
   $X4 += 0.00000000000*cos(5.27675905248 + 4552.1973145423*$t);
   $X4 += 0.00000000000*cos(0.97938730115 + 51116.6681704427*$t);
   $X4 += 0.00000000000*cos(2.90146638781 + 5661.0882316687*$t);
   $X4 += 0.00000000000*cos(3.37193339699 + 21536.1934619989*$t);
   $X4 += 0.00000000000*cos(1.47858093383 + 182615.07817353586*$t);
   $X4 += 0.00000000000*cos(3.30664239042 + 46514.7180514797*$t);
   $X4 += 0.00000000000*cos(2.38442876069 + 1589.3167127673*$t);
   $X4 += 0.00000000000*cos(4.43080795748 + 27147.5288892469*$t);
   $X4 += 0.00000000000*cos(5.33267823849 + 25132.5472174491*$t);
   $X4 += 0.00000000000*cos(0.89978296758 + 26617.8379241523*$t);
   $X4 += 0.00000000000*cos(4.07365069575 + 14765.48286075331*$t);
   $X4 += 0.00000000000*cos(1.63297628773 + 25558.4559939631*$t);
   $X4 += 0.00000000000*cos(3.35368510638 + 27043.7467006663*$t);
   $X4 += 0.00000000000*cos(4.71304947972 + 529.9347825781*$t);
   $X4 += 0.00000000000*cos(5.15326778299 + 57837.3821497841*$t);
   return $X4*$t*$t*$t*$t;
}



   function Mercury_X5($t) // 16 terms of order 5
{
   $X5  = 0.00000000414*cos(4.09017660105 + 0.2438174835*$t);
   $X5 += 0.00000000327*cos(2.83894329980 + 26088.1469590577*$t);
   $X5 += 0.00000000134*cos(4.51536199764 + 52176.0501006319*$t);
   $X5 += 0.00000000046*cos(1.23267980717 + 78263.95324220609*$t);
   $X5 += 0.00000000016*cos(4.45794773259 + 104351.85638378029*$t);
   $X5 += 0.00000000007*cos(5.57199695746 + 26087.65932409069*$t);
   $X5 += 0.00000000006*cos(1.55726840151 + 130439.75952535449*$t);
   $X5 += 0.00000000003*cos(4.94192470876 + 156527.66266692868*$t);
   $X5 += 0.00000000001*cos(1.93929522999 + 182615.56580850288*$t);
   $X5 += 0.00000000001*cos(4.16271885947 + 52175.56246566489*$t);
   $X5 += 0.00000000001*cos(5.10948519211 + 208703.46895007708*$t);
   $X5 += 0.00000000000*cos(0.99915185773 + 78263.46560723908*$t);
   $X5 += 0.00000000000*cos(1.90802069686 + 234791.37209165128*$t);
   $X5 += 0.00000000000*cos(3.92135630671 + 104351.36874881329*$t);
   $X5 += 0.00000000000*cos(1.30030594321 + 24978.7684069643*$t);
   $X5 += 0.00000000000*cos(0.96944549328 + 27197.5255111511*$t);
   return $X5*$t*$t*$t*$t*$t;
}



   function Mercury_Y0($t) // 1853 terms of order 0
{
   $Y0  = 0.37749277893*cos(2.83179506899 + 26088.1469590577*$t);
   $Y0 += 0.11918926148*cos(2.91948125760 + 0.2438174835*$t);
   $Y0 += 0.03840153904*cos(5.88254544140 + 52176.0501006319*$t);
   $Y0 += 0.00585979278*cos(2.65010770289 + 78263.95324220609*$t);
   $Y0 += 0.00305833424*cos(3.67378306016 + 26087.65932409069*$t);
   $Y0 += 0.00105974941*cos(5.70085415459 + 104351.85638378029*$t);
   $Y0 += 0.00024906132*cos(0.55066770933 + 52175.56246566489*$t);
   $Y0 += 0.00021056065*cos(2.46841472315 + 130439.75952535449*$t);
   $Y0 += 0.00004441671*cos(5.51916065495 + 156527.66266692868*$t);
   $Y0 += 0.00003347442*cos(3.67952842081 + 78263.46560723908*$t);
   $Y0 += 0.00000976617*cos(2.28672075339 + 182615.56580850288*$t);
   $Y0 += 0.00000703903*cos(2.88960689088 + 24978.7684069643*$t);
   $Y0 += 0.00000640528*cos(5.91381352466 + 27197.5255111511*$t);
   $Y0 += 0.00000558149*cos(0.50510861725 + 104351.36874881329*$t);
   $Y0 += 0.00000447775*cos(1.40511442556 + 1059.6257476727*$t);
   $Y0 += 0.00000400281*cos(0.29865270517 + 20426.8149099055*$t);
   $Y0 += 0.00000283882*cos(2.22271091529 + 31749.4790082099*$t);
   $Y0 += 0.00000191007*cos(2.70458121832 + 53285.4286527253*$t);
   $Y0 += 0.00000181454*cos(0.23779467119 + 1109.1347346099*$t);
   $Y0 += 0.00000193895*cos(5.38872313263 + 4552.1973145423*$t);
   $Y0 += 0.00000221371*cos(5.33746575111 + 208703.46895007708*$t);
   $Y0 += 0.00000139001*cos(5.94193853313 + 51066.6715485385*$t);
   $Y0 += 0.00000183933*cos(2.76579938720 + 5661.0882316687*$t);
   $Y0 += 0.00000153303*cos(1.11372235868 + 51116.6681704427*$t);
   $Y0 += 0.00000104855*cos(3.60039284031 + 130439.27189038748*$t);
   $Y0 += 0.00000115202*cos(5.27930045344 + 57837.3821497841*$t);
   $Y0 += 0.00000090628*cos(4.97031050861 + 529.9347825781*$t);
   $Y0 += 0.00000075318*cos(4.50136079719 + 27147.5288892469*$t);
   $Y0 += 0.00000072957*cos(3.43332933363 + 21536.1934619989*$t);
   $Y0 += 0.00000074803*cos(3.35834807468 + 46514.7180514797*$t);
   $Y0 += 0.00000068710*cos(4.91618713593 + 25132.5472174491*$t);
   $Y0 += 0.00000083504*cos(1.60859812856 + 10213.5293636945*$t);
   $Y0 += 0.00000060985*cos(3.88048699951 + 27043.7467006663*$t);
   $Y0 += 0.00000057987*cos(4.13400021557 + 14765.48286075331*$t);
   $Y0 += 0.00000060953*cos(3.43164694662 + 47624.0966035731*$t);
   $Y0 += 0.00000053356*cos(0.72676419246 + 26617.8379241523*$t);
   $Y0 += 0.00000054964*cos(3.74064645856 + 12566.3955174663*$t);
   $Y0 += 0.00000047881*cos(5.75865881516 + 79373.33179429949*$t);
   $Y0 += 0.00000051263*cos(1.96665333979 + 426.8420083595*$t);
   $Y0 += 0.00000051361*cos(2.10502555376 + 234791.37209165128*$t);
   $Y0 += 0.00000050374*cos(2.03207321104 + 25558.4559939631*$t);
   $Y0 += 0.00000048449*cos(1.94914263411 + 1589.3167127673*$t);
   $Y0 += 0.00000048867*cos(4.16469048525 + 77204.57131201689*$t);
   $Y0 += 0.00000034739*cos(4.11430856351 + 51646.3591355373*$t);
   $Y0 += 0.00000032851*cos(4.56963272977 + 955.3559241251*$t);
   $Y0 += 0.00000044998*cos(0.91167682267 + 41962.7645544209*$t);
   $Y0 += 0.00000031618*cos(4.66914248946 + 37410.8110573621*$t);
   $Y0 += 0.00000028634*cos(5.42748718604 + 30640.1004561165*$t);
   $Y0 += 0.00000031480*cos(2.70995810641 + 77154.57469011268*$t);
   $Y0 += 0.00000032102*cos(2.04798101755 + 83925.28529135829*$t);
   $Y0 += 0.00000027670*cos(5.06128264443 + 39609.8984006491*$t);
   $Y0 += 0.00000026872*cos(4.68921320015 + 36301.4325052687*$t);
   $Y0 += 0.00000023054*cos(0.71973276708 + 53131.6498422405*$t);
   $Y0 += 0.00000026193*cos(5.26902812193 + 11322.42028082089*$t);
   $Y0 += 0.00000021235*cos(0.40309333526 + 156527.17503196168*$t);
   $Y0 += 0.00000026946*cos(0.19172960930 + 6283.3196674749*$t);
   $Y0 += 0.00000020875*cos(4.09807664196 + 15874.8614128467*$t);
   $Y0 += 0.00000016454*cos(0.12816102587 + 72602.62119305388*$t);
   $Y0 += 0.00000016101*cos(1.65540440480 + 9104.1508116011*$t);
   $Y0 += 0.00000022241*cos(5.60722857321 + 13521.50762410789*$t);
   $Y0 += 0.00000021188*cos(0.19996828748 + 73711.99974514729*$t);
   $Y0 += 0.00000015123*cos(1.24465016017 + 18849.4713674577*$t);
   $Y0 += 0.00000017255*cos(0.24107386270 + 27197.03787618409*$t);
   $Y0 += 0.00000017287*cos(0.55372068563 + 51749.45190975589*$t);
   $Y0 += 0.00000013862*cos(1.29323907537 + 53235.43203082109*$t);
   $Y0 += 0.00000015239*cos(1.96671567039 + 7238.4317741165*$t);
   $Y0 += 0.00000016863*cos(0.57148727289 + 50586.97720534809*$t);
   $Y0 += 0.00000013546*cos(3.64906926506 + 52705.7410657265*$t);
   $Y0 += 0.00000013134*cos(4.21391538202 + 25028.7650288685*$t);
   $Y0 += 0.00000014145*cos(1.46555737893 + 63498.71419893629*$t);
   $Y0 += 0.00000013081*cos(0.20810129185 + 26068.47719815791*$t);
   $Y0 += 0.00000013058*cos(2.31384723416 + 26107.81671995749*$t);
   $Y0 += 0.00000013609*cos(1.68775421835 + 51220.4503590233*$t);
   $Y0 += 0.00000013539*cos(0.93214332140 + 103292.47445359109*$t);
   $Y0 += 0.00000012138*cos(5.15577059992 + 260879.27523322542*$t);
   $Y0 += 0.00000011433*cos(0.41025670835 + 19317.43635781211*$t);
   $Y0 += 0.00000010174*cos(0.82322453273 + 77734.26227711148*$t);
   $Y0 += 0.00000012016*cos(3.96439926693 + 68050.66769599509*$t);
   $Y0 += 0.00000012094*cos(2.52834929119 + 105461.23493587368*$t);
   $Y0 += 0.00000009215*cos(0.91145814574 + 40853.3860023275*$t);
   $Y0 += 0.00000009157*cos(1.25590715075 + 33326.8225506577*$t);
   $Y0 += 0.00000009552*cos(0.53954398597 + 38654.2986590405*$t);
   $Y0 += 0.00000012500*cos(2.32164805011 + 45892.9742506405*$t);
   $Y0 += 0.00000008978*cos(5.18856241237 + 26084.2656236997*$t);
   $Y0 += 0.00000008975*cos(3.61663563272 + 26092.0282944157*$t);
   $Y0 += 0.00000012160*cos(1.83585138946 + 65697.80154222329*$t);
   $Y0 += 0.00000008880*cos(5.05045852302 + 26514.7451499337*$t);
   $Y0 += 0.00000008892*cos(5.46009752557 + 3442.81876244891*$t);
   $Y0 += 0.00000008503*cos(5.09915668367 + 110013.18843293248*$t);
   $Y0 += 0.00000010244*cos(4.07406090643 + 21535.70582703189*$t);
   $Y0 += 0.00000008816*cos(3.29850433474 + 32371.2228090491*$t);
   $Y0 += 0.00000009705*cos(0.73577020420 + 529.44714761109*$t);
   $Y0 += 0.00000007663*cos(2.16404811803 + 56728.0035976907*$t);
   $Y0 += 0.00000007852*cos(5.36793581356 + 5661.5758666357*$t);
   $Y0 += 0.00000008166*cos(5.04025521360 + 27677.2198543415*$t);
   $Y0 += 0.00000007299*cos(2.72074453751 + 6770.46678376209*$t);
   $Y0 += 0.00000007437*cos(2.10814922209 + 32858.8575603033*$t);
   $Y0 += 0.00000007796*cos(2.76073375309 + 31748.99137324289*$t);
   $Y0 += 0.00000006786*cos(0.86898827574 + 43072.1431065143*$t);
   $Y0 += 0.00000007408*cos(2.97710007179 + 23869.3898548709*$t);
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   $Y0 += 0.00000000002*cos(3.83932556111 + 148532.64658993746*$t);
   $Y0 += 0.00000000002*cos(0.69773290752 + 148533.13422490445*$t);
   $Y0 += 0.00000000002*cos(3.08932581659 + 77307.17645126847*$t);
   $Y0 += 0.00000000002*cos(4.53508525261 + 191.6920835951*$t);
   $Y0 += 0.00000000002*cos(1.91266463584 + 23976.00901071309*$t);
   $Y0 += 0.00000000002*cos(2.51070394013 + 206370.27255720507*$t);
   $Y0 += 0.00000000002*cos(3.48548328265 + 4268.3379956771*$t);
   $Y0 += 0.00000000002*cos(0.27071972210 + 23962.2695516785*$t);
   $Y0 += 0.00000000002*cos(3.41231237569 + 23961.78191671149*$t);
   $Y0 += 0.00000000002*cos(2.77965182012 + 3776.6747032183*$t);
   $Y0 += 0.00000000002*cos(0.63445271713 + 24918.55870764909*$t);
   $Y0 += 0.00000000002*cos(4.78488159185 + 102769.40940053028*$t);
   $Y0 += 0.00000000002*cos(0.55778477986 + 25889.0749576213*$t);
   $Y0 += 0.00000000002*cos(1.96424759776 + 26287.21896049409*$t);
   $Y0 += 0.00000000002*cos(3.23447204926 + 2648.2110079895*$t);
   $Y0 += 0.00000000002*cos(4.14592395979 + 80432.71372448868*$t);
   $Y0 += 0.00000000002*cos(1.34549805675 + 13989.9602494293*$t);
   $Y0 += 0.00000000002*cos(1.17653432087 + 38186.3336686861*$t);
   $Y0 += 0.00000000002*cos(2.04577034444 + 8194.5191506921*$t);
   $Y0 += 0.00000000002*cos(5.70902071155 + 237009.64156087102*$t);
   $Y0 += 0.00000000002*cos(3.82569277203 + 24863.84148331209*$t);
   $Y0 += 0.00000000002*cos(5.50674253073 + 76064.86589891909*$t);
   $Y0 += 0.00000000002*cos(1.39914737585 + 71492.75500599349*$t);
   $Y0 += 0.00000000002*cos(6.18696209768 + 30831.5487222281*$t);
   $Y0 += 0.00000000002*cos(2.61825558712 + 21344.7451958873*$t);
   $Y0 += 0.00000000002*cos(1.07023698053 + 124663.98818751707*$t);
   $Y0 += 0.00000000001*cos(5.98706010174 + 101702.91392334028*$t);
   $Y0 += 0.00000000002*cos(1.35473982240 + 105404.12476696869*$t);
   $Y0 += 0.00000000002*cos(3.48042408913 + 307.31380348609*$t);
   $Y0 += 0.00000000002*cos(5.91402019226 + 184834.32291268966*$t);
   $Y0 += 0.00000000002*cos(5.91402019226 + 184833.83527772261*$t);
   $Y0 += 0.00000000001*cos(0.49434611754 + 124156.19604039608*$t);
   $Y0 += 0.00000000001*cos(4.86177343922 + 22909.51353352309*$t);
   $Y0 += 0.00000000001*cos(1.72018078563 + 22910.0011684901*$t);
   $Y0 += 0.00000000001*cos(5.79706734000 + 958.87904247409*$t);
   $Y0 += 0.00000000002*cos(2.31704185815 + 77196.97013004909*$t);
   $Y0 += 0.00000000002*cos(4.18763806284 + 9591.29792788829*$t);
   $Y0 += 0.00000000002*cos(2.60184968404 + 189385.78877478145*$t);
   $Y0 += 0.00000000001*cos(5.29048508788 + 24919.2481220111*$t);
   $Y0 += 0.00000000001*cos(3.51473259692 + 27257.0457961043*$t);
   $Y0 += 0.00000000002*cos(5.03520614299 + 25440.64849077589*$t);
   $Y0 += 0.00000000001*cos(5.16795059538 + 26010.3964150738*$t);
   $Y0 += 0.00000000002*cos(5.13757006415 + 43693.8869073535*$t);
   $Y0 += 0.00000000002*cos(5.04394896979 + 25014.05029989989*$t);
   $Y0 += 0.00000000001*cos(3.77902331302 + 9385.0848255587*$t);
   $Y0 += 0.00000000002*cos(6.17372295311 + 26202.09861277591*$t);
   $Y0 += 0.00000000001*cos(3.35135060198 + 52499.55551728929*$t);
   $Y0 += 0.00000000002*cos(5.03234764639 + 14650.55593710108*$t);
   $Y0 += 0.00000000002*cos(0.37520258538 + 78690.06379811508*$t);
   $Y0 += 0.00000000001*cos(1.65843797188 + 5039.34443082949*$t);
   $Y0 += 0.00000000002*cos(2.53532060227 + 2214.98690507971*$t);
   $Y0 += 0.00000000001*cos(5.07384686444 + 77211.19722405069*$t);
   $Y0 += 0.00000000001*cos(4.11905908237 + 233202.29919636747*$t);
   $Y0 += 0.00000000002*cos(3.92094587643 + 21516.52370109911*$t);
   $Y0 += 0.00000000002*cos(4.88427180837 + 30659.77021701629*$t);
   $Y0 += 0.00000000002*cos(0.59200954056 + 621.49998335569*$t);
   $Y0 += 0.00000000002*cos(2.70800261719 + 25764.15390743329*$t);
   $Y0 += 0.00000000001*cos(3.75051661568 + 26.5421372833*$t);
   $Y0 += 0.00000000001*cos(3.87625546504 + 226796.35601466001*$t);
   $Y0 += 0.00000000001*cos(3.87625546504 + 226796.84364962706*$t);
   $Y0 += 0.00000000002*cos(5.04685227536 + 28839.69455874929*$t);
   $Y0 += 0.00000000002*cos(3.93268001276 + 102225.97897640108*$t);
   $Y0 += 0.00000000002*cos(6.27298790851 + 129971.79453500008*$t);
   $Y0 += 0.00000000002*cos(5.63544803962 + 27139.92770727909*$t);
   $Y0 += 0.00000000001*cos(1.05389010615 + 50807.38984778689*$t);
   $Y0 += 0.00000000001*cos(1.45067645500 + 78187.19953596349*$t);
   $Y0 += 0.00000000002*cos(3.49292360736 + 51472.41691601449*$t);
   return $Y0;
}



   function Mercury_Y1($t) // 1023 terms of order 1
{
   $Y1  = 0.00328639517*cos(4.46949126315 + 0.2438174835*$t);
   $Y1 += 0.00106107047*cos(4.34458837257 + 52176.0501006319*$t);
   $Y1 += 0.00032448440*cos(1.11324531456 + 78263.95324220609*$t);
   $Y1 += 0.00009699418*cos(0.71696945020 + 26087.65932409069*$t);
   $Y1 += 0.00008808490*cos(4.16435393159 + 104351.85638378029*$t);
   $Y1 += 0.00004833058*cos(4.93174326512 + 26088.1469590577*$t);
   $Y1 += 0.00002334329*cos(0.93209482754 + 130439.75952535449*$t);
   $Y1 += 0.00000890250*cos(4.18838297765 + 52175.56246566489*$t);
   $Y1 += 0.00000615643*cos(3.98294823708 + 156527.66266692868*$t);
   $Y1 += 0.00000147225*cos(1.38491342638 + 78263.46560723908*$t);
   $Y1 += 0.00000162460*cos(0.75058057907 + 182615.56580850288*$t);
   $Y1 += 0.00000069502*cos(1.34859955230 + 24978.7684069643*$t);
   $Y1 += 0.00000063529*cos(1.17140322075 + 27197.5255111511*$t);
   $Y1 += 0.00000042967*cos(3.80137602608 + 208703.46895007708*$t);
   $Y1 += 0.00000032514*cos(4.75515678790 + 104351.36874881329*$t);
   $Y1 += 0.00000017597*cos(4.40134253408 + 51066.6715485385*$t);
   $Y1 += 0.00000013287*cos(4.22067115617 + 53285.4286527253*$t);
   $Y1 += 0.00000011758*cos(1.75773369521 + 1109.1347346099*$t);
   $Y1 += 0.00000012502*cos(6.11835337393 + 1059.6257476727*$t);
   $Y1 += 0.00000011468*cos(5.06247506599 + 20426.8149099055*$t);
   $Y1 += 0.00000011394*cos(0.56897531807 + 234791.37209165128*$t);
   $Y1 += 0.00000008221*cos(3.74149753253 + 31749.4790082099*$t);
   $Y1 += 0.00000008067*cos(1.73031128392 + 130439.27189038748*$t);
   $Y1 += 0.00000006176*cos(3.89018803821 + 4552.1973145423*$t);
   $Y1 += 0.00000004784*cos(4.97654366187 + 21536.1934619989*$t);
   $Y1 += 0.00000004858*cos(1.16998032311 + 77154.57469011268*$t);
   $Y1 += 0.00000004269*cos(1.82558089427 + 46514.7180514797*$t);
   $Y1 += 0.00000004412*cos(3.53054557745 + 25132.5472174491*$t);
   $Y1 += 0.00000003922*cos(0.80899339690 + 1589.3167127673*$t);
   $Y1 += 0.00000004017*cos(2.84593275079 + 27147.5288892469*$t);
   $Y1 += 0.00000003763*cos(2.60830060517 + 14765.48286075331*$t);
   $Y1 += 0.00000004285*cos(2.70027245882 + 51116.6681704427*$t);
   $Y1 += 0.00000003901*cos(5.26131971011 + 27043.7467006663*$t);
   $Y1 += 0.00000003221*cos(5.81041475267 + 26617.8379241523*$t);
   $Y1 += 0.00000003080*cos(3.11167500886 + 25558.4559939631*$t);
   $Y1 += 0.00000003030*cos(3.61976417137 + 260879.27523322542*$t);
   $Y1 += 0.00000002907*cos(4.94283048350 + 26068.47719815791*$t);
   $Y1 += 0.00000002906*cos(3.86228296506 + 26107.81671995749*$t);
   $Y1 += 0.00000002383*cos(0.50751116011 + 26084.2656236997*$t);
   $Y1 += 0.00000002381*cos(2.01445897738 + 26092.0282944157*$t);
   $Y1 += 0.00000002069*cos(6.19366221907 + 37410.8110573621*$t);
   $Y1 += 0.00000002028*cos(3.87421613919 + 30640.1004561165*$t);
   $Y1 += 0.00000002088*cos(4.91615750193 + 156527.17503196168*$t);
   $Y1 += 0.00000001998*cos(0.93225615522 + 79373.33179429949*$t);
   $Y1 += 0.00000001880*cos(4.93819019021 + 47624.0966035731*$t);
   $Y1 += 0.00000001580*cos(0.12078980001 + 9104.1508116011*$t);
   $Y1 += 0.00000001575*cos(5.88747787298 + 955.3559241251*$t);
   $Y1 += 0.00000001508*cos(5.14798771540 + 19317.43635781211*$t);
   $Y1 += 0.00000001397*cos(4.87619009368 + 72602.62119305388*$t);
   $Y1 += 0.00000001363*cos(1.71613837922 + 50586.97720534809*$t);
   $Y1 += 0.00000001495*cos(2.20742717983 + 12566.3955174663*$t);
   $Y1 += 0.00000001401*cos(0.47782643773 + 426.8420083595*$t);
   $Y1 += 0.00000001215*cos(2.36706136703 + 52705.7410657265*$t);
   $Y1 += 0.00000001310*cos(0.91525566474 + 26095.2605060585*$t);
   $Y1 += 0.00000001272*cos(1.65165069758 + 26081.03341205689*$t);
   $Y1 += 0.00000001476*cos(1.42289389144 + 23869.3898548709*$t);
   $Y1 += 0.00000001169*cos(3.92032031637 + 3442.81876244891*$t);
   $Y1 += 0.00000001103*cos(5.93142816578 + 53235.43203082109*$t);
   $Y1 += 0.00000001375*cos(4.22153989222 + 103242.47783168689*$t);
   $Y1 += 0.00000001244*cos(0.25422201490 + 51220.4503590233*$t);
   $Y1 += 0.00000001238*cos(1.09570749211 + 28306.90406324449*$t);
   $Y1 += 0.00000000967*cos(2.00095625807 + 53131.6498422405*$t);
   $Y1 += 0.00000000986*cos(3.65234674915 + 32858.8575603033*$t);
   $Y1 += 0.00000000911*cos(5.86347762782 + 529.44714761109*$t);
   $Y1 += 0.00000000859*cos(5.65763791955 + 40853.3860023275*$t);
   $Y1 += 0.00000000855*cos(3.76170634741 + 27677.2198543415*$t);
   $Y1 += 0.00000000844*cos(5.74887533238 + 25874.8478636197*$t);
   $Y1 += 0.00000001042*cos(4.90279640329 + 22645.57201409229*$t);
   $Y1 += 0.00000000924*cos(5.45463398257 + 640.1411037975*$t);
   $Y1 += 0.00000000810*cos(3.07111874736 + 26301.4460544957*$t);
   $Y1 += 0.00000000807*cos(0.38735610376 + 286967.17837479962*$t);
   $Y1 += 0.00000000875*cos(0.56063513084 + 83925.28529135829*$t);
   $Y1 += 0.00000000874*cos(3.97964673458 + 529.9347825781*$t);
   $Y1 += 0.00000000821*cos(3.19953070235 + 36301.4325052687*$t);
   $Y1 += 0.00000000823*cos(0.48663689329 + 11322.42028082089*$t);
   $Y1 += 0.00000000738*cos(0.62901815542 + 56728.0035976907*$t);
   $Y1 += 0.00000000724*cos(6.21294643252 + 18849.4713674577*$t);
   $Y1 += 0.00000000714*cos(4.24977924185 + 6770.46678376209*$t);
   $Y1 += 0.00000000667*cos(2.40282291967 + 43072.1431065143*$t);
   $Y1 += 0.00000000665*cos(1.71193023872 + 52156.38033973211*$t);
   $Y1 += 0.00000000893*cos(1.99786430454 + 27197.03787618409*$t);
   $Y1 += 0.00000000752*cos(0.31686311777 + 39609.8984006491*$t);
   $Y1 += 0.00000000673*cos(3.24236433600 + 1052.51220067191*$t);
   $Y1 += 0.00000000688*cos(5.57273946980 + 15874.8614128467*$t);
   $Y1 += 0.00000000618*cos(0.55635839524 + 5661.5758666357*$t);
   $Y1 += 0.00000000808*cos(2.76566323402 + 1066.7392946735*$t);
   $Y1 += 0.00000000616*cos(5.41694945887 + 51646.3591355373*$t);
   $Y1 += 0.00000000650*cos(6.10338500409 + 25028.7650288685*$t);
   $Y1 += 0.00000000550*cos(1.77567872746 + 182615.07817353586*$t);
   $Y1 += 0.00000000554*cos(1.44404571039 + 2119.00767786191*$t);
   $Y1 += 0.00000000535*cos(5.07158844336 + 52179.9314359899*$t);
   $Y1 += 0.00000000657*cos(3.92169541273 + 29530.7219040231*$t);
   $Y1 += 0.00000000527*cos(3.36241476084 + 26514.7451499337*$t);
   $Y1 += 0.00000000502*cos(5.23707918628 + 38654.2986590405*$t);
   $Y1 += 0.00000000568*cos(1.89274232427 + 24978.28077199729*$t);
   $Y1 += 0.00000000498*cos(2.94458194590 + 63498.71419893629*$t);
   $Y1 += 0.00000000469*cos(3.58596298240 + 110013.18843293248*$t);
   $Y1 += 0.00000000521*cos(0.62400943535 + 52195.71986153169*$t);
   $Y1 += 0.00000000440*cos(1.64399949118 + 98690.52433462809*$t);
   $Y1 += 0.00000000580*cos(4.69289380268 + 7.3573644843*$t);
   $Y1 += 0.00000000438*cos(2.54950574588 + 33326.8225506577*$t);
   $Y1 += 0.00000000530*cos(1.70361729355 + 2218.51328670329*$t);
   $Y1 += 0.00000000483*cos(2.07663666251 + 51749.45190975589*$t);
   $Y1 += 0.00000000434*cos(3.55771117131 + 52172.1687652739*$t);
   $Y1 += 0.00000000408*cos(3.22512461303 + 7238.4317741165*$t);
   $Y1 += 0.00000000390*cos(5.33070151567 + 78793.64420730069*$t);
   $Y1 += 0.00000000374*cos(0.44775435653 + 58946.76070187749*$t);
   $Y1 += 0.00000000404*cos(4.44096026376 + 52168.93655363109*$t);
   $Y1 += 0.00000000356*cos(6.23046854548 + 62389.33564684289*$t);
   $Y1 += 0.00000000373*cos(5.69827259585 + 103292.47445359109*$t);
   $Y1 += 0.00000000326*cos(2.72823636104 + 79323.33517239528*$t);
   $Y1 += 0.00000000393*cos(0.98972344950 + 129330.38097326108*$t);
   $Y1 += 0.00000000385*cos(3.94475257678 + 52183.1636476327*$t);
   $Y1 += 0.00000000316*cos(4.54068234172 + 76674.88034692229*$t);
   $Y1 += 0.00000000390*cos(4.17402259459 + 54394.80720481869*$t);
   $Y1 += 0.00000000323*cos(4.47818749821 + 49957.2929964451*$t);
   $Y1 += 0.00000000299*cos(3.00180406182 + 16983.75232997309*$t);
   $Y1 += 0.00000000328*cos(2.47784503610 + 68050.66769599509*$t);
   $Y1 += 0.00000000314*cos(3.34927785340 + 51536.15281431789*$t);
   $Y1 += 0.00000000367*cos(3.28176962437 + 77308.35350059748*$t);
   $Y1 += 0.00000000316*cos(1.92123984210 + 45405.3394993863*$t);
   $Y1 += 0.00000000319*cos(2.66908913597 + 13656.10430865991*$t);
   $Y1 += 0.00000000266*cos(4.93516999025 + 48733.47515566649*$t);
   $Y1 += 0.00000000289*cos(1.34161862787 + 6.86972951729*$t);
   $Y1 += 0.00000000261*cos(2.43104654910 + 16984.2399649401*$t);
   $Y1 += 0.00000000261*cos(6.20453445714 + 52389.3491960699*$t);
   $Y1 += 0.00000000233*cos(5.55470184122 + 51123.7817174435*$t);
   $Y1 += 0.00000000231*cos(3.67240300147 + 82815.90673926489*$t);
   $Y1 += 0.00000000239*cos(1.23297150719 + 213.5429129215*$t);
   $Y1 += 0.00000000222*cos(2.42341131487 + 66941.2891439017*$t);
   $Y1 += 0.00000000216*cos(3.43857770880 + 313055.08151637383*$t);
   $Y1 += 0.00000000276*cos(6.03736928820 + 51109.55462344189*$t);
   $Y1 += 0.00000000222*cos(1.79769065581 + 32371.2228090491*$t);
   $Y1 += 0.00000000198*cos(0.48217448832 + 53765.1229959157*$t);
   $Y1 += 0.00000000197*cos(5.45332171285 + 69160.04624808849*$t);
   $Y1 += 0.00000000196*cos(1.08031906323 + 50057.2862402535*$t);
   $Y1 += 0.00000000202*cos(2.45524349258 + 129380.37759516528*$t);
   $Y1 += 0.00000000201*cos(2.89680722301 + 44937.3745090319*$t);
   $Y1 += 0.00000000216*cos(3.72207636306 + 213.0552779545*$t);
   $Y1 += 0.00000000185*cos(0.34499909570 + 136101.09157450669*$t);
   $Y1 += 0.00000000183*cos(0.69231889541 + 419.72846135871*$t);
   $Y1 += 0.00000000186*cos(5.71673843636 + 57837.3821497841*$t);
   $Y1 += 0.00000000178*cos(3.70090079088 + 105461.23493587368*$t);
   $Y1 += 0.00000000177*cos(2.18468434488 + 51962.7510051939*$t);
   $Y1 += 0.00000000170*cos(4.76419946756 + 78244.28348130629*$t);
   $Y1 += 0.00000000229*cos(0.17271876456 + 433.9555553603*$t);
   $Y1 += 0.00000000173*cos(5.50271484365 + 94138.57083756929*$t);
   $Y1 += 0.00000000157*cos(2.02010274317 + 64742.2018006147*$t);
   $Y1 += 0.00000000153*cos(5.58836484297 + 59414.7256922319*$t);
   $Y1 += 0.00000000159*cos(4.59819683221 + 853.4401992355*$t);
   $Y1 += 0.00000000155*cos(3.11896173244 + 35192.0539531753*$t);
   $Y1 += 0.00000000149*cos(5.04913257055 + 24499.0740637739*$t);
   $Y1 += 0.00000000152*cos(1.43713086803 + 4551.7096795753*$t);
   $Y1 += 0.00000000147*cos(0.13661195710 + 52602.6482915079*$t);
   $Y1 += 0.00000000147*cos(0.58488249671 + 19805.0711090663*$t);
   $Y1 += 0.00000000182*cos(0.68589997649 + 55618.6250455973*$t);
   $Y1 += 0.00000000140*cos(4.81668277749 + 23754.95056618569*$t);
   $Y1 += 0.00000000146*cos(4.89226138375 + 208702.98131511007*$t);
   $Y1 += 0.00000000154*cos(1.81985059116 + 99799.90288672148*$t);
   $Y1 += 0.00000000139*cos(4.63018939309 + 25973.70767037247*$t);
   $Y1 += 0.00000000138*cos(4.17371703563 + 26202.58624774291*$t);
   $Y1 += 0.00000000191*cos(2.30404978778 + 26728.0442453717*$t);
   $Y1 += 0.00000000152*cos(4.17149146165 + 1109.6223695769*$t);
   $Y1 += 0.00000000162*cos(6.13333012195 + 38520.1896094555*$t);
   $Y1 += 0.00000000141*cos(5.95496888155 + 77734.26227711148*$t);
   $Y1 += 0.00000000135*cos(1.84463199555 + 78267.83457756409*$t);
   $Y1 += 0.00000000128*cos(2.99907290513 + 88477.23878841709*$t);
   $Y1 += 0.00000000147*cos(0.62089024684 + 31748.99137324289*$t);
   $Y1 += 0.00000000135*cos(4.69617813235 + 124778.42747620228*$t);
   $Y1 += 0.00000000148*cos(5.85857347873 + 27154.6424362477*$t);
   $Y1 += 0.00000000134*cos(0.45601803820 + 12431.79883291429*$t);
   $Y1 += 0.00000000121*cos(2.04615713494 + 104881.54734887488*$t);
   $Y1 += 0.00000000116*cos(3.19167458045 + 25934.3681485729*$t);
   $Y1 += 0.00000000116*cos(4.22027620935 + 32858.36992533629*$t);
   $Y1 += 0.00000000115*cos(5.61211222559 + 26241.9257695425*$t);
   $Y1 += 0.00000000148*cos(5.73338066299 + 25661.5487681817*$t);
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   $Y1 += 0.00000000001*cos(1.92944311048 + 26934.2297938089*$t);
   $Y1 += 0.00000000001*cos(0.85501733527 + 42153.72518556549*$t);
   $Y1 += 0.00000000001*cos(5.28557867032 + 50380.79165691089*$t);
   $Y1 += 0.00000000001*cos(3.30348432730 + 241562.08269289686*$t);
   $Y1 += 0.00000000001*cos(1.53016890390 + 55618.1374106303*$t);
   $Y1 += 0.00000000001*cos(0.20150489504 + 92740.81679043909*$t);
   $Y1 += 0.00000000002*cos(4.04923139057 + 27567.01353312209*$t);
   $Y1 += 0.00000000002*cos(2.43602091587 + 98690.03669966108*$t);
   $Y1 += 0.00000000001*cos(5.40866392547 + 173511.17117941826*$t);
   $Y1 += 0.00000000001*cos(2.26707127188 + 173511.65881438529*$t);
   $Y1 += 0.00000000001*cos(5.30789985746 + 102018.17235594128*$t);
   $Y1 += 0.00000000001*cos(2.40978376724 + 49954.19346603489*$t);
   $Y1 += 0.00000000001*cos(5.41274037425 + 155461.16718973868*$t);
   $Y1 += 0.00000000001*cos(2.80860052221 + 193937.74227184022*$t);
   $Y1 += 0.00000000001*cos(2.80241855615 + 26927.11624680809*$t);
   $Y1 += 0.00000000001*cos(6.00279912865 + 25249.1776713073*$t);
   $Y1 += 0.00000000001*cos(5.41436875302 + 149642.51277699786*$t);
   $Y1 += 0.00000000001*cos(4.06699271013 + 112231.45790215228*$t);
   $Y1 += 0.00000000001*cos(4.88680216829 + 639.6534688305*$t);
   $Y1 += 0.00000000001*cos(4.38938154703 + 28420.8557169627*$t);
   $Y1 += 0.00000000002*cos(1.63653705415 + 55503.69812194508*$t);
   $Y1 += 0.00000000001*cos(1.19212507226 + 35472.50033216589*$t);
   $Y1 += 0.00000000001*cos(6.22889842286 + 48997.9043100643*$t);
   $Y1 += 0.00000000001*cos(3.64991019877 + 27006.0772450395*$t);
   $Y1 += 0.00000000001*cos(5.15530748603 + 25170.2166730759*$t);
   $Y1 += 0.00000000001*cos(0.21655513602 + 106263.05586699749*$t);
   $Y1 += 0.00000000001*cos(3.15004684273 + 90989.40667698109*$t);
   $Y1 += 0.00000000001*cos(3.42636128355 + 50690.06997956669*$t);
   $Y1 += 0.00000000001*cos(1.90636858110 + 77836.86741636308*$t);
   $Y1 += 0.00000000001*cos(1.74306827310 + 125112.2834169717*$t);
   $Y1 += 0.00000000001*cos(0.83861407900 + 26610.23674218449*$t);
   $Y1 += 0.00000000001*cos(6.19974077735 + 143980.69309287866*$t);
   $Y1 += 0.00000000001*cos(2.30573879835 + 153084.60008699627*$t);
   $Y1 += 0.00000000001*cos(2.74311464361 + 45404.8518644193*$t);
   $Y1 += 0.00000000001*cos(4.11780710445 + 2332.9525753885*$t);
   $Y1 += 0.00000000001*cos(2.50393985667 + 76152.30292882849*$t);
   $Y1 += 0.00000000001*cos(3.70443537393 + 45494.33761226529*$t);
   $Y1 += 0.00000000001*cos(1.90974220877 + 24925.18461968289*$t);
   $Y1 += 0.00000000001*cos(3.79471530054 + 50593.60311738189*$t);
   $Y1 += 0.00000000001*cos(0.35163928497 + 115674.03284711768*$t);
   $Y1 += 0.00000000001*cos(4.64759915605 + 151200.18655854589*$t);
   $Y1 += 0.00000000001*cos(6.12692757039 + 84308.18182358149*$t);
   $Y1 += 0.00000000001*cos(2.49793910811 + 129379.88996019828*$t);
   $Y1 += 0.00000000001*cos(4.24960627112 + 24073.1652872599*$t);
   $Y1 += 0.00000000001*cos(4.55561141368 + 28103.1286308555*$t);
   $Y1 += 0.00000000001*cos(3.64820977115 + 19406.43447069109*$t);
   $Y1 += 0.00000000001*cos(5.22888939483 + 24844.6593573793*$t);
   $Y1 += 0.00000000001*cos(3.57632828997 + 27331.6345607361*$t);
   $Y1 += 0.00000000001*cos(0.38918442414 + 154408.89880655028*$t);
   $Y1 += 0.00000000001*cos(4.58125009028 + 163298.37326817428*$t);
   $Y1 += 0.00000000001*cos(4.05552152915 + 58220.2786820073*$t);
   $Y1 += 0.00000000001*cos(0.81056243735 + 97670.63153038069*$t);
   $Y1 += 0.00000000001*cos(1.70406295246 + 22759.5236678105*$t);
   $Y1 += 0.00000000001*cos(0.17160219777 + 24395.9812895553*$t);
   $Y1 += 0.00000000001*cos(4.19916792884 + 92741.3044254061*$t);
   $Y1 += 0.00000000001*cos(0.46762289675 + 128850.19899510368*$t);
   $Y1 += 0.00000000001*cos(3.27962382087 + 25984.56654987209*$t);
   $Y1 += 0.00000000001*cos(3.06090263008 + 24357.0246061251*$t);
   $Y1 += 0.00000000001*cos(5.74431505472 + 27819.2693119903*$t);
   $Y1 += 0.00000000001*cos(1.47564589622 + 183724.45672562926*$t);
   $Y1 += 0.00000000001*cos(2.32406253516 + 26624.46383618609*$t);
   $Y1 += 0.00000000001*cos(0.16830959152 + 25455.3632197445*$t);
   $Y1 += 0.00000000001*cos(3.30990224511 + 25454.87558477749*$t);
   $Y1 += 0.00000000001*cos(0.20081607790 + 189385.78877478145*$t);
   $Y1 += 0.00000000001*cos(3.34240873149 + 189386.27640974846*$t);
   $Y1 += 0.00000000001*cos(5.05200956798 + 209659.06869168568*$t);
   $Y1 += 0.00000000001*cos(2.14910744070 + 109.9625037359*$t);
   $Y1 += 0.00000000001*cos(4.58272161819 + 82815.41910429788*$t);
   $Y1 += 0.00000000001*cos(0.56829620714 + 147423.26803784407*$t);
   $Y1 += 0.00000000001*cos(3.84356790046 + 23704.95394428149*$t);
   $Y1 += 0.00000000001*cos(4.96164978434 + 28471.3399738339*$t);
   $Y1 += 0.00000000001*cos(3.64905591301 + 51440.17358710009*$t);
   $Y1 += 0.00000000001*cos(1.10275035993 + 25035.39094090229*$t);
   $Y1 += 0.00000000001*cos(0.92306365199 + 26555.6243144451*$t);
   $Y1 += 0.00000000001*cos(2.45569831568 + 26177.63270690369*$t);
   $Y1 += 0.00000000001*cos(0.06633406194 + 25998.6612112117*$t);
   $Y1 += 0.00000000001*cos(0.41633866770 + 233681.99353955788*$t);
   $Y1 += 0.00000000001*cos(1.60238548900 + 21650.63275068411*$t);
   $Y1 += 0.00000000001*cos(0.91964688862 + 30525.66116743129*$t);
   $Y1 += 0.00000000001*cos(3.50363747347 + 111590.04434041328*$t);
   $Y1 += 0.00000000001*cos(2.57975917809 + 24203.24579564031*$t);
   $Y1 += 0.00000000001*cos(6.22545850671 + 27973.04812247509*$t);
   $Y1 += 0.00000000001*cos(5.61388226798 + 99799.41525175449*$t);
   $Y1 += 0.00000000001*cos(0.90114538219 + 128106.56313248246*$t);
   $Y1 += 0.00000000001*cos(2.25118383839 + 104198.07757329549*$t);
   $Y1 += 0.00000000001*cos(0.23482210375 + 132350.95900857169*$t);
   $Y1 += 0.00000000001*cos(5.46489469781 + 6680.98103591609*$t);
   $Y1 += 0.00000000001*cos(4.59107671722 + 26202.09861277591*$t);
   $Y1 += 0.00000000001*cos(1.28948419377 + 50167.49256147289*$t);
   $Y1 += 0.00000000001*cos(4.70995069593 + 313054.59388140672*$t);
   $Y1 += 0.00000000001*cos(1.61351002182 + 131548.65044248088*$t);
   $Y1 += 0.00000000001*cos(0.21134212997 + 85502.14119883909*$t);
   $Y1 += 0.00000000001*cos(3.59852250423 + 51542.77872635169*$t);
   $Y1 += 0.00000000001*cos(4.35050776234 + 102018.65999090829*$t);
   $Y1 += 0.00000000001*cos(5.00190822272 + 51322.36608391289*$t);
   $Y1 += 0.00000000001*cos(6.26093145675 + 78413.51643934069*$t);
   $Y1 += 0.00000000001*cos(4.71083057280 + 156531.54400228668*$t);
   $Y1 += 0.00000000001*cos(2.77611181285 + 105306.96849042189*$t);
   $Y1 += 0.00000000001*cos(4.15505663410 + 35077.12702952309*$t);
   $Y1 += 0.00000000001*cos(2.66891943800 + 155467.79310177248*$t);
   $Y1 += 0.00000000001*cos(2.90242040099 + 45290.41257573408*$t);
   $Y1 += 0.00000000001*cos(5.09454263682 + 1162.23088692429*$t);
   $Y1 += 0.00000000001*cos(5.85832218706 + 77211.19722405069*$t);
   $Y1 += 0.00000000001*cos(2.94258825469 + 25152.2169783489*$t);
   $Y1 += 0.00000000001*cos(5.86262943011 + 27024.07693976651*$t);
   $Y1 += 0.00000000001*cos(2.69263645947 + 247223.41474204906*$t);
   $Y1 += 0.00000000001*cos(2.39382184066 + 183674.94773869208*$t);
   $Y1 += 0.00000000001*cos(4.71424763358 + 25131.37016812009*$t);
   $Y1 += 0.00000000001*cos(4.49841046349 + 26126.2799946955*$t);
   $Y1 += 0.00000000001*cos(4.30680722131 + 26050.0139234199*$t);
   $Y1 += 0.00000000001*cos(2.54564315044 + 71980.38975724769*$t);
   $Y1 += 0.00000000001*cos(3.77812730736 + 27388.97377726269*$t);
   $Y1 += 0.00000000001*cos(5.02709037744 + 24787.3201408527*$t);
   $Y1 += 0.00000000001*cos(5.22928116569 + 155475.39428374029*$t);
   $Y1 += 0.00000000001*cos(2.23214428102 + 51756.07782178969*$t);
   $Y1 += 0.00000000001*cos(3.75930601793 + 54086.76194888209*$t);
   $Y1 += 0.00000000001*cos(5.71244644048 + 94138.08320260228*$t);
   $Y1 += 0.00000000001*cos(3.60259923599 + 24602.8562523545*$t);
   $Y1 += 0.00000000001*cos(5.20261844881 + 27573.4376657609*$t);
   $Y1 += 0.00000000001*cos(5.97633149627 + 121335.36489626988*$t);
   $Y1 += 0.00000000001*cos(5.11853435105 + 198490.18340386607*$t);
   $Y1 += 0.00000000001*cos(2.41668452027 + 181555.69624334667*$t);
   $Y1 += 0.00000000001*cos(3.56429469477 + 156534.77621392948*$t);
   $Y1 += 0.00000000001*cos(0.16534790503 + 12725.6972522585*$t);
   $Y1 += 0.00000000001*cos(5.23354450332 + 130006.04778747768*$t);
   $Y1 += 0.00000000001*cos(3.16983107219 + 89586.12970554348*$t);
   $Y1 += 0.00000000001*cos(5.31492826690 + 131394.87163199608*$t);
   $Y1 += 0.00000000001*cos(2.18749112623 + 77039.64776646046*$t);
   return $Y1*$t;
}



   function Mercury_Y2($t) // 413 terms of order 2
{
   $Y2  = 0.00020000263*cos(4.39813856862 + 26088.1469590577*$t);
   $Y2 += 0.00008268782*cos(5.12831925217 + 0.2438174835*$t);
   $Y2 += 0.00002498175*cos(1.81785035615 + 52176.0501006319*$t);
   $Y2 += 0.00000949347*cos(5.50772040452 + 78263.95324220609*$t);
   $Y2 += 0.00000776108*cos(0.81508927377 + 26087.65932409069*$t);
   $Y2 += 0.00000371109*cos(2.46339631518 + 104351.85638378029*$t);
   $Y2 += 0.00000130259*cos(5.58371836146 + 130439.75952535449*$t);
   $Y2 += 0.00000069902*cos(3.59145684280 + 52175.56246566489*$t);
   $Y2 += 0.00000042865*cos(2.38418074575 + 156527.66266692868*$t);
   $Y2 += 0.00000013564*cos(5.45308914681 + 182615.56580850288*$t);
   $Y2 += 0.00000011344*cos(0.18546869670 + 78263.46560723908*$t);
   $Y2 += 0.00000004184*cos(2.23177226385 + 208703.46895007708*$t);
   $Y2 += 0.00000002952*cos(5.92358038862 + 24978.7684069643*$t);
   $Y2 += 0.00000002715*cos(2.62856029278 + 27197.5255111511*$t);
   $Y2 += 0.00000002412*cos(3.20116782795 + 104351.36874881329*$t);
   $Y2 += 0.00000001268*cos(5.28987764263 + 234791.37209165128*$t);
   $Y2 += 0.00000001017*cos(2.76352422322 + 51066.6715485385*$t);
   $Y2 += 0.00000000591*cos(0.02739486208 + 130439.27189038748*$t);
   $Y2 += 0.00000000372*cos(5.53602920422 + 53285.4286527253*$t);
   $Y2 += 0.00000000379*cos(2.06228553945 + 260879.27523322542*$t);
   $Y2 += 0.00000000353*cos(5.84872228977 + 77154.57469011268*$t);
   $Y2 += 0.00000000353*cos(3.64262209095 + 1109.1347346099*$t);
   $Y2 += 0.00000000259*cos(2.45927570893 + 20426.8149099055*$t);
   $Y2 += 0.00000000259*cos(3.62787658106 + 1059.6257476727*$t);
   $Y2 += 0.00000000198*cos(6.08219469431 + 27043.7467006663*$t);
   $Y2 += 0.00000000178*cos(4.39645894496 + 31749.4790082099*$t);
   $Y2 += 0.00000000161*cos(5.71880342023 + 1589.3167127673*$t);
   $Y2 += 0.00000000148*cos(1.40374146640 + 4552.1973145423*$t);
   $Y2 += 0.00000000145*cos(0.02368396611 + 21536.1934619989*$t);
   $Y2 += 0.00000000158*cos(3.17661979051 + 156527.17503196168*$t);
   $Y2 += 0.00000000169*cos(2.43702666403 + 25132.5472174491*$t);
   $Y2 += 0.00000000134*cos(4.36077570655 + 25558.4559939631*$t);
   $Y2 += 0.00000000112*cos(5.11701683724 + 286967.17837479962*$t);
   $Y2 += 0.00000000111*cos(4.08624415081 + 26617.8379241523*$t);
   $Y2 += 0.00000000122*cos(6.20816277459 + 46514.7180514797*$t);
   $Y2 += 0.00000000125*cos(6.10874998399 + 23869.3898548709*$t);
   $Y2 += 0.00000000111*cos(0.71893259930 + 14765.48286075331*$t);
   $Y2 += 0.00000000106*cos(3.19958057200 + 51116.6681704427*$t);
   $Y2 += 0.00000000120*cos(2.63555930925 + 103242.47783168689*$t);
   $Y2 += 0.00000000113*cos(1.00068732157 + 27147.5288892469*$t);
   $Y2 += 0.00000000105*cos(2.62816055600 + 28306.90406324449*$t);
   $Y2 += 0.00000000086*cos(3.50491777711 + 19317.43635781211*$t);
   $Y2 += 0.00000000103*cos(1.19071414957 + 5661.0882316687*$t);
   $Y2 += 0.00000000067*cos(4.69029936211 + 9104.1508116011*$t);
   $Y2 += 0.00000000076*cos(0.32408375390 + 529.9347825781*$t);
   $Y2 += 0.00000000066*cos(2.87399773118 + 50586.97720534809*$t);
   $Y2 += 0.00000000066*cos(2.27463939345 + 3442.81876244891*$t);
   $Y2 += 0.00000000061*cos(1.26603377840 + 37410.8110573621*$t);
   $Y2 += 0.00000000059*cos(3.16922770991 + 72602.62119305388*$t);
   $Y2 += 0.00000000074*cos(0.14312537861 + 22645.57201409229*$t);
   $Y2 += 0.00000000056*cos(0.87699245253 + 52705.7410657265*$t);
   $Y2 += 0.00000000061*cos(1.98731213334 + 30640.1004561165*$t);
   $Y2 += 0.00000000053*cos(3.72430094233 + 640.1411037975*$t);
   $Y2 += 0.00000000056*cos(5.15278563625 + 32858.8575603033*$t);
   $Y2 += 0.00000000062*cos(5.26544507482 + 51220.4503590233*$t);
   $Y2 += 0.00000000050*cos(2.61090296354 + 53131.6498422405*$t);
   $Y2 += 0.00000000046*cos(2.37745190465 + 27677.2198543415*$t);
   $Y2 += 0.00000000045*cos(0.02572397068 + 25973.70767037247*$t);
   $Y2 += 0.00000000045*cos(2.48433200554 + 26202.58624774291*$t);
   $Y2 += 0.00000000044*cos(0.04666322888 + 182615.07817353586*$t);
   $Y2 += 0.00000000046*cos(4.10779409868 + 27197.03787618409*$t);
   $Y2 += 0.00000000046*cos(4.21737357836 + 53235.43203082109*$t);
   $Y2 += 0.00000000058*cos(0.51456998627 + 57837.3821497841*$t);
   $Y2 += 0.00000000043*cos(4.72097651637 + 529.44714761109*$t);
   $Y2 += 0.00000000042*cos(5.81334759172 + 47624.0966035731*$t);
   $Y2 += 0.00000000041*cos(1.35360879608 + 26301.4460544957*$t);
   $Y2 += 0.00000000039*cos(3.95217511506 + 40853.3860023275*$t);
   $Y2 += 0.00000000038*cos(1.01923360930 + 25874.8478636197*$t);
   $Y2 += 0.00000000045*cos(2.30681711799 + 29530.7219040231*$t);
   $Y2 += 0.00000000045*cos(3.25992009502 + 10213.5293636945*$t);
   $Y2 += 0.00000000035*cos(0.20035334587 + 2119.00767786191*$t);
   $Y2 += 0.00000000034*cos(5.21776132031 + 56728.0035976907*$t);
   $Y2 += 0.00000000040*cos(0.28616417785 + 24978.28077199729*$t);
   $Y2 += 0.00000000040*cos(5.69976040495 + 129330.38097326108*$t);
   $Y2 += 0.00000000033*cos(1.88435460588 + 313055.08151637383*$t);
   $Y2 += 0.00000000039*cos(0.71277136304 + 955.3559241251*$t);
   $Y2 += 0.00000000031*cos(5.95336552931 + 6770.46678376209*$t);
   $Y2 += 0.00000000038*cos(3.30701415262 + 2218.51328670329*$t);
   $Y2 += 0.00000000031*cos(5.89629431306 + 12566.3955174663*$t);
   $Y2 += 0.00000000032*cos(2.89503281988 + 49957.2929964451*$t);
   $Y2 += 0.00000000029*cos(4.08747500636 + 426.8420083595*$t);
   $Y2 += 0.00000000028*cos(3.89028250879 + 43072.1431065143*$t);
   $Y2 += 0.00000000025*cos(0.01043820952 + 98690.52433462809*$t);
   $Y2 += 0.00000000030*cos(1.58323308741 + 79373.33179429949*$t);
   $Y2 += 0.00000000023*cos(3.87566855556 + 78793.64420730069*$t);
   $Y2 += 0.00000000030*cos(5.69174979475 + 77204.57131201689*$t);
   $Y2 += 0.00000000020*cos(2.91659016078 + 11322.42028082089*$t);
   $Y2 += 0.00000000027*cos(5.66737798141 + 54394.80720481869*$t);
   $Y2 += 0.00000000023*cos(1.92399700068 + 77308.35350059748*$t);
   $Y2 += 0.00000000019*cos(4.33796152575 + 83925.28529135829*$t);
   $Y2 += 0.00000000022*cos(0.31026735565 + 45405.3394993863*$t);
   $Y2 += 0.00000000020*cos(0.76233233344 + 36301.4325052687*$t);
   $Y2 += 0.00000000018*cos(1.06684593234 + 79323.33517239528*$t);
   $Y2 += 0.00000000021*cos(1.06633987406 + 13656.10430865991*$t);
   $Y2 += 0.00000000020*cos(3.26662752657 + 33326.8225506577*$t);
   $Y2 += 0.00000000018*cos(0.08918897822 + 52156.38033973211*$t);
   $Y2 += 0.00000000023*cos(2.56517709904 + 41962.7645544209*$t);
   $Y2 += 0.00000000018*cos(4.49923548064 + 52389.3491960699*$t);
   $Y2 += 0.00000000017*cos(1.90164043236 + 58946.76070187749*$t);
   $Y2 += 0.00000000016*cos(0.07721057973 + 23754.95056618569*$t);
   $Y2 += 0.00000000019*cos(0.79767727082 + 39609.8984006491*$t);
   $Y2 += 0.00000000017*cos(4.96752330955 + 51536.15281431789*$t);
   $Y2 += 0.00000000018*cos(5.05941872394 + 18849.4713674577*$t);
   $Y2 += 0.00000000015*cos(5.67105202528 + 76674.88034692229*$t);
   $Y2 += 0.00000000015*cos(0.18434972499 + 48733.47515566649*$t);
   $Y2 += 0.00000000015*cos(2.77916270049 + 853.4401992355*$t);
   $Y2 += 0.00000000014*cos(2.04393411320 + 82815.90673926489*$t);
   $Y2 += 0.00000000014*cos(3.45421098562 + 52179.9314359899*$t);
   $Y2 += 0.00000000014*cos(0.12812152173 + 15874.8614128467*$t);
   $Y2 += 0.00000000014*cos(0.79649939505 + 66941.2891439017*$t);
   $Y2 += 0.00000000015*cos(3.92393517562 + 16984.2399649401*$t);
   $Y2 += 0.00000000015*cos(3.48624645549 + 38654.2986590405*$t);
   $Y2 += 0.00000000013*cos(5.35926600957 + 53765.1229959157*$t);
   $Y2 += 0.00000000013*cos(3.19246765373 + 208702.98131511007*$t);
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   $Y2 += 0.00000000001*cos(1.17801372459 + 6.86972951729*$t);
   $Y2 += 0.00000000001*cos(5.00258165716 + 16703.3059509825*$t);
   $Y2 += 0.00000000001*cos(3.75732229340 + 35472.9879671329*$t);
   $Y2 += 0.00000000001*cos(5.03560870343 + 42154.2128205325*$t);
   $Y2 += 0.00000000001*cos(2.82069930264 + 77410.75686045409*$t);
   $Y2 += 0.00000000001*cos(1.94570699226 + 103925.25819290428*$t);
   $Y2 += 0.00000000001*cos(0.43527786277 + 52329.8289111167*$t);
   $Y2 += 0.00000000001*cos(1.53490250185 + 6681.46867088311*$t);
   $Y2 += 0.00000000001*cos(5.27958367842 + 6770.9544187291*$t);
   $Y2 += 0.00000000001*cos(3.09122313934 + 955.8435590921*$t);
   $Y2 += 0.00000000001*cos(5.47023024103 + 51109.55462344189*$t);
   $Y2 += 0.00000000001*cos(2.82652928734 + 29530.2342690561*$t);
   $Y2 += 0.00000000001*cos(3.34999395144 + 26067.9895631909*$t);
   $Y2 += 0.00000000001*cos(5.60842191407 + 25447.76203777669*$t);
   $Y2 += 0.00000000001*cos(1.24359184874 + 52705.25343075949*$t);
   $Y2 += 0.00000000001*cos(2.58826883392 + 33967.74847742969*$t);
   $Y2 += 0.00000000001*cos(1.58743932556 + 25035.39094090229*$t);
   $Y2 += 0.00000000001*cos(1.49321197683 + 26107.32908499049*$t);
   $Y2 += 0.00000000001*cos(5.64817713358 + 23969.3830986793*$t);
   $Y2 += 0.00000000001*cos(4.09696575895 + 19316.9487228451*$t);
   $Y2 += 0.00000000001*cos(0.38657846461 + 26091.5406594487*$t);
   $Y2 += 0.00000000001*cos(3.96518956917 + 53131.16220727349*$t);
   $Y2 += 0.00000000001*cos(1.17035557979 + 95247.94938966268*$t);
   $Y2 += 0.00000000001*cos(3.79316376096 + 103299.58800059189*$t);
   $Y2 += 0.00000000001*cos(6.16466999792 + 26094.77287109149*$t);
   $Y2 += 0.00000000001*cos(1.55660546282 + 102233.09252340188*$t);
   $Y2 += 0.00000000001*cos(3.72893918712 + 25668.17468021549*$t);
   $Y2 += 0.00000000000*cos(1.31187403896 + 12565.9078824993*$t);
   $Y2 += 0.00000000000*cos(0.36788997270 + 54394.31956985169*$t);
   $Y2 += 0.00000000000*cos(1.40783572565 + 111122.56698502589*$t);
   $Y2 += 0.00000000001*cos(1.72210842613 + 12432.2864678813*$t);
   $Y2 += 0.00000000001*cos(2.54599021645 + 115674.52048208468*$t);
   $Y2 += 0.00000000000*cos(3.09980373381 + 25234.46294233869*$t);
   $Y2 += 0.00000000001*cos(2.39000910681 + 25661.06113321469*$t);
   $Y2 += 0.00000000001*cos(3.51239889125 + 39609.41076568209*$t);
   $Y2 += 0.00000000000*cos(6.00302318824 + 45892.48661567349*$t);
   $Y2 += 0.00000000000*cos(3.95111212963 + 77830.24150432929*$t);
   $Y2 += 0.00000000000*cos(4.29974909652 + 116783.89903417809*$t);
   $Y2 += 0.00000000000*cos(2.30803098529 + 28420.8557169627*$t);
   $Y2 += 0.00000000000*cos(3.48757973551 + 103241.99019671988*$t);
   $Y2 += 0.00000000000*cos(5.47063609410 + 52026.4869034973*$t);
   $Y2 += 0.00000000000*cos(3.31063006560 + 19804.5834740993*$t);
   $Y2 += 0.00000000001*cos(4.42730882654 + 26083.7779887327*$t);
   $Y2 += 0.00000000000*cos(0.97906814023 + 53242.5455778219*$t);
   $Y2 += 0.00000000000*cos(5.69544477873 + 1588.82907780029*$t);
   $Y2 += 0.00000000000*cos(5.67543121769 + 51219.96272405629*$t);
   $Y2 += 0.00000000000*cos(3.92348521122 + 157637.04121902208*$t);
   $Y2 += 0.00000000000*cos(3.88298321255 + 72602.13355808688*$t);
   $Y2 += 0.00000000000*cos(6.24610291970 + 83924.79765639128*$t);
   $Y2 += 0.00000000000*cos(2.99531203217 + 130420.08976445469*$t);
   $Y2 += 0.00000000000*cos(3.68023238451 + 25668.6623151825*$t);
   $Y2 += 0.00000000000*cos(5.98068946715 + 3340.8562441833*$t);
   $Y2 += 0.00000000000*cos(2.59880667110 + 77204.08367704989*$t);
   $Y2 += 0.00000000000*cos(2.26912005110 + 207594.09039798369*$t);
   $Y2 += 0.00000000000*cos(0.62064943415 + 419.72846135871*$t);
   $Y2 += 0.00000000000*cos(0.91508299271 + 32370.73517408209*$t);
   $Y2 += 0.00000000000*cos(0.42512526285 + 78903.8505285201*$t);
   $Y2 += 0.00000000000*cos(1.63629020299 + 44936.88687406489*$t);
   $Y2 += 0.00000000000*cos(6.12146886950 + 286966.69073983253*$t);
   return $Y2*$t*$t;
}



   function Mercury_Y3($t) // 135 terms of order 3
{
   $Y3  = 0.00000180660*cos(6.24763771127 + 0.2438174835*$t);
   $Y3 += 0.00000056109*cos(6.21607723411 + 52176.0501006319*$t);
   $Y3 += 0.00000023909*cos(3.52205756332 + 78263.95324220609*$t);
   $Y3 += 0.00000011317*cos(0.65434522049 + 104351.85638378029*$t);
   $Y3 += 0.00000011202*cos(4.63472742214 + 26088.1469590577*$t);
   $Y3 += 0.00000007321*cos(3.06113980531 + 26087.65932409069*$t);
   $Y3 += 0.00000005011*cos(3.87936295964 + 130439.75952535449*$t);
   $Y3 += 0.00000002025*cos(0.73521591485 + 156527.66266692868*$t);
   $Y3 += 0.00000001152*cos(1.69823188077 + 52175.56246566489*$t);
   $Y3 += 0.00000000763*cos(3.83589288112 + 182615.56580850288*$t);
   $Y3 += 0.00000000387*cos(4.87852090068 + 78263.46560723908*$t);
   $Y3 += 0.00000000274*cos(0.63429416338 + 208703.46895007708*$t);
   $Y3 += 0.00000000112*cos(1.64880744224 + 104351.36874881329*$t);
   $Y3 += 0.00000000095*cos(3.70512425843 + 234791.37209165128*$t);
   $Y3 += 0.00000000037*cos(2.93820472611 + 24978.7684069643*$t);
   $Y3 += 0.00000000034*cos(2.70920545196 + 27197.5255111511*$t);
   $Y3 += 0.00000000032*cos(0.48595621544 + 260879.27523322542*$t);
   $Y3 += 0.00000000024*cos(0.88877136179 + 51066.6715485385*$t);
   $Y3 += 0.00000000032*cos(4.71795792013 + 130439.27189038748*$t);
   $Y3 += 0.00000000013*cos(4.14981392057 + 77154.57469011268*$t);
   $Y3 += 0.00000000010*cos(3.54374573861 + 286967.17837479962*$t);
   $Y3 += 0.00000000013*cos(4.83147497313 + 53285.4286527253*$t);
   $Y3 += 0.00000000010*cos(1.53331553777 + 156527.17503196168*$t);
   $Y3 += 0.00000000006*cos(0.11733989890 + 1109.1347346099*$t);
   $Y3 += 0.00000000007*cos(1.42096187453 + 1059.6257476727*$t);
   $Y3 += 0.00000000006*cos(0.36688147081 + 20426.8149099055*$t);
   $Y3 += 0.00000000006*cos(0.99179814069 + 103242.47783168689*$t);
   $Y3 += 0.00000000004*cos(5.28779415998 + 31749.4790082099*$t);
   $Y3 += 0.00000000004*cos(1.32226409901 + 79373.33179429949*$t);
   $Y3 += 0.00000000003*cos(0.32143664919 + 313055.08151637383*$t);
   $Y3 += 0.00000000003*cos(5.50927594249 + 4552.1973145423*$t);
   $Y3 += 0.00000000003*cos(4.66013795345 + 182615.07817353586*$t);
   $Y3 += 0.00000000003*cos(4.10710790486 + 46514.7180514797*$t);
   $Y3 += 0.00000000003*cos(0.25274361593 + 21536.1934619989*$t);
   $Y3 += 0.00000000002*cos(4.79995023814 + 27147.5288892469*$t);
   $Y3 += 0.00000000002*cos(2.39000042999 + 1589.3167127673*$t);
   $Y3 += 0.00000000002*cos(5.16055835758 + 25132.5472174491*$t);
   $Y3 += 0.00000000002*cos(4.23604489079 + 14765.48286075331*$t);
   $Y3 += 0.00000000002*cos(4.24590446693 + 51116.6681704427*$t);
   $Y3 += 0.00000000002*cos(4.07863052508 + 129330.38097326108*$t);
   $Y3 += 0.00000000002*cos(6.04806962418 + 27197.03787618409*$t);
   $Y3 += 0.00000000002*cos(1.19379164655 + 26617.8379241523*$t);
   $Y3 += 0.00000000002*cos(0.44240554373 + 27043.7467006663*$t);
   $Y3 += 0.00000000002*cos(4.67526593433 + 25558.4559939631*$t);
   $Y3 += 0.00000000002*cos(1.31409357670 + 72602.62119305388*$t);
   $Y3 += 0.00000000002*cos(0.23323058095 + 26068.47719815791*$t);
   $Y3 += 0.00000000002*cos(5.43511468464 + 26107.81671995749*$t);
   $Y3 += 0.00000000001*cos(3.58800786511 + 26092.0282944157*$t);
   $Y3 += 0.00000000001*cos(2.08042717023 + 26084.2656236997*$t);
   $Y3 += 0.00000000001*cos(5.04284012325 + 24978.28077199729*$t);
   $Y3 += 0.00000000001*cos(1.47519959792 + 37410.8110573621*$t);
   $Y3 += 0.00000000001*cos(5.02608519942 + 30640.1004561165*$t);
   $Y3 += 0.00000000001*cos(5.10218274945 + 52705.7410657265*$t);
   $Y3 += 0.00000000001*cos(3.44712662114 + 51220.4503590233*$t);
   $Y3 += 0.00000000001*cos(0.20321095099 + 47624.0966035731*$t);
   $Y3 += 0.00000000001*cos(1.50125338315 + 208702.98131511007*$t);
   $Y3 += 0.00000000001*cos(1.69903209468 + 9104.1508116011*$t);
   $Y3 += 0.00000000001*cos(4.53006298092 + 98690.52433462809*$t);
   $Y3 += 0.00000000001*cos(4.29961422700 + 955.3559241251*$t);
   $Y3 += 0.00000000001*cos(1.16934270913 + 1109.6223695769*$t);
   $Y3 += 0.00000000001*cos(0.43847536572 + 19317.43635781211*$t);
   $Y3 += 0.00000000001*cos(3.28791774568 + 50586.97720534809*$t);
   $Y3 += 0.00000000001*cos(3.80818275289 + 12566.3955174663*$t);
   $Y3 += 0.00000000001*cos(1.94170233989 + 40853.3860023275*$t);
   $Y3 += 0.00000000001*cos(2.16988291625 + 53235.43203082109*$t);
   $Y3 += 0.00000000001*cos(3.36850892547 + 339142.98465794802*$t);
   $Y3 += 0.00000000001*cos(2.07799856696 + 426.8420083595*$t);
   $Y3 += 0.00000000001*cos(1.13583428934 + 49957.2929964451*$t);
   $Y3 += 0.00000000001*cos(2.48860782643 + 26095.2605060585*$t);
   $Y3 += 0.00000000001*cos(3.22444138778 + 26081.03341205689*$t);
   $Y3 += 0.00000000001*cos(2.99647624764 + 23869.3898548709*$t);
   $Y3 += 0.00000000001*cos(0.34236528707 + 77308.35350059748*$t);
   $Y3 += 0.00000000001*cos(4.24503082495 + 105461.23493587368*$t);
   $Y3 += 0.00000000001*cos(0.10746803930 + 51646.3591355373*$t);
   $Y3 += 0.00000000001*cos(0.85601964696 + 155418.28411483529*$t);
   $Y3 += 0.00000000001*cos(3.18986978065 + 56728.0035976907*$t);
   $Y3 += 0.00000000001*cos(1.94353556293 + 53131.6498422405*$t);
   $Y3 += 0.00000000001*cos(5.49395066730 + 3442.81876244891*$t);
   $Y3 += 0.00000000001*cos(2.08016019343 + 78793.64420730069*$t);
   $Y3 += 0.00000000001*cos(4.54434565803 + 54394.80720481869*$t);
   $Y3 += 0.00000000001*cos(5.42235344143 + 79323.33517239528*$t);
   $Y3 += 0.00000000001*cos(2.66875497262 + 28306.90406324449*$t);
   $Y3 += 0.00000000001*cos(4.76053635454 + 45405.3394993863*$t);
   $Y3 += 0.00000000001*cos(5.22561098934 + 32858.8575603033*$t);
   $Y3 += 0.00000000000*cos(4.27647999319 + 529.44714761109*$t);
   $Y3 += 0.00000000001*cos(0.08839061971 + 25028.7650288685*$t);
   $Y3 += 0.00000000000*cos(1.03862778956 + 25874.8478636197*$t);
   $Y3 += 0.00000000001*cos(0.19202613793 + 22645.57201409229*$t);
   $Y3 += 0.00000000000*cos(0.74532357887 + 640.1411037975*$t);
   $Y3 += 0.00000000000*cos(5.60594877309 + 529.9347825781*$t);
   $Y3 += 0.00000000000*cos(4.64452132771 + 26301.4460544957*$t);
   $Y3 += 0.00000000000*cos(2.15255497625 + 83925.28529135829*$t);
   $Y3 += 0.00000000000*cos(0.24839982675 + 82815.90673926489*$t);
   $Y3 += 0.00000000001*cos(0.02689519967 + 27677.2198543415*$t);
   $Y3 += 0.00000000000*cos(5.17804795670 + 11322.42028082089*$t);
   $Y3 += 0.00000000000*cos(4.78725393347 + 36301.4325052687*$t);
   $Y3 += 0.00000000000*cos(2.95601248059 + 5661.5758666357*$t);
   $Y3 += 0.00000000000*cos(1.50383537850 + 18849.4713674577*$t);
   $Y3 += 0.00000000000*cos(2.67564423190 + 6770.46678376209*$t);
   $Y3 += 0.00000000000*cos(3.97584628325 + 43072.1431065143*$t);
   $Y3 += 0.00000000000*cos(3.28546823218 + 52156.38033973211*$t);
   $Y3 += 0.00000000000*cos(1.87043752965 + 39609.8984006491*$t);
   $Y3 += 0.00000000000*cos(4.81536972160 + 1052.51220067191*$t);
   $Y3 += 0.00000000000*cos(0.85194708260 + 15874.8614128467*$t);
   $Y3 += 0.00000000000*cos(4.33911068639 + 1066.7392946735*$t);
   $Y3 += 0.00000000000*cos(5.18479261632 + 24499.0740637739*$t);
   $Y3 += 0.00000000000*cos(3.01728960403 + 2119.00767786191*$t);
   $Y3 += 0.00000000000*cos(0.36191373868 + 52179.9314359899*$t);
   $Y3 += 0.00000000000*cos(4.28779427258 + 27043.2590656993*$t);
   $Y3 += 0.00000000000*cos(5.49560028256 + 29530.7219040231*$t);
   $Y3 += 0.00000000000*cos(2.44474876799 + 20426.32727493849*$t);
   $Y3 += 0.00000000000*cos(4.93651363037 + 26514.7451499337*$t);
   $Y3 += 0.00000000000*cos(0.52831113499 + 38654.2986590405*$t);
   $Y3 += 0.00000000000*cos(1.94862504810 + 51066.18391357149*$t);
   $Y3 += 0.00000000000*cos(4.51508383281 + 63498.71419893629*$t);
   $Y3 += 0.00000000000*cos(4.63260338147 + 234790.88445668427*$t);
   $Y3 += 0.00000000000*cos(5.16055252636 + 110013.18843293248*$t);
   $Y3 += 0.00000000000*cos(2.19677657341 + 52195.71986153169*$t);
   $Y3 += 0.00000000000*cos(4.97627187962 + 76674.88034692229*$t);
   $Y3 += 0.00000000000*cos(4.63491468562 + 4551.7096795753*$t);
   $Y3 += 0.00000000000*cos(6.26527903795 + 7.3573644843*$t);
   $Y3 += 0.00000000000*cos(4.12020457586 + 33326.8225506577*$t);
   $Y3 += 0.00000000000*cos(0.12999351127 + 2218.51328670329*$t);
   $Y3 += 0.00000000000*cos(3.64724829310 + 51749.45190975589*$t);
   $Y3 += 0.00000000000*cos(1.65008357433 + 7238.4317741165*$t);
   $Y3 += 0.00000000000*cos(5.13058700728 + 52172.1687652739*$t);
   $Y3 += 0.00000000000*cos(2.61914963849 + 53284.94101775829*$t);
   $Y3 += 0.00000000000*cos(5.02388999987 + 66941.2891439017*$t);
   $Y3 += 0.00000000000*cos(6.01418094422 + 52168.93655363109*$t);
   $Y3 += 0.00000000000*cos(2.01993495347 + 58946.76070187749*$t);
   $Y3 += 0.00000000000*cos(0.98221708355 + 30639.61282114949*$t);
   $Y3 += 0.00000000000*cos(1.52131721681 + 62389.33564684289*$t);
   $Y3 += 0.00000000000*cos(2.07662809015 + 105411.23831396949*$t);
   $Y3 += 0.00000000000*cos(0.99094878754 + 103292.47445359109*$t);
   $Y3 += 0.00000000000*cos(5.07197491918 + 23868.9022199039*$t);
   return $Y3*$t*$t*$t;
}



   function Mercury_Y4($t) // 42 terms of order 4
{
   $Y4  = 0.00000043303*cos(1.13774685024 + 26088.1469590577*$t);
   $Y4 += 0.00000016746*cos(1.28029969371 + 0.2438174835*$t);
   $Y4 += 0.00000005097*cos(4.24955975906 + 52176.0501006319*$t);
   $Y4 += 0.00000001110*cos(1.28336867360 + 78263.95324220609*$t);
   $Y4 += 0.00000000968*cos(4.75917629222 + 26087.65932409069*$t);
   $Y4 += 0.00000000362*cos(4.81899532084 + 104351.85638378029*$t);
   $Y4 += 0.00000000161*cos(1.99262264168 + 130439.75952535449*$t);
   $Y4 += 0.00000000075*cos(5.26842672327 + 156527.66266692868*$t);
   $Y4 += 0.00000000076*cos(1.36013166836 + 52175.56246566489*$t);
   $Y4 += 0.00000000033*cos(2.15747243303 + 182615.56580850288*$t);
   $Y4 += 0.00000000014*cos(3.97795789451 + 78263.46560723908*$t);
   $Y4 += 0.00000000014*cos(5.27638874760 + 208703.46895007708*$t);
   $Y4 += 0.00000000005*cos(2.08976600519 + 234791.37209165128*$t);
   $Y4 += 0.00000000004*cos(0.41935591421 + 104351.36874881329*$t);
   $Y4 += 0.00000000002*cos(1.30411243109 + 24978.7684069643*$t);
   $Y4 += 0.00000000002*cos(4.27909717270 + 27197.5255111511*$t);
   $Y4 += 0.00000000002*cos(5.16384952851 + 260879.27523322542*$t);
   $Y4 += 0.00000000001*cos(3.31456236049 + 130439.27189038748*$t);
   $Y4 += 0.00000000001*cos(1.94555546011 + 286967.17837479962*$t);
   $Y4 += 0.00000000001*cos(4.78035947332 + 51066.6715485385*$t);
   $Y4 += 0.00000000001*cos(6.04727171347 + 1059.6257476727*$t);
   $Y4 += 0.00000000001*cos(4.90982478671 + 20426.8149099055*$t);
   $Y4 += 0.00000000000*cos(0.02105735648 + 156527.17503196168*$t);
   $Y4 += 0.00000000000*cos(1.46282089336 + 53285.4286527253*$t);
   $Y4 += 0.00000000000*cos(1.85776832505 + 1109.1347346099*$t);
   $Y4 += 0.00000000000*cos(0.55166694814 + 31749.4790082099*$t);
   $Y4 += 0.00000000000*cos(2.05256123583 + 77154.57469011268*$t);
   $Y4 += 0.00000000000*cos(3.70596272569 + 4552.1973145423*$t);
   $Y4 += 0.00000000000*cos(5.69177628153 + 51116.6681704427*$t);
   $Y4 += 0.00000000000*cos(4.47226271461 + 5661.0882316687*$t);
   $Y4 += 0.00000000000*cos(1.80113707019 + 21536.1934619989*$t);
   $Y4 += 0.00000000000*cos(3.04937726063 + 182615.07817353586*$t);
   $Y4 += 0.00000000000*cos(1.73584606362 + 46514.7180514797*$t);
   $Y4 += 0.00000000000*cos(0.81363243390 + 1589.3167127673*$t);
   $Y4 += 0.00000000000*cos(2.86001163068 + 27147.5288892469*$t);
   $Y4 += 0.00000000000*cos(3.76188191169 + 25132.5472174491*$t);
   $Y4 += 0.00000000000*cos(5.61217194797 + 26617.8379241523*$t);
   $Y4 += 0.00000000000*cos(2.50285436895 + 14765.48286075331*$t);
   $Y4 += 0.00000000000*cos(0.06217996093 + 25558.4559939631*$t);
   $Y4 += 0.00000000000*cos(1.78288877958 + 27043.7467006663*$t);
   $Y4 += 0.00000000000*cos(3.14225315293 + 529.9347825781*$t);
   $Y4 += 0.00000000000*cos(3.58247145620 + 57837.3821497841*$t);
   return $Y4*$t*$t*$t*$t;
}



   function Mercury_Y5($t) // 16 terms of order 5
{
   $Y5  = 0.00000000414*cos(2.51938027426 + 0.2438174835*$t);
   $Y5 += 0.00000000327*cos(1.26814697300 + 26088.1469590577*$t);
   $Y5 += 0.00000000134*cos(2.94456567084 + 52176.0501006319*$t);
   $Y5 += 0.00000000046*cos(5.94506878756 + 78263.95324220609*$t);
   $Y5 += 0.00000000016*cos(2.88715140580 + 104351.85638378029*$t);
   $Y5 += 0.00000000007*cos(0.85960797708 + 26087.65932409069*$t);
   $Y5 += 0.00000000006*cos(6.26965738190 + 130439.75952535449*$t);
   $Y5 += 0.00000000003*cos(3.37112838196 + 156527.66266692868*$t);
   $Y5 += 0.00000000001*cos(0.36849890320 + 182615.56580850288*$t);
   $Y5 += 0.00000000001*cos(5.73351518627 + 52175.56246566489*$t);
   $Y5 += 0.00000000001*cos(3.53868886531 + 208703.46895007708*$t);
   $Y5 += 0.00000000000*cos(2.56994818453 + 78263.46560723908*$t);
   $Y5 += 0.00000000000*cos(0.33722437006 + 234791.37209165128*$t);
   $Y5 += 0.00000000000*cos(5.49215263350 + 104351.36874881329*$t);
   $Y5 += 0.00000000000*cos(6.01269492359 + 24978.7684069643*$t);
   $Y5 += 0.00000000000*cos(5.68183447366 + 27197.5255111511*$t);
   return $Y5*$t*$t*$t*$t*$t;
}



   function Mercury_Z0($t) // 598 terms of order 0
{
   $Z0  = 0.04607665326*cos(1.99295081967 + 26087.9031415742*$t);
   $Z0 -= 0.00708734365;
   $Z0 += 0.00469171617*cos(5.04215742764 + 52175.8062831484*$t);
   $Z0 += 0.00071626395*cos(1.80894256071 + 78263.70942472259*$t);
   $Z0 += 0.00012957446*cos(4.85922032010 + 104351.61256629678*$t);
   $Z0 += 0.00002575002*cos(1.62646731545 + 130439.51570787099*$t);
   $Z0 += 0.00000543259*cos(4.67698860167 + 156527.41884944518*$t);
   $Z0 += 0.00000119462*cos(1.44437994097 + 182615.32199101939*$t);
   $Z0 += 0.00000079477*cos(4.94442849343 + 27197.2816936676*$t);
   $Z0 += 0.00000082635*cos(2.03127961938 + 24978.5245894808*$t);
   $Z0 += 0.00000044712*cos(0.52659463739 + 1059.3819301892*$t);
   $Z0 += 0.00000043131*cos(5.66922412963 + 20426.571092422*$t);
   $Z0 += 0.00000034677*cos(2.36736170874 + 25028.521211385*$t);
   $Z0 += 0.00000032337*cos(1.29099631099 + 31749.2351907264*$t);
   $Z0 += 0.00000027465*cos(3.57680072404 + 5661.3320491522*$t);
   $Z0 += 0.00000027081*cos(4.49499356963 + 208703.22513259358*$t);
   $Z0 += 0.00000020978*cos(4.46131555233 + 4551.9534970588*$t);
   $Z0 += 0.00000020602*cos(1.12768557199 + 1109.3785520934*$t);
   $Z0 += 0.00000020252*cos(0.11722157720 + 51116.4243529592*$t);
   $Z0 += 0.00000023561*cos(1.82361021215 + 53285.1848352418*$t);
   $Z0 += 0.00000014150*cos(4.42485698284 + 57837.1383323006*$t);
   $Z0 += 0.00000016632*cos(5.09118864825 + 51066.427731055*$t);
   $Z0 += 0.00000011609*cos(3.48812792468 + 21535.9496445154*$t);
   $Z0 += 0.00000009897*cos(2.80940292918 + 27043.5028831828*$t);
   $Z0 += 0.00000008380*cos(2.46820093103 + 46514.4742339962*$t);
   $Z0 += 0.00000007950*cos(0.44767912341 + 10213.285546211*$t);
   $Z0 += 0.00000009234*cos(3.80445817621 + 529.6909650946*$t);
   $Z0 += 0.00000007834*cos(4.08006285427 + 25132.3033999656*$t);
   $Z0 += 0.00000007169*cos(2.43861625280 + 47623.8527860896*$t);
   $Z0 += 0.00000006283*cos(1.26244592145 + 234791.12827416777*$t);
   $Z0 += 0.00000006189*cos(3.24598311063 + 77204.32749453338*$t);
   $Z0 += 0.00000006312*cos(3.60156222051 + 27147.28507176339*$t);
   $Z0 += 0.00000005874*cos(3.18517530495 + 14765.2390432698*$t);
   $Z0 += 0.00000005464*cos(0.18067146403 + 13521.7514415914*$t);
   $Z0 += 0.00000005844*cos(4.88684915394 + 79373.08797681599*$t);
   $Z0 += 0.00000005207*cos(1.04360609206 + 426.598190876*$t);
   $Z0 += 0.00000005084*cos(2.88826076001 + 12566.1516999828*$t);
   $Z0 += 0.00000004862*cos(1.05211425705 + 1589.0728952838*$t);
   $Z0 += 0.00000005778*cos(4.74518603718 + 30639.856638633*$t);
   $Z0 += 0.00000004470*cos(5.94243776120 + 11322.6640983044*$t);
   $Z0 += 0.00000004084*cos(6.10730721947 + 41962.5207369374*$t);
   $Z0 += 0.00000003921*cos(1.19592374632 + 83925.04147387479*$t);
   $Z0 += 0.00000003933*cos(1.60795544806 + 25661.3049506982*$t);
   $Z0 += 0.00000004046*cos(3.08469176646 + 51646.11531805379*$t);
   $Z0 += 0.00000003739*cos(2.04428825509 + 15874.6175953632*$t);
   $Z0 += 0.00000003728*cos(1.74332154184 + 24498.8302462904*$t);
   $Z0 += 0.00000003797*cos(1.86233694539 + 77154.33087262919*$t);
   $Z0 += 0.00000003417*cos(4.10830949198 + 39609.6545831656*$t);
   $Z0 += 0.00000003691*cos(3.50893180252 + 37410.5672398786*$t);
   $Z0 += 0.00000002644*cos(5.60089521868 + 73711.75592766379*$t);
   $Z0 += 0.00000003230*cos(5.39015797984 + 955.5997416086*$t);
   $Z0 += 0.00000002653*cos(5.52156950287 + 26617.5941066688*$t);
   $Z0 += 0.00000002526*cos(5.49112478707 + 6283.0758499914*$t);
   $Z0 += 0.00000003017*cos(6.08863660917 + 53131.406024757*$t);
   $Z0 += 0.00000003020*cos(5.46768108443 + 25558.2121764796*$t);
   $Z0 += 0.00000002169*cos(5.85843688724 + 50586.73338786459*$t);
   $Z0 += 0.00000002217*cos(5.81930894103 + 51749.20809227239*$t);
   $Z0 += 0.00000002036*cos(2.79411907992 + 7238.67559160*$t);
   $Z0 += 0.00000001904*cos(0.02429449494 + 33326.5787331742*$t);
   $Z0 += 0.00000001841*cos(3.31987542265 + 36301.18868778519*$t);
   $Z0 += 0.00000001693*cos(0.04022611885 + 103292.23063610759*$t);
   $Z0 += 0.00000001814*cos(0.58414302882 + 63498.47038145279*$t);
   $Z0 += 0.00000001910*cos(5.54302892735 + 72602.37737557039*$t);
   $Z0 += 0.00000001560*cos(0.96215455240 + 65697.55772473979*$t);
   $Z0 += 0.00000001605*cos(0.84854708960 + 51220.20654153979*$t);
   $Z0 += 0.00000001595*cos(5.65216619091 + 26068.2333806744*$t);
   $Z0 += 0.00000001487*cos(1.66950376778 + 105460.99111839019*$t);
   $Z0 += 0.00000001595*cos(1.47238921630 + 26107.57290247399*$t);
   $Z0 += 0.00000001485*cos(4.31307667056 + 260879.03141574195*$t);
   $Z0 += 0.00000001344*cos(3.05188579262 + 68050.42387851159*$t);
   $Z0 += 0.00000001601*cos(0.69333064931 + 9103.9069941176*$t);
   $Z0 += 0.00000001224*cos(3.56543079781 + 19804.8272915828*$t);
   $Z0 += 0.00000001258*cos(2.62817126488 + 52705.49724824299*$t);
   $Z0 += 0.00000001386*cos(0.42909271065 + 53235.18821333759*$t);
   $Z0 += 0.00000001392*cos(0.41896396083 + 18849.2275499742*$t);
   $Z0 += 0.00000001104*cos(1.37365365216 + 45892.73043315699*$t);
   $Z0 += 0.00000001191*cos(5.76715631957 + 19317.1925403286*$t);
   $Z0 += 0.00000001218*cos(6.16642870453 + 77734.01845962799*$t);
   $Z0 += 0.00000000991*cos(0.77508695125 + 32858.61374281979*$t);
   $Z0 += 0.00000001039*cos(4.25003847002 + 110012.94461544899*$t);
   $Z0 += 0.00000001155*cos(1.83291524170 + 16983.9961474566*$t);
   $Z0 += 0.00000000913*cos(4.91386835375 + 103242.23401420339*$t);
   $Z0 += 0.00000001096*cos(2.77782845562 + 26091.7844769322*$t);
   $Z0 += 0.00000000843*cos(2.10283893013 + 23869.1460373874*$t);
   $Z0 += 0.00000001147*cos(1.40069226758 + 56727.7597802072*$t);
   $Z0 += 0.00000001096*cos(4.34969785012 + 26084.0218062162*$t);
   $Z0 += 0.00000000888*cos(5.96405172933 + 38654.05484155699*$t);
   $Z0 += 0.00000000798*cos(5.90979724117 + 43071.8992890308*$t);
   $Z0 += 0.00000000894*cos(6.20891949330 + 40853.142184844*$t);
   $Z0 += 0.00000000751*cos(2.38280961577 + 99799.65906923798*$t);
   $Z0 += 0.00000000858*cos(3.48194203031 + 59414.4818747484*$t);
   $Z0 += 0.00000000903*cos(4.51539427543 + 3442.5749449654*$t);
   $Z0 += 0.00000000816*cos(4.68549846425 + 28306.66024576099*$t);
   $Z0 += 0.00000000739*cos(4.03898100455 + 26514.5013324502*$t);
   $Z0 += 0.00000000874*cos(3.33462533468 + 22645.32819660879*$t);
   $Z0 += 0.00000000685*cos(2.68994541603 + 76674.63652943878*$t);
   $Z0 += 0.00000000933*cos(3.52008984237 + 6770.7106012456*$t);
   $Z0 += 0.00000000668*cos(2.67447570603 + 77837.11123384659*$t);
   $Z0 += 0.00000000688*cos(4.13735845510 + 27676.976036858*$t);
   $Z0 += 0.00000000643*cos(0.26212576857 + 639.897286314*$t);
   $Z0 += 0.00000000747*cos(2.88413728742 + 79219.30916633119*$t);
   $Z0 += 0.00000000594*cos(4.72204801083 + 29530.4780865396*$t);
   $Z0 += 0.00000000580*cos(0.49131159361 + 62389.09182935939*$t);
   $Z0 += 0.00000000560*cos(0.58980434738 + 26080.78959457339*$t);
   $Z0 += 0.00000000636*cos(5.01277329265 + 7.1135470008*$t);
   $Z0 += 0.00000000664*cos(5.40615713600 + 213.299095438*$t);
   $Z0 += 0.00000000460*cos(2.41008353609 + 25448.00585526019*$t);
   $Z0 += 0.00000000453*cos(4.02646064195 + 91785.46086631398*$t);
   $Z0 += 0.00000000441*cos(3.60120922804 + 89586.37352302698*$t);
   $Z0 += 0.00000000473*cos(3.19147656788 + 25874.6040461362*$t);
   $Z0 += 0.00000000452*cos(3.10205575226 + 129380.13377768178*$t);
   $Z0 += 0.00000000406*cos(1.57776301723 + 2118.7638603784*$t);
   $Z0 += 0.00000000495*cos(4.35094686160 + 58946.51688439399*$t);
   $Z0 += 0.00000000395*cos(0.29737033271 + 25934.1243310894*$t);
   $Z0 += 0.00000000392*cos(0.53546585935 + 26241.681952059*$t);
   $Z0 += 0.00000000382*cos(4.72731471129 + 131548.89425996438*$t);
   $Z0 += 0.00000000382*cos(4.49198737842 + 71980.63357473118*$t);
   $Z0 += 0.00000000368*cos(3.89892172772 + 77308.10968311399*$t);
   $Z0 += 0.00000000351*cos(1.04745682138 + 2218.7571041868*$t);
   $Z0 += 0.00000000356*cos(6.12309999532 + 94138.32702008578*$t);
   $Z0 += 0.00000000458*cos(2.31746139528 + 98690.28051714458*$t);
   $Z0 += 0.00000000327*cos(4.52406643775 + 52195.47604404819*$t);
   $Z0 += 0.00000000393*cos(3.09725258397 + 69159.80243060499*$t);
   $Z0 += 0.00000000310*cos(1.10653094623 + 23969.1392811958*$t);
   $Z0 += 0.00000000356*cos(1.08062840940 + 286966.93455731616*$t);
   $Z0 += 0.00000000345*cos(5.71957868514 + 78793.40038981718*$t);
   $Z0 += 0.00000000293*cos(1.74897333943 + 54394.56338733519*$t);
   $Z0 += 0.00000000275*cos(4.05372155800 + 149.5631971346*$t);
   $Z0 += 0.00000000325*cos(2.41844865673 + 52156.1365222486*$t);
   $Z0 += 0.00000000273*cos(0.34374545554 + 51535.90899683439*$t);
   $Z0 += 0.00000000256*cos(3.57544759221 + 1066.49547719*$t);
   $Z0 += 0.00000000252*cos(2.07789295059 + 48733.23133818299*$t);
   $Z0 += 0.00000000326*cos(3.49941746899 + 79323.09135491178*$t);
   $Z0 += 0.00000000327*cos(2.94651885500 + 103821.92160120218*$t);
   $Z0 += 0.00000000300*cos(3.53612598449 + 26301.2022370122*$t);
   $Z0 += 0.00000000253*cos(0.67254115542 + 1052.2683831884*$t);
   $Z0 += 0.00000000274*cos(1.02128544399 + 136100.84775702319*$t);
   $Z0 += 0.00000000227*cos(1.68291413296 + 129330.13715577759*$t);
   $Z0 += 0.00000000264*cos(4.42527687575 + 82815.66292178139*$t);
   $Z0 += 0.00000000280*cos(3.47711681992 + 44937.1306915484*$t);
   $Z0 += 0.00000000207*cos(5.26698515692 + 25938.3399444396*$t);
   $Z0 += 0.00000000233*cos(1.58956295605 + 26095.016688575*$t);
   $Z0 += 0.00000000211*cos(2.55179422569 + 45405.0956819028*$t);
   $Z0 += 0.00000000223*cos(1.11566460119 + 52171.9249477904*$t);
   $Z0 += 0.00000000195*cos(5.61180266071 + 25021.4076643842*$t);
   $Z0 += 0.00000000204*cos(5.44212122344 + 125887.56221081219*$t);
   $Z0 += 0.00000000193*cos(2.20507758963 + 25035.6347583858*$t);
   $Z0 += 0.00000000189*cos(5.78823648500 + 102762.53967101299*$t);
   $Z0 += 0.00000000213*cos(1.31985764486 + 26555.8681319286*$t);
   $Z0 += 0.00000000191*cos(0.24359410467 + 85502.38501632259*$t);
   $Z0 += 0.00000000195*cos(5.97596513107 + 105307.21230790539*$t);
   $Z0 += 0.00000000218*cos(5.85009667782 + 25619.9381512198*$t);
   $Z0 += 0.00000000181*cos(5.75215140812 + 103925.01437542078*$t);
   $Z0 += 0.00000000190*cos(3.25444605074 + 13655.8604911764*$t);
   $Z0 += 0.00000000177*cos(5.31586012519 + 50057.04242277*$t);
   $Z0 += 0.00000000207*cos(2.75433176036 + 64741.95798313119*$t);
   $Z0 += 0.00000000224*cos(5.82663546732 + 52179.6876185064*$t);
   $Z0 += 0.00000000164*cos(3.65486891804 + 76.2660712756*$t);
   $Z0 += 0.00000000166*cos(5.16708694657 + 49957.0491789616*$t);
   $Z0 += 0.00000000171*cos(1.99193197138 + 26094.53170047421*$t);
   $Z0 += 0.00000000159*cos(2.10978774324 + 32370.9789915656*$t);
   $Z0 += 0.00000000164*cos(5.82981713266 + 12432.0426503978*$t);
   $Z0 += 0.00000000155*cos(5.39879388941 + 6681.2248533996*$t);
   $Z0 += 0.00000000199*cos(3.05926705479 + 66941.04532641819*$t);
   $Z0 += 0.00000000171*cos(5.13520423660 + 26081.27458267419*$t);
   $Z0 += 0.00000000150*cos(0.90885651206 + 52389.1053785864*$t);
   $Z0 += 0.00000000184*cos(1.74487163243 + 51962.5071877104*$t);
   $Z0 += 0.00000000164*cos(0.91431121775 + 52602.4044740244*$t);
   $Z0 += 0.00000000138*cos(5.40226519416 + 26011.6370702986*$t);
   $Z0 += 0.00000000149*cos(2.17444239275 + 52168.69273614759*$t);
   $Z0 += 0.00000000184*cos(1.61828580097 + 20760.4270331914*$t);
   $Z0 += 0.00000000152*cos(0.96120452018 + 53764.8791784322*$t);
   $Z0 += 0.00000000146*cos(5.57207251195 + 58458.88213313979*$t);
   $Z0 += 0.00000000150*cos(3.58807734183 + 88476.99497093359*$t);
   $Z0 += 0.00000000124*cos(1.42633058836 + 55618.3812281138*$t);
   $Z0 += 0.00000000141*cos(1.44033578815 + 5327.4761083828*$t);
   $Z0 += 0.00000000126*cos(0.80278847447 + 117873.36400788819*$t);
   $Z0 += 0.00000000118*cos(3.91167705851 + 19406.6782881746*$t);
   $Z0 += 0.00000000117*cos(4.68118162480 + 52182.9198301492*$t);
   $Z0 += 0.00000000130*cos(3.12963980623 + 38519.945791972*$t);
   $Z0 += 0.00000000123*cos(2.90959272560 + 52026.2430860138*$t);
   $Z0 += 0.00000000114*cos(3.34729061863 + 51109.31080595839*$t);
   $Z0 += 0.00000000109*cos(0.37062017000 + 115674.27666460119*$t);
   $Z0 += 0.00000000108*cos(5.35523619654 + 46848.3301747656*$t);
   $Z0 += 0.00000000120*cos(6.15890498480 + 155468.03691925599*$t);
   $Z0 += 0.00000000105*cos(1.26949313866 + 98068.53671630539*$t);
   $Z0 += 0.00000000124*cos(5.59073645014 + 74821.13447975718*$t);
   $Z0 += 0.00000000113*cos(5.37283602123 + 124778.18365871879*$t);
   $Z0 += 0.00000000101*cos(1.50859657746 + 157636.79740153858*$t);
   $Z0 += 0.00000000112*cos(6.24044765899 + 51123.53789995999*$t);
   $Z0 += 0.00000000089*cos(0.66689996363 + 103396.01282468818*$t);
   $Z0 += 0.00000000088*cos(3.24234443321 + 26727.8004278882*$t);
   $Z0 += 0.00000000083*cos(3.46887356727 + 77623.81213840858*$t);
   $Z0 += 0.00000000082*cos(3.58489505049 + 52329.58509363319*$t);
   $Z0 += 0.00000000082*cos(2.76598729250 + 35191.8101356918*$t);
   $Z0 += 0.00000000092*cos(2.89919284588 + 120226.23016165999*$t);
   $Z0 += 0.00000000081*cos(3.34888362248 + 52022.0274726636*$t);
   $Z0 += 0.00000000080*cos(1.61800826930 + 45494.58142974879*$t);
   $Z0 += 0.00000000087*cos(5.99930110618 + 129909.82474277639*$t);
   $Z0 += 0.00000000075*cos(1.29165560989 + 78283.37918562238*$t);
   $Z0 += 0.00000000097*cos(0.94285631414 + 85034.42002596818*$t);
   $Z0 += 0.00000000075*cos(0.93132779667 + 433.7117378768*$t);
   $Z0 += 0.00000000087*cos(3.29295494560 + 3340.6124266998*$t);
   $Z0 += 0.00000000083*cos(4.56076128644 + 419.4846438752*$t);
   $Z0 += 0.00000000080*cos(0.27627260080 + 105410.99449648599*$t);
   $Z0 += 0.00000000079*cos(5.99645052852 + 95247.70557217918*$t);
   $Z0 += 0.00000000074*cos(0.63932580906 + 64607.84893354619*$t);
   $Z0 += 0.00000000066*cos(4.71152255697 + 80482.46652890938*$t);
   $Z0 += 0.00000000073*cos(3.21815072307 + 52099.5402118728*$t);
   $Z0 += 0.00000000066*cos(2.98683203711 + 23754.70674870219*$t);
   $Z0 += 0.00000000091*cos(2.50052149852 + 104881.30353139139*$t);
   $Z0 += 0.00000000062*cos(5.73156315784 + 853.196381752*$t);
   $Z0 += 0.00000000086*cos(4.13151425024 + 313054.83769889036*$t);
   $Z0 += 0.00000000064*cos(1.17129038283 + 108903.56606335558*$t);
   $Z0 += 0.00000000059*cos(0.79111914848 + 7994.5284420242*$t);
   $Z0 += 0.00000000065*cos(0.25068571900 + 71025.03383312259*$t);
   $Z0 += 0.00000000057*cos(6.23642054033 + 1692.1656695024*$t);
   $Z0 += 0.00000000057*cos(4.67121384993 + 28206.6670019526*$t);
   $Z0 += 0.00000000059*cos(4.92822158961 + 78050.41032928458*$t);
   $Z0 += 0.00000000056*cos(2.09215892689 + 76144.94556434419*$t);
   $Z0 += 0.00000000056*cos(1.73304008242 + 25654.19140369739*$t);
   $Z0 += 0.00000000057*cos(4.73385475413 + 155418.04029735178*$t);
   $Z0 += 0.00000000056*cos(5.88720785632 + 26037.90651966999*$t);
   $Z0 += 0.00000000074*cos(5.46823409002 + 78244.0396638228*$t);
   $Z0 += 0.00000000061*cos(4.50066150046 + 25668.418497699*$t);
   $Z0 += 0.00000000071*cos(4.06855895670 + 162188.75089859738*$t);
   $Z0 += 0.00000000052*cos(2.74630211595 + 131395.11544947959*$t);
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   $Z0 += 0.00000000008*cos(3.48746520229 + 53242.3017603384*$t);
   $Z0 += 0.00000000008*cos(5.56477337187 + 27177.6119327678*$t);
   $Z0 += 0.00000000009*cos(5.00034866965 + 102132.85546210999*$t);
   $Z0 += 0.00000000007*cos(0.40751314845 + 2111.6503133776*$t);
   $Z0 += 0.00000000008*cos(1.66471235682 + 52290.24557183361*$t);
   $Z0 += 0.00000000007*cos(0.77215567463 + 26073.67604757259*$t);
   $Z0 += 0.00000000007*cos(5.32306426879 + 52595.29092702359*$t);
   $Z0 += 0.00000000007*cos(2.57023734016 + 24448.8336243862*$t);
   $Z0 += 0.00000000007*cos(1.40330361432 + 150244.34299945379*$t);
   $Z0 += 0.00000000008*cos(3.96541390761 + 52325.36948028299*$t);
   $Z0 += 0.00000000008*cos(0.64215744063 + 53228.07466633679*$t);
   $Z0 += 0.00000000007*cos(5.40994893955 + 25508.2155545754*$t);
   $Z0 += 0.00000000009*cos(0.63097343517 + 170049.17029103659*$t);
   $Z0 += 0.00000000006*cos(2.73735624509 + 153.7788104848*$t);
   $Z0 += 0.00000000006*cos(1.57808561874 + 49842.60989027639*$t);
   $Z0 += 0.00000000006*cos(5.85639973088 + 182085.63102592478*$t);
   $Z0 += 0.00000000007*cos(1.22602076365 + 107794.18751126219*$t);
   $Z0 += 0.00000000007*cos(2.99828544115 + 22625.658435709*$t);
   $Z0 += 0.00000000007*cos(3.38113527243 + 12546.481939083*$t);
   $Z0 += 0.00000000006*cos(5.98824736570 + 76667.52298243798*$t);
   $Z0 += 0.00000000007*cos(2.75252330601 + 172402.03644480839*$t);
   $Z0 += 0.00000000007*cos(0.93184314111 + 3328.13565628019*$t);
   $Z0 += 0.00000000006*cos(2.72361970528 + 26709.6469424134*$t);
   $Z0 += 0.00000000008*cos(1.81192469081 + 78270.33798362259*$t);
   $Z0 += 0.00000000006*cos(2.31595886989 + 157057.10981453978*$t);
   $Z0 += 0.00000000006*cos(1.73557063122 + 26667.590728573*$t);
   $Z0 += 0.00000000006*cos(4.37863242786 + 25466.159340735*$t);
   $Z0 += 0.00000000006*cos(3.19403160700 + 104275.34649502118*$t);
   $Z0 += 0.00000000006*cos(1.09823646265 + 25867.49049913539*$t);
   $Z0 += 0.00000000007*cos(0.11236053840 + 25764.39772491679*$t);
   $Z0 += 0.00000000007*cos(5.69537766284 + 66653.15746634839*$t);
   $Z0 += 0.00000000007*cos(1.98238737869 + 846.0828347512*$t);
   $Z0 += 0.00000000006*cos(0.65894058731 + 116783.65521669458*$t);
   $Z0 += 0.00000000005*cos(4.66761334131 + 2125.8774073792*$t);
   $Z0 += 0.00000000006*cos(4.52221761723 + 27726.9726587622*$t);
   $Z0 += 0.00000000006*cos(0.09840227420 + 167850.08294774959*$t);
   $Z0 += 0.00000000006*cos(3.36608415071 + 129799.61842155698*$t);
   $Z0 += 0.00000000007*cos(5.27549434329 + 52061.36699446317*$t);
   $Z0 += 0.00000000007*cos(1.32305784951 + 209812.60368468695*$t);
   $Z0 += 0.00000000006*cos(3.60884349448 + 78903.60671103658*$t);
   $Z0 += 0.00000000005*cos(3.76183094594 + 28256.66362385679*$t);
   $Z0 += 0.00000000006*cos(5.26397966812 + 75930.51303185058*$t);
   $Z0 += 0.00000000006*cos(3.23097479261 + 27669.86248985719*$t);
   $Z0 += 0.00000000005*cos(5.68060753615 + 1265.5674786264*$t);
   $Z0 += 0.00000000005*cos(3.87273283224 + 214364.55718174578*$t);
   $Z0 += 0.00000000005*cos(3.93047654027 + 365230.64398203876*$t);
   $Z0 += 0.00000000006*cos(2.60562458198 + 44295.7171298094*$t);
   $Z0 += 0.00000000005*cos(1.56438384826 + 60370.08161635699*$t);
   $Z0 += 0.00000000005*cos(0.91437456221 + 27684.0895838588*$t);
   $Z0 += 0.00000000005*cos(2.78304413268 + 25169.9728555924*$t);
   $Z0 += 0.00000000006*cos(5.76131236705 + 58857.03113654799*$t);
   $Z0 += 0.00000000005*cos(2.67085954875 + 38.1330356378*$t);
   $Z0 += 0.00000000006*cos(0.50453577398 + 155571.81910783658*$t);
   $Z0 += 0.00000000005*cos(3.86250449828 + 52381.99183158559*$t);
   $Z0 += 0.00000000005*cos(4.32361771821 + 27005.83342755599*$t);
   $Z0 += 0.00000000005*cos(1.63783306460 + 34082.4315835984*$t);
   $Z0 += 0.00000000006*cos(4.13235037436 + 29550.14784743939*$t);
   $Z0 += 0.00000000005*cos(0.09069856194 + 13541.42120249119*$t);
   $Z0 += 0.00000000005*cos(5.50663993071 + 26402.0893214438*$t);
   $Z0 += 0.00000000004*cos(5.22554265930 + 28736.3579670472*$t);
   $Z0 += 0.00000000005*cos(5.88997457155 + 78188.92782615528*$t);
   $Z0 += 0.00000000005*cos(1.29427545799 + 77630.92568540938*$t);
   $Z0 += 0.00000000006*cos(3.65818107099 + 76681.75007643958*$t);
   $Z0 += 0.00000000005*cos(1.59378640261 + 25773.71696170459*$t);
   $Z0 += 0.00000000005*cos(5.53985466815 + 24203.0019781568*$t);
   $Z0 += 0.00000000005*cos(1.10121885185 + 130459.18546877075*$t);
   $Z0 += 0.00000000005*cos(3.55866759420 + 52252.07235442399*$t);
   $Z0 += 0.00000000004*cos(5.49843651098 + 52712.61079524379*$t);
   $Z0 += 0.00000000005*cos(3.39959787962 + 104505.39137678158*$t);
   $Z0 += 0.00000000005*cos(1.94175393423 + 1272.6810256272*$t);
   $Z0 += 0.00000000004*cos(0.58115883263 + 26118.2300025786*$t);
   $Z0 += 0.00000000004*cos(0.54682947961 + 157586.80077963437*$t);
   $Z0 += 0.00000000004*cos(2.04212740892 + 148.0787244263*$t);
   $Z0 += 0.00000000005*cos(1.64853656178 + 26198.1094627936*$t);
   $Z0 += 0.00000000005*cos(0.18946812001 + 1.4844727083*$t);
   $Z0 += 0.00000000004*cos(5.04774492766 + 112231.70171963578*$t);
   $Z0 += 0.00000000004*cos(3.24889530044 + 26312.2479372761*$t);
   $Z0 += 0.00000000005*cos(2.14793916248 + 128320.75184749259*$t);
   $Z0 += 0.00000000004*cos(3.03681019540 + 151.0476698429*$t);
   $Z0 += 0.00000000004*cos(0.23608219351 + 26057.57628056979*$t);
   $Z0 += 0.00000000004*cos(2.78449581166 + 25138.7275326044*$t);
   $Z0 += 0.00000000004*cos(1.74750321635 + 27044.1922975448*$t);
   $Z0 += 0.00000000004*cos(5.26585590029 + 138319.60486120995*$t);
   $Z0 += 0.00000000004*cos(2.16361705057 + 78366.80219894118*$t);
   $Z0 += 0.00000000005*cos(1.86438708559 + 51653.22886505459*$t);
   $Z0 += 0.00000000004*cos(3.67745684549 + 148532.89040742096*$t);
   $Z0 += 0.00000000005*cos(3.36418574107 + 86457.98475793119*$t);
   $Z0 += 0.00000000004*cos(4.39817949768 + 78896.49316403578*$t);
   $Z0 += 0.00000000004*cos(3.16495363173 + 104197.83375581198*$t);
   $Z0 += 0.00000000004*cos(5.96720583626 + 1485.9801210652*$t);
   $Z0 += 0.00000000003*cos(3.62369510287 + 51852.30086649099*$t);
   $Z0 += 0.00000000004*cos(4.95850373202 + 80382.47328510099*$t);
   $Z0 += 0.00000000003*cos(0.24273955075 + 128106.31931499895*$t);
   $Z0 += 0.00000000004*cos(6.09423095974 + 51528.79544983359*$t);
   $Z0 += 0.00000000004*cos(2.26832726016 + 64901.25971792339*$t);
   $Z0 += 0.00000000004*cos(5.37231956323 + 99024.13645791399*$t);
   $Z0 += 0.00000000004*cos(5.83099981006 + 26411.4085582316*$t);
   $Z0 += 0.00000000003*cos(5.27877050710 + 14.2270940016*$t);
   $Z0 += 0.00000000004*cos(1.01079656557 + 16703.062133499*$t);
   $Z0 += 0.00000000003*cos(5.29624442233 + 51432.81622261579*$t);
   $Z0 += 0.00000000003*cos(1.99372517333 + 9384.8410080752*$t);
   $Z0 += 0.00000000003*cos(1.08549694329 + 92741.06060792258*$t);
   $Z0 += 0.00000000004*cos(2.61532511231 + 27250.37784598199*$t);
   $Z0 += 0.00000000004*cos(3.84384246230 + 65831.6667743248*$t);
   $Z0 += 0.00000000004*cos(5.07647835306 + 118828.96374949679*$t);
   $Z0 += 0.00000000004*cos(0.95691561960 + 1795.258443721*$t);
   $Z0 += 0.00000000003*cos(4.56071055194 + 130419.8459469712*$t);
   $Z0 += 0.00000000004*cos(3.21002699852 + 51969.62073471119*$t);
   $Z0 += 0.00000000003*cos(0.53542089836 + 25985.94062330859*$t);
   $Z0 += 0.00000000003*cos(0.86346795613 + 27972.80430499159*$t);
   $Z0 += 0.00000000004*cos(1.11850373850 + 52609.51802102519*$t);
   $Z0 += 0.00000000003*cos(5.13697350283 + 26189.8656598398*$t);
   $Z0 += 0.00000000003*cos(3.83162907268 + 207593.84658050018*$t);
   $Z0 += 0.00000000003*cos(3.70405700948 + 193937.98608932378*$t);
   $Z0 += 0.00000000003*cos(1.82907554275 + 153084.84390447979*$t);
   $Z0 += 0.00000000003*cos(1.75677414102 + 158746.17595363196*$t);
   $Z0 += 0.00000000003*cos(0.34579536632 + 161079.37234650398*$t);
   $Z0 += 0.00000000003*cos(3.85483830173 + 39629.32434406539*$t);
   $Z0 += 0.00000000003*cos(0.82694378727 + 51868.2486621788*$t);
   $Z0 += 0.00000000003*cos(0.16328069810 + 27463.67694142*$t);
   $Z0 += 0.00000000003*cos(4.08971647963 + 130226.21661243298*$t);
   $Z0 += 0.00000000004*cos(3.70176043302 + 163766.09444104518*$t);
   $Z0 += 0.00000000003*cos(1.31853873267 + 204151.27163553478*$t);
   $Z0 += 0.00000000004*cos(2.50849600287 + 220.4126424388*$t);
   $Z0 += 0.00000000003*cos(3.29076294593 + 125112.03959948818*$t);
   $Z0 += 0.00000000003*cos(5.82527117029 + 49953.94964855139*$t);
   $Z0 += 0.00000000003*cos(1.83258674312 + 37698.4550999484*$t);
   $Z0 += 0.00000000003*cos(1.84707936363 + 26076.8574413103*$t);
   $Z0 += 0.00000000003*cos(3.96840940578 + 130432.40216087017*$t);
   $Z0 += 0.00000000003*cos(0.01192870778 + 26098.9488418381*$t);
   $Z0 += 0.00000000003*cos(2.24128507678 + 78160.61665050399*$t);
   $Z0 += 0.00000000003*cos(1.67457691866 + 182188.72380014337*$t);
   $Z0 += 0.00000000003*cos(1.36021422148 + 136722.59155786238*$t);
   return $Z0;
}



   function Mercury_Z1($t) // 360 terms of order 1
{
   $Z1  = 0.00172388569*cos(3.47961470688 + 26087.9031415742*$t);
   $Z1 -= 0.00084745328;
   $Z1 += 0.00004790619*cos(6.21921644635 + 52175.8062831484*$t);
   $Z1 += 0.00001359100*cos(0.49329143004 + 78263.70942472259*$t);
   $Z1 += 0.00000602217*cos(3.41138035633 + 104351.61256629678*$t);
   $Z1 += 0.00000191001*cos(0.14519065991 + 130439.51570787099*$t);
   $Z1 += 0.00000055361*cos(3.18058121998 + 156527.41884944518*$t);
   $Z1 += 0.00000015488*cos(6.22255945229 + 182615.32199101939*$t);
   $Z1 += 0.00000010854*cos(0.29329316365 + 27197.2816936676*$t);
   $Z1 += 0.00000004262*cos(2.98444809115 + 208703.22513259358*$t);
   $Z1 += 0.00000004999*cos(0.56827577867 + 24978.5245894808*$t);
   $Z1 += 0.00000002282*cos(2.87281226699 + 31749.2351907264*$t);
   $Z1 += 0.00000002500*cos(3.37464102020 + 53285.1848352418*$t);
   $Z1 += 0.00000001480*cos(3.59930190722 + 51066.427731055*$t);
   $Z1 += 0.00000001163*cos(6.03119799366 + 234791.12827416777*$t);
   $Z1 += 0.00000001151*cos(1.94233400975 + 51116.4243529592*$t);
   $Z1 += 0.00000000808*cos(0.63296975442 + 25028.521211385*$t);
   $Z1 += 0.00000000781*cos(1.83801930165 + 5661.3320491522*$t);
   $Z1 += 0.00000000676*cos(4.44275341808 + 27043.5028831828*$t);
   $Z1 += 0.00000000873*cos(3.99274661843 + 21535.9496445154*$t);
   $Z1 += 0.00000000636*cos(0.60897167697 + 20426.571092422*$t);
   $Z1 += 0.00000000538*cos(5.92697698725 + 57837.1383323006*$t);
   $Z1 += 0.00000000528*cos(1.89223267777 + 1059.3819301892*$t);
   $Z1 += 0.00000000503*cos(4.12049535056 + 47623.8527860896*$t);
   $Z1 += 0.00000000450*cos(6.08529735298 + 529.6909650946*$t);
   $Z1 += 0.00000000553*cos(2.50090977683 + 1109.3785520934*$t);
   $Z1 += 0.00000000445*cos(0.35693140869 + 77154.33087262919*$t);
   $Z1 += 0.00000000459*cos(0.10915184787 + 79373.08797681599*$t);
   $Z1 += 0.00000000370*cos(2.24953657104 + 10213.285546211*$t);
   $Z1 += 0.00000000414*cos(3.01450201380 + 26107.57290247399*$t);
   $Z1 += 0.00000000417*cos(5.31402407370 + 37410.5672398786*$t);
   $Z1 += 0.00000000306*cos(3.10769212775 + 25558.2121764796*$t);
   $Z1 += 0.00000000316*cos(2.79570706285 + 260879.03141574195*$t);
   $Z1 += 0.00000000296*cos(4.12556468959 + 26068.2333806744*$t);
   $Z1 += 0.00000000332*cos(5.93758113684 + 26084.0218062162*$t);
   $Z1 += 0.00000000234*cos(3.03370038245 + 25132.3033999656*$t);
   $Z1 += 0.00000000250*cos(1.18440188253 + 26091.7844769322*$t);
   $Z1 += 0.00000000215*cos(1.41611963529 + 41962.5207369374*$t);
   $Z1 += 0.00000000206*cos(4.97267994525 + 77204.32749453338*$t);
   $Z1 += 0.00000000208*cos(5.60196522278 + 4551.9534970588*$t);
   $Z1 += 0.00000000251*cos(3.12319370712 + 30639.856638633*$t);
   $Z1 += 0.00000000230*cos(0.95862112790 + 50586.73338786459*$t);
   $Z1 += 0.00000000193*cos(4.90260211702 + 13521.7514415914*$t);
   $Z1 += 0.00000000243*cos(0.30112320330 + 1589.0728952838*$t);
   $Z1 += 0.00000000186*cos(5.87650538684 + 39609.6545831656*$t);
   $Z1 += 0.00000000211*cos(1.27593674125 + 53131.406024757*$t);
   $Z1 += 0.00000000188*cos(0.09339135236 + 28306.66024576099*$t);
   $Z1 += 0.00000000191*cos(4.77084065304 + 51646.11531805379*$t);
   $Z1 += 0.00000000167*cos(2.62739427985 + 32858.61374281979*$t);
   $Z1 += 0.00000000162*cos(5.02172677195 + 15874.6175953632*$t);
   $Z1 += 0.00000000140*cos(1.37984211372 + 51749.20809227239*$t);
   $Z1 += 0.00000000134*cos(0.57882342916 + 23869.1460373874*$t);
   $Z1 += 0.00000000132*cos(3.40338891449 + 103242.23401420339*$t);
   $Z1 += 0.00000000144*cos(4.41836879515 + 22645.32819660879*$t);
   $Z1 += 0.00000000143*cos(5.55896069473 + 25661.3049506982*$t);
   $Z1 += 0.00000000131*cos(2.17510821075 + 63498.47038145279*$t);
   $Z1 += 0.00000000143*cos(1.22805602725 + 46514.4742339962*$t);
   $Z1 += 0.00000000136*cos(2.45569156259 + 24498.8302462904*$t);
   $Z1 += 0.00000000120*cos(2.89969435814 + 7.1135470008*$t);
   $Z1 += 0.00000000104*cos(0.89744950821 + 73711.75592766379*$t);
   $Z1 += 0.00000000119*cos(1.44014554390 + 43071.8992890308*$t);
   $Z1 += 0.00000000126*cos(1.93369301602 + 14765.2390432698*$t);
   $Z1 += 0.00000000107*cos(4.29215813932 + 19317.1925403286*$t);
   $Z1 += 0.00000000089*cos(5.84175706917 + 51220.20654153979*$t);
   $Z1 += 0.00000000093*cos(2.27928877976 + 19804.8272915828*$t);
   $Z1 += 0.00000000083*cos(3.17188415740 + 29530.4780865396*$t);
   $Z1 += 0.00000000076*cos(5.10839374532 + 36301.18868778519*$t);
   $Z1 += 0.00000000079*cos(2.34370769368 + 1052.2683831884*$t);
   $Z1 += 0.00000000080*cos(2.11190196063 + 426.598190876*$t);
   $Z1 += 0.00000000076*cos(6.05836593763 + 52195.47604404819*$t);
   $Z1 += 0.00000000072*cos(1.89073508118 + 1066.49547719*$t);
   $Z1 += 0.00000000082*cos(3.03552784633 + 3442.5749449654*$t);
   $Z1 += 0.00000000075*cos(3.11962204135 + 105460.99111839019*$t);
   $Z1 += 0.00000000086*cos(5.84461147075 + 286966.93455731616*$t);
   $Z1 += 0.00000000069*cos(1.89458844998 + 27147.28507176339*$t);
   $Z1 += 0.00000000089*cos(4.10904716360 + 72602.37737557039*$t);
   $Z1 += 0.00000000077*cos(5.34990441360 + 213.299095438*$t);
   $Z1 += 0.00000000087*cos(5.53929952701 + 9103.9069941176*$t);
   $Z1 += 0.00000000070*cos(4.43072071341 + 639.897286314*$t);
   $Z1 += 0.00000000059*cos(3.32089922507 + 54394.56338733519*$t);
   $Z1 += 0.00000000061*cos(0.53721787795 + 25035.6347583858*$t);
   $Z1 += 0.00000000062*cos(1.36724381328 + 6283.0758499914*$t);
   $Z1 += 0.00000000073*cos(6.16650137658 + 56727.7597802072*$t);
   $Z1 += 0.00000000069*cos(0.88932506586 + 52156.1365222486*$t);
   $Z1 += 0.00000000055*cos(2.54693938612 + 65697.55772473979*$t);
   $Z1 += 0.00000000061*cos(2.70208782780 + 52171.9249477904*$t);
   $Z1 += 0.00000000058*cos(3.90075823666 + 76674.63652943878*$t);
   $Z1 += 0.00000000064*cos(6.09232375776 + 26080.78959457339*$t);
   $Z1 += 0.00000000052*cos(2.85118534529 + 16983.9961474566*$t);
   $Z1 += 0.00000000063*cos(5.90351345253 + 58946.51688439399*$t);
   $Z1 += 0.00000000052*cos(1.08065292487 + 25021.4076643842*$t);
   $Z1 += 0.00000000050*cos(5.98403755810 + 955.5997416086*$t);
   $Z1 += 0.00000000050*cos(2.34891444356 + 51535.90899683439*$t);
   $Z1 += 0.00000000048*cos(4.15049070651 + 12566.1516999828*$t);
   $Z1 += 0.00000000047*cos(3.35524401909 + 52168.69273614759*$t);
   $Z1 += 0.00000000060*cos(3.40462418234 + 25874.6040461362*$t);
   $Z1 += 0.00000000059*cos(4.98660394607 + 6770.7106012456*$t);
   $Z1 += 0.00000000065*cos(1.57121191195 + 52705.49724824299*$t);
   $Z1 += 0.00000000055*cos(5.05311644127 + 53235.18821333759*$t);
   $Z1 += 0.00000000056*cos(4.79703863542 + 25448.00585526019*$t);
   $Z1 += 0.00000000045*cos(3.87928453463 + 48733.23133818299*$t);
   $Z1 += 0.00000000054*cos(2.11712920969 + 33326.5787331742*$t);
   $Z1 += 0.00000000044*cos(2.58011573987 + 2218.7571041868*$t);
   $Z1 += 0.00000000057*cos(4.23895384399 + 52179.6876185064*$t);
   $Z1 += 0.00000000042*cos(2.38859796348 + 83925.04147387479*$t);
   $Z1 += 0.00000000040*cos(5.07476924931 + 51109.31080595839*$t);
   $Z1 += 0.00000000039*cos(0.16837719613 + 129330.13715577759*$t);
   $Z1 += 0.00000000041*cos(5.06879737373 + 59414.4818747484*$t);
   $Z1 += 0.00000000045*cos(0.74507723970 + 2118.7638603784*$t);
   $Z1 += 0.00000000045*cos(3.04665350718 + 27676.976036858*$t);
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   $Z1 += 0.00000000001*cos(5.08144757931 + 32769.1279949738*$t);
   $Z1 += 0.00000000001*cos(2.90527234589 + 124156.43985787958*$t);
   $Z1 += 0.00000000001*cos(6.04124419781 + 16066.0658614748*$t);
   $Z1 += 0.00000000001*cos(0.82693925421 + 1692.1656695024*$t);
   $Z1 += 0.00000000001*cos(1.72510786190 + 26237.46633870879*$t);
   $Z1 += 0.00000000001*cos(0.74557141998 + 29428.515568274*$t);
   $Z1 += 0.00000000001*cos(1.18363932898 + 130012.91751699499*$t);
   $Z1 += 0.00000000001*cos(5.53709511500 + 26720.68688088739*$t);
   $Z1 += 0.00000000001*cos(2.22421236230 + 25984.8103673556*$t);
   $Z1 += 0.00000000001*cos(4.51546243970 + 48835.19385644859*$t);
   $Z1 += 0.00000000001*cos(3.61219119527 + 131395.11544947959*$t);
   return $Z1*$t;
}



   function Mercury_Z2($t) // 167 terms of order 2
{
   $Z2  = 0.00004475377*cos(4.81703460547 + 26087.9031415742*$t);
   $Z2 += 0.00001109532;
   $Z2 += 0.00000180327*cos(1.19420644188 + 52175.8062831484*$t);
   $Z2 += 0.00000032581*cos(4.62632031743 + 78263.70942472259*$t);
   $Z2 += 0.00000017342*cos(1.72679813654 + 104351.61256629678*$t);
   $Z2 += 0.00000007781*cos(4.84181443647 + 130439.51570787099*$t);
   $Z2 += 0.00000002976*cos(1.62432394721 + 156527.41884944518*$t);
   $Z2 += 0.00000001040*cos(4.67846690150 + 182615.32199101939*$t);
   $Z2 += 0.00000000680*cos(1.83005840786 + 27197.2816936676*$t);
   $Z2 += 0.00000000344*cos(1.44603022303 + 208703.22513259358*$t);
   $Z2 += 0.00000000110*cos(4.49542230374 + 234791.12827416777*$t);
   $Z2 += 0.00000000124*cos(4.86657119280 + 53285.1848352418*$t);
   $Z2 += 0.00000000112*cos(5.14312161072 + 24978.5245894808*$t);
   $Z2 += 0.00000000079*cos(4.25092448424 + 31749.2351907264*$t);
   $Z2 += 0.00000000058*cos(2.00193276015 + 51066.427731055*$t);
   $Z2 += 0.00000000046*cos(5.63734699624 + 27043.5028831828*$t);
   $Z2 += 0.00000000054*cos(5.70534232394 + 21535.9496445154*$t);
   $Z2 += 0.00000000048*cos(3.15710696395 + 51116.4243529592*$t);
   $Z2 += 0.00000000034*cos(1.26182479499 + 260879.03141574195*$t);
   $Z2 += 0.00000000027*cos(5.76991833962 + 529.6909650946*$t);
   $Z2 += 0.00000000024*cos(5.07488580193 + 77154.33087262919*$t);
   $Z2 += 0.00000000024*cos(0.95399123610 + 5661.3320491522*$t);
   $Z2 += 0.00000000019*cos(1.78858873244 + 28306.66024576099*$t);
   $Z2 += 0.00000000021*cos(3.57893007020 + 25558.2121764796*$t);
   $Z2 += 0.00000000022*cos(0.13783545204 + 25028.521211385*$t);
   $Z2 += 0.00000000018*cos(5.52049109830 + 47623.8527860896*$t);
   $Z2 += 0.00000000022*cos(1.64692693544 + 20426.571092422*$t);
   $Z2 += 0.00000000014*cos(5.59601085083 + 22645.32819660879*$t);
   $Z2 += 0.00000000014*cos(3.31820162449 + 1059.3819301892*$t);
   $Z2 += 0.00000000018*cos(0.54978030810 + 37410.5672398786*$t);
   $Z2 += 0.00000000016*cos(1.54285068472 + 79373.08797681599*$t);
   $Z2 += 0.00000000015*cos(4.49153081628 + 26107.57290247399*$t);
   $Z2 += 0.00000000014*cos(0.87791325175 + 57837.1383323006*$t);
   $Z2 += 0.00000000013*cos(5.18106920630 + 1109.3785520934*$t);
   $Z2 += 0.00000000011*cos(2.36351366554 + 53131.406024757*$t);
   $Z2 += 0.00000000012*cos(4.34261596283 + 32858.61374281979*$t);
   $Z2 += 0.00000000015*cos(2.28255722706 + 50586.73338786459*$t);
   $Z2 += 0.00000000012*cos(5.63353087898 + 26068.2333806744*$t);
   $Z2 += 0.00000000013*cos(2.08539778974 + 25132.3033999656*$t);
   $Z2 += 0.00000000013*cos(3.31771880069 + 10213.285546211*$t);
   $Z2 += 0.00000000013*cos(0.37928151736 + 4551.9534970588*$t);
   $Z2 += 0.00000000009*cos(5.32896907669 + 23869.1460373874*$t);
   $Z2 += 0.00000000009*cos(1.85195473467 + 103242.23401420339*$t);
   $Z2 += 0.00000000010*cos(2.69290690744 + 26091.7844769322*$t);
   $Z2 += 0.00000000012*cos(1.13570211007 + 26084.0218062162*$t);
   $Z2 += 0.00000000010*cos(4.31085447586 + 286966.93455731616*$t);
   $Z2 += 0.00000000008*cos(5.82534551009 + 25874.6040461362*$t);
   $Z2 += 0.00000000008*cos(6.17561594460 + 51646.11531805379*$t);
   $Z2 += 0.00000000008*cos(2.73528822352 + 41962.5207369374*$t);
   $Z2 += 0.00000000008*cos(0.86132391139 + 39609.6545831656*$t);
   $Z2 += 0.00000000007*cos(5.90586936446 + 77204.32749453338*$t);
   $Z2 += 0.00000000006*cos(2.23725426587 + 26080.78959457339*$t);
   $Z2 += 0.00000000007*cos(5.14284397401 + 1589.0728952838*$t);
   $Z2 += 0.00000000007*cos(3.13934336281 + 43071.8992890308*$t);
   $Z2 += 0.00000000005*cos(4.86318139233 + 54394.56338733519*$t);
   $Z2 += 0.00000000007*cos(2.45439783289 + 213.299095438*$t);
   $Z2 += 0.00000000006*cos(1.58442144371 + 26095.016688575*$t);
   $Z2 += 0.00000000006*cos(5.45060244038 + 25973.46385288896*$t);
   $Z2 += 0.00000000005*cos(4.79894457233 + 46514.4742339962*$t);
   $Z2 += 0.00000000005*cos(2.20020439243 + 6283.0758499914*$t);
   $Z2 += 0.00000000005*cos(5.38203064600 + 15874.6175953632*$t);
   $Z2 += 0.00000000005*cos(2.75432060530 + 19317.1925403286*$t);
   $Z2 += 0.00000000004*cos(2.96762251508 + 33326.5787331742*$t);
   $Z2 += 0.00000000005*cos(3.58879974911 + 63498.47038145279*$t);
   $Z2 += 0.00000000004*cos(6.00635657777 + 7.1135470008*$t);
   $Z2 += 0.00000000004*cos(3.43811673157 + 1066.49547719*$t);
   $Z2 += 0.00000000004*cos(3.46360896326 + 25661.3049506982*$t);
   $Z2 += 0.00000000004*cos(4.83154673482 + 51220.20654153979*$t);
   $Z2 += 0.00000000005*cos(1.65155678587 + 26202.34243025941*$t);
   $Z2 += 0.00000000004*cos(4.05043524436 + 51535.90899683439*$t);
   $Z2 += 0.00000000004*cos(3.87269622429 + 1052.2683831884*$t);
   $Z2 += 0.00000000004*cos(1.10462215070 + 58946.51688439399*$t);
   $Z2 += 0.00000000004*cos(5.41502198784 + 14765.2390432698*$t);
   $Z2 += 0.00000000004*cos(2.03873056084 + 26617.5941066688*$t);
   $Z2 += 0.00000000003*cos(2.19389680754 + 30639.856638633*$t);
   $Z2 += 0.00000000003*cos(4.90884264121 + 129330.13715577759*$t);
   $Z2 += 0.00000000004*cos(6.22828785556 + 36301.18868778519*$t);
   $Z2 += 0.00000000004*cos(3.68258570333 + 13521.7514415914*$t);
   $Z2 += 0.00000000003*cos(5.62688231105 + 48733.23133818299*$t);
   $Z2 += 0.00000000004*cos(2.45849991842 + 51749.20809227239*$t);
   $Z2 += 0.00000000003*cos(3.06502787272 + 16983.9961474566*$t);
   $Z2 += 0.00000000003*cos(4.57742754340 + 24498.8302462904*$t);
   $Z2 += 0.00000000003*cos(1.46286237530 + 3442.5749449654*$t);
   $Z2 += 0.00000000003*cos(1.55999070785 + 29530.4780865396*$t);
   $Z2 += 0.00000000003*cos(5.14417203650 + 76674.63652943878*$t);
   $Z2 += 0.00000000003*cos(1.09829861469 + 313054.83769889036*$t);
   $Z2 += 0.00000000003*cos(2.10570480254 + 49957.0491789616*$t);
   $Z2 += 0.00000000002*cos(0.49635100411 + 38519.945791972*$t);
   $Z2 += 0.00000000003*cos(3.19744325207 + 426.598190876*$t);
   $Z2 += 0.00000000003*cos(2.27361066514 + 72602.37737557039*$t);
   $Z2 += 0.00000000002*cos(5.42166315666 + 12566.1516999828*$t);
   $Z2 += 0.00000000002*cos(4.11021645418 + 2218.7571041868*$t);
   $Z2 += 0.00000000002*cos(6.01977464255 + 2118.7638603784*$t);
   $Z2 += 0.00000000003*cos(3.82490235305 + 9103.9069941176*$t);
   $Z2 += 0.00000000002*cos(1.55999258470 + 50057.04242277*$t);
   $Z2 += 0.00000000002*cos(2.83741388675 + 639.897286314*$t);
   $Z2 += 0.00000000003*cos(5.50522133834 + 23754.70674870219*$t);
   $Z2 += 0.00000000002*cos(4.64349469451 + 56727.7597802072*$t);
   $Z2 += 0.00000000002*cos(1.95986167578 + 73711.75592766379*$t);
   $Z2 += 0.00000000002*cos(0.55672894560 + 955.5997416086*$t);
   $Z2 += 0.00000000002*cos(1.93244538678 + 103292.23063610759*$t);
   $Z2 += 0.00000000002*cos(6.05929958767 + 25448.00585526019*$t);
   $Z2 += 0.00000000002*cos(3.03995453086 + 40853.142184844*$t);
   $Z2 += 0.00000000001*cos(2.47665559131 + 77734.01845962799*$t);
   $Z2 += 0.00000000002*cos(6.25822253418 + 52705.49724824299*$t);
   $Z2 += 0.00000000002*cos(1.38627663309 + 77308.10968311399*$t);
   $Z2 += 0.00000000001*cos(1.59643416291 + 27147.28507176339*$t);
   $Z2 += 0.00000000002*cos(3.54992576302 + 83925.04147387479*$t);
   $Z2 += 0.00000000001*cos(5.82473062390 + 45405.0956819028*$t);
   $Z2 += 0.00000000001*cos(0.32361625099 + 13655.8604911764*$t);
   $Z2 += 0.00000000001*cos(4.59226455833 + 55618.3812281138*$t);
   $Z2 += 0.00000000001*cos(1.77801233677 + 52156.1365222486*$t);
   $Z2 += 0.00000000001*cos(3.59899238770 + 53235.18821333759*$t);
   $Z2 += 0.00000000001*cos(0.75186170269 + 52195.47604404819*$t);
   $Z2 += 0.00000000002*cos(4.21419422689 + 105460.99111839019*$t);
   $Z2 += 0.00000000001*cos(3.02724177299 + 51962.5071877104*$t);
   $Z2 += 0.00000000001*cos(5.54016425013 + 98690.28051714458*$t);
   $Z2 += 0.00000000001*cos(4.96163083687 + 18849.2275499742*$t);
   $Z2 += 0.00000000001*cos(5.13453198510 + 52179.6876185064*$t);
   $Z2 += 0.00000000001*cos(4.54050452164 + 52168.69273614759*$t);
   $Z2 += 0.00000000001*cos(3.67122666149 + 52171.9249477904*$t);
   $Z2 += 0.00000000001*cos(4.16002499033 + 45892.73043315699*$t);
   $Z2 += 0.00000000001*cos(3.11767834677 + 78793.40038981718*$t);
   $Z2 += 0.00000000001*cos(4.70607503583 + 52290.24557183361*$t);
   $Z2 += 0.00000000001*cos(1.72196789636 + 155418.04029735178*$t);
   $Z2 += 0.00000000001*cos(1.43678225289 + 82815.66292178139*$t);
   $Z2 += 0.00000000001*cos(3.64195400420 + 65697.55772473979*$t);
   $Z2 += 0.00000000001*cos(2.34232573897 + 27676.976036858*$t);
   $Z2 += 0.00000000001*cos(2.22519315150 + 52061.36699446317*$t);
   $Z2 += 0.00000000001*cos(4.06167314974 + 339142.74084046457*$t);
   $Z2 += 0.00000000001*cos(1.84893906586 + 853.196381752*$t);
   $Z2 += 0.00000000001*cos(5.42775732068 + 26514.5013324502*$t);
   $Z2 += 0.00000000001*cos(6.03028910593 + 59414.4818747484*$t);
   $Z2 += 0.00000000001*cos(5.09856883029 + 76044.9523205358*$t);
   $Z2 += 0.00000000001*cos(1.68523311659 + 28421.0995344462*$t);
   $Z2 += 0.00000000001*cos(5.32883383904 + 79219.30916633119*$t);
   $Z2 += 0.00000000001*cos(0.84570925458 + 19804.8272915828*$t);
   $Z2 += 0.00000000001*cos(1.06906655760 + 124778.18365871879*$t);
   $Z2 += 0.00000000001*cos(5.63868454693 + 69159.80243060499*$t);
   $Z2 += 0.00000000001*cos(5.38153004139 + 26301.2022370122*$t);
   $Z2 += 0.00000000001*cos(4.77073547131 + 104881.30353139139*$t);
   $Z2 += 0.00000000001*cos(4.74588142049 + 129380.13377768178*$t);
   $Z2 += 0.00000000001*cos(2.25545108286 + 52602.4044740244*$t);
   $Z2 += 0.00000000001*cos(3.98601687793 + 11322.6640983044*$t);
   $Z2 += 0.00000000001*cos(0.07845866028 + 66941.04532641819*$t);
   $Z2 += 0.00000000001*cos(2.88984683172 + 38654.05484155699*$t);
   $Z2 += 0.00000000001*cos(4.00503893845 + 52182.9198301492*$t);
   $Z2 += 0.00000000001*cos(3.49574656538 + 52389.1053785864*$t);
   $Z2 += 0.00000000001*cos(0.33429045009 + 7238.67559160*$t);
   $Z2 += 0.00000000001*cos(0.31985247795 + 79323.09135491178*$t);
   $Z2 += 0.00000000001*cos(6.10860920195 + 51109.31080595839*$t);
   $Z2 += 0.00000000001*cos(2.84676327671 + 7994.5284420242*$t);
   $Z2 += 0.00000000001*cos(3.11496551907 + 25934.1243310894*$t);
   $Z2 += 0.00000000001*cos(5.40172380413 + 78477.00852016058*$t);
   $Z2 += 0.00000000001*cos(0.41949488018 + 6770.7106012456*$t);
   $Z2 += 0.00000000001*cos(4.62233743377 + 64741.95798313119*$t);
   $Z2 += 0.00000000001*cos(4.27662369360 + 12432.0426503978*$t);
   $Z2 += 0.00000000000*cos(0.88019140659 + 110012.94461544899*$t);
   $Z2 += 0.00000000000*cos(1.18882526931 + 28206.6670019526*$t);
   $Z2 += 0.00000000000*cos(5.60067399390 + 51123.53789995999*$t);
   $Z2 += 0.00000000000*cos(0.66520680194 + 419.4846438752*$t);
   $Z2 += 0.00000000000*cos(4.17948666644 + 78267.59076008058*$t);
   $Z2 += 0.00000000000*cos(5.93970677792 + 68050.42387851159*$t);
   $Z2 += 0.00000000000*cos(4.76480820754 + 78244.0396638228*$t);
   $Z2 += 0.00000000001*cos(0.17150693291 + 433.7117378768*$t);
   $Z2 += 0.00000000000*cos(2.10468974660 + 25619.9381512198*$t);
   $Z2 += 0.00000000001*cos(5.16942669114 + 77837.11123384659*$t);
   return $Z2*$t*$t;
}



   function Mercury_Z3($t) // 47 terms of order 3
{
   $Z3  = 0.00000099250*cos(0.29443229590 + 26087.9031415742*$t);
   $Z3 += 0.00000092976;
   $Z3 += 0.00000003230*cos(4.02309993038 + 52175.8062831484*$t);
   $Z3 += 0.00000000640*cos(2.16717843388 + 78263.70942472259*$t);
   $Z3 += 0.00000000369*cos(6.09477192866 + 104351.61256629678*$t);
   $Z3 += 0.00000000224*cos(3.14630379889 + 130439.51570787099*$t);
   $Z3 += 0.00000000111*cos(0.00722359195 + 156527.41884944518*$t);
   $Z3 += 0.00000000048*cos(3.09594836549 + 182615.32199101939*$t);
   $Z3 += 0.00000000019*cos(6.16655603798 + 208703.22513259358*$t);
   $Z3 += 0.00000000021*cos(3.31046636942 + 27197.2816936676*$t);
   $Z3 += 0.00000000007*cos(2.94356012175 + 234791.12827416777*$t);
   $Z3 += 0.00000000007*cos(0.65628834083 + 24978.5245894808*$t);
   $Z3 += 0.00000000002*cos(5.99334261589 + 260879.03141574195*$t);
   $Z3 += 0.00000000002*cos(6.22873921629 + 53285.1848352418*$t);
   $Z3 += 0.00000000002*cos(5.78810325925 + 31749.2351907264*$t);
   $Z3 += 0.00000000001*cos(0.84479650691 + 27043.5028831828*$t);
   $Z3 += 0.00000000001*cos(1.53587211633 + 1109.3785520934*$t);
   $Z3 += 0.00000000001*cos(0.78761433232 + 21535.9496445154*$t);
   $Z3 += 0.00000000001*cos(4.53925772521 + 51116.4243529592*$t);
   $Z3 += 0.00000000001*cos(2.76184993272 + 286966.93455731616*$t);
   $Z3 += 0.00000000001*cos(4.91700706367 + 25558.2121764796*$t);
   $Z3 += 0.00000000001*cos(5.91899219772 + 1059.3819301892*$t);
   $Z3 += 0.00000000001*cos(3.91598529129 + 25132.3033999656*$t);
   $Z3 += 0.00000000000*cos(0.95989869222 + 1589.0728952838*$t);
   $Z3 += 0.00000000001*cos(4.83279660629 + 20426.571092422*$t);
   $Z3 += 0.00000000000*cos(3.46721290636 + 77154.33087262919*$t);
   $Z3 += 0.00000000000*cos(1.74357991507 + 37410.5672398786*$t);
   $Z3 += 0.00000000000*cos(5.52724719384 + 5661.3320491522*$t);
   $Z3 += 0.00000000000*cos(2.42242414793 + 46514.4742339962*$t);
   $Z3 += 0.00000000000*cos(3.95720083996 + 4551.9534970588*$t);
   $Z3 += 0.00000000000*cos(0.55620001878 + 47623.8527860896*$t);
   $Z3 += 0.00000000000*cos(2.51891896481 + 57837.1383323006*$t);
   $Z3 += 0.00000000000*cos(4.06757949551 + 51066.427731055*$t);
   $Z3 += 0.00000000000*cos(2.83782582761 + 79373.08797681599*$t);
   $Z3 += 0.00000000000*cos(3.41743579353 + 50586.73338786459*$t);
   $Z3 += 0.00000000000*cos(0.30267502280 + 103242.23401420339*$t);
   $Z3 += 0.00000000000*cos(2.80685029082 + 28306.66024576099*$t);
   $Z3 += 0.00000000000*cos(5.70633333610 + 26107.57290247399*$t);
   $Z3 += 0.00000000000*cos(0.34541196749 + 22645.32819660879*$t);
   $Z3 += 0.00000000000*cos(0.46757777229 + 26068.2333806744*$t);
   $Z3 += 0.00000000000*cos(5.38981564610 + 32858.61374281979*$t);
   $Z3 += 0.00000000000*cos(2.34364280368 + 26084.0218062162*$t);
   $Z3 += 0.00000000000*cos(3.81913361795 + 26091.7844769322*$t);
   $Z3 += 0.00000000000*cos(5.09641110635 + 10213.285546211*$t);
   $Z3 += 0.00000000000*cos(1.30349643922 + 51646.11531805379*$t);
   $Z3 += 0.00000000000*cos(3.55639554083 + 53131.406024757*$t);
   $Z3 += 0.00000000000*cos(1.15022684382 + 25874.6040461362*$t);
   return $Z3*$t*$t*$t;
}



   function Mercury_Z4($t) // 12 terms of order 4
{
   $Z4  = 0.00000001500*cos(1.82376153122 + 26087.9031415742*$t);
   $Z4 -= 0.00000000592;
   $Z4 += 0.00000000056*cos(3.48599666355 + 52175.8062831484*$t);
   $Z4 += 0.00000000022*cos(0.17608711147 + 78263.70942472259*$t);
   $Z4 += 0.00000000009*cos(3.89825290813 + 104351.61256629678*$t);
   $Z4 += 0.00000000005*cos(1.27729295657 + 130439.51570787099*$t);
   $Z4 += 0.00000000003*cos(4.59766720323 + 156527.41884944518*$t);
   $Z4 += 0.00000000002*cos(1.46273885253 + 182615.32199101939*$t);
   $Z4 += 0.00000000001*cos(4.58832110028 + 208703.22513259358*$t);
   $Z4 += 0.00000000000*cos(4.64908450350 + 27197.2816936676*$t);
   $Z4 += 0.00000000000*cos(1.37450705839 + 234791.12827416777*$t);
   $Z4 += 0.00000000000*cos(1.42617733060 + 24978.5245894808*$t);
   return $Z4*$t*$t*$t*$t;
}



   function Mercury_Z5($t) // 7 terms of order 5
{
   $Z5  = 0.00000000045*cos(3.82268203713 + 26087.9031415742*$t);
   $Z5 -= 0.00000000043;
   $Z5 += 0.00000000003*cos(1.05444326177 + 52175.8062831484*$t);
   $Z5 += 0.00000000001*cos(4.50060145511 + 78263.70942472259*$t);
   $Z5 += 0.00000000000*cos(1.68820918658 + 104351.61256629678*$t);
   $Z5 += 0.00000000000*cos(5.41907824804 + 130439.51570787099*$t);
   $Z5 += 0.00000000000*cos(2.90287004404 + 156527.41884944518*$t);
   return $Z5*$t*$t*$t*$t*$t;
}


?>