<?php
/*
This is an example usage of the VSOP87C Sun Module functions.
---------------------------
AUTHOR : Jay Tanner - Revised: 2025
LANGUAGE : PHP v8.2.12
LICENSE : Public Domain
--------------------------------------------------------------------
*/
// -----------------------------------------
// Get current year from system clock. (GMT)
$cYear = gmdate("Y");
// --------------------------------------------------------------
// Read user arguments (-+yyyy, mm, dd) numerical date arguments.
$yNum = trim(Filter_Input(@INPUT_POST,'yNum'));
$mNum = trim(Filter_Input(@INPUT_POST,'mNum'));
$dNum = trim(Filter_Input(@INPUT_POST,'dNum'));
/* --------------------------------------
Account for empty argument, such as on
initial startup. Default = Date UT.
Actually, the TT scale is assumed in
the computations.
*/
$yNum = ($yNum == '')? gmdate('Y'):$yNum;
$mNum = ($mNum == '')? gmdate('m'):$mNum;
$dNum = ($dNum == '')? gmdate('d'):$dNum;
$yNum = SPrintF("%+05d", $yNum);
$mNum = SPrintF("%02d", $mNum);
$dNum = SPrintF("%02d", $dNum);
$yNum = Str_Replace('+', '', $yNum);
// Initial current date UT on startup.
$yNumi = gmdate('Y');
$mNumi = gmdate('m');
$dNumi = gmdate('d');
/* -------------------------------
Compute the Julian Date for the
given test date at 00:00:00 TT.
*/
$JD00 = JD_Num_For_Ymd ($yNum,$mNum,$dNum) - 0.5;
/* ------------------------------------------------
Compute VSOP87 geocentric Sun statistics. These
values are returned in a space-delimited string.
*/
$VSOP87StatsStr = VSOP87C_Geocentric_Sun ($JD00);
// --------------------------------------
// Extract statistics for the given date.
list
(
$RAHrs,
$DeclDeg,
$DistAU,
$AngDiamDeg,
$EclLngDeg,
$EclLatDeg
)
= PReg_Split("[ ]", $VSOP87StatsStr);
// --------------------------------------------
// Construct output text block.
$out =
"<pre>
------------------------------------------------------
VSOP87C Geocentric Astronomical Statistics For the Sun
For Ecliptic and Equinox of Date
yyyy mm dd = $yNum $mNum $dNum
JDate 00h = $JD00
------------------------------------
Statistics returned by the function:
VSOP87C_Geocentric_Sun (JDTT)
RAHrs = $RAHrs = Equatorial RA of the Sun in hours
DeclDeg = $DeclDeg = Equatorial declination of the Sun in degrees
DistAU = $DistAU = True Earth/Sun distance in AUs
AngDiamDeg = $AngDiamDeg = Angular diameter of the Sun in degrees
EclLngDeg = $EclLngDeg = Ecliptical longitude of the sun in degrees
EclLatDeg = $EclLatDeg = Ecliptical latitude of the sun in degrees
</pre>";
// END OF TEST CALL DEMO CODE
// **************************************************************************
print <<< _HTML
<!doctype HTML>
<HTML lang='en-us'>
<head>
<title>VSOP87C Sun Module Example/Test - PHP Science Labs</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<meta name="googlebot" content="index,nofollow">
<style>
PRE
{
font-family:monospace; font-size:11pt; font-weight:bold;
}
INPUT[type='text']::-ms-clear {width:0; height:0;}
INPUT[type='text']
{
background:white; color:black; font-family:monospace; font-size:13pt;
font-weight:bold; text-align:center; box-shadow:2px 2px 3px #666666;
border:2px solid black; border-radius:4px;
}
INPUT[type='text']:focus
{
font-family:monospace; background:white; box-shadow:2px 2px 3px #666666;
font-size:13pt; border:2px solid blue; text-align:center; font-weight:bold;
border-radius:4px;
}
INPUT[type='submit']
{
background:black; color:silver; font-family:Verdana; font-size:10pt;
font-weight:bold; border-radius:4px; border:4px solid black;
padding:3pt; box-shadow:1px 1px 3px #222222;
}
INPUT[type='submit']:hover
{
background:black; color:GreenYellow; font-family:Verdana; font-size:10pt;
font-weight:bold; border-radius:4px; border:4px solid red;
padding:3pt; box-shadow:1px 1px 3px #222222;
}
::selection{background-color:yellow !important; color:black !important;}
::-moz-selection{background-color:yellow !important; color:black !important;}
</style>
</head>
<body style='background:black; color:white; font-family:verdana; font-size:11pt;'>
<table width="666" style='color:black; background:white; border-radius:8px;' cellpadding='6'>
<!-- Yellow source code view link. --->
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<td style='background:transparent; color:black; font-size:10pt;
text-align:left;'>
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<a href='View-Source-Code.php' target='_blank'
style='font-family:Verdana; color:black; background:yellow;
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border-radius:4px;'>
<span style='font-weight:normal;'>View/Copy PHP Source Code</span> </a>
</td>
</tr>
<tr><td>
<h3>VSOP87C Sun Module Example / Test Demo</h3>
<div>
This simple example/test program computes the basic astronomical<br>
statistics for the Sun at 00h TDB on any given date according to the<br>
The VSOP87 C series.
<br><br>
<b style='color:red;'>NOTES</b>:<br>
<ul>
<li>This demo version automatically adjusts for Julian or Gregorian<br>calendar dates.<br><br></li>
<li>Dates up to 1582 Oct 04 = Julian Calendar Dates.<br><br></li>
<li>Dates from 1582 Oct 15 onwards = Gregorian Calendar Dates.<br><br></li>
<li>BC years are represented here by using negative year values.<br>
However, there is no calendar year 0 (zero), by definition.<br><br></li>
</ul>
<hr>
<b>Enter Numerical Calendar Date Elements</b> (yNum mNum dNum)
<br><br>
Initial default startup date = Current date ($yNumi $mNumi $dNumi) at 00:00:00 TT.
<br><br>
The program does not check for errors and simply assumes the calendar<br>
date elements (yNum, mNum, dNum) are valid values.<br>
Valid date elements should return a valid result.
<br><br>
If possible, check the test computations against another VSOP87 C<br>
source to see how closely they match.
<br><br>
EXAMPLE:<br>
October 5th, 1991 date elements would be entered as: <b><code>1991 10 05</code></b>
<br><br>
<form name="form1" method="post" action="">
<input type="text" name="yNum" value="$yNum" size='6' maxlength='5' style='text-align:center;'>
<input type="text" name="mNum" value="$mNum" size='3' maxlength='2' style='text-align:center;'>
<input type="text" name="dNum" value="$dNum" size='3' maxlength='2' style='text-align:center;'>
<input type="submit" name="compute_button" value="Compute">
</form>
<br>
$out
</div>
</td></tr>
</table>
<br><br><br><br><br><br><br><br><br><br><br><br>
<br><br><br><br><br><br><br><br><br><br><br><br>
</body>
</html>
_HTML;
/* ***************************************************************************
VSOP87 ASTRONOMICAL COORDINATES COMPUTATION MODULE
FOR THE SUN (2000 BC to 6000 AD).
REVISED: 2012 AUG 14
This revised version replaces the IAU 1980 nutation
series with the IAU 2000B nutation series.
This module contains the functions to compute the raw
heliocentric coordinates of the Earth and geocentric
coordinates of the Sun based on the VSOP87 theory
heliocentric model version C. Raw coordinates are
the true geometric coordinates prior to any kind of
corrections.
The geocentric coordinates of the Sun are the inverse
of the heliocentric coordinates of the Earth.
---------------------
The time scale is TDB
Distances are in AUs (Astronomical Units)
1.0 AU = 149597870691 m ±30 (NASA/JPL)
-------------------------------------
AUTHOR : Jay Tanner - Revised: 2025
LANGUAGE : PHP v8.2.12
LICENSE : Public Domain
--------------------------------------------------------------------
*/
/*
############################################################################
This function computes basic geocentric solar ephemeris
statistics based on the full-precsion VSOP87 theory and
the IAU 2000B nutation series.
The final coordinates are expressed in the FK5 system.
-------------
DEPENDENCIES:
JD_Num_For_Ymd()
Earth_hXYZR()
Epsilon_Mean()
Delta_Epsilon_2000B()
Delta_Psi_2000B()
--------------------------------------------------------
The space-delimited values returned by the function are:
RAHrs = Equatorial RA of Sun in hours
DeclDeg = Equatorial declination of Sun in degrees
DistAU = Earth/Sun true distance in AU
AngDiamDeg = Angular diameter of Sun in degrees
EclLngDeg = Ecliptical longitude of Sun
EclLatDeg = Ecliptical latitude of Sun
*/
function VSOP87C_Geocentric_Sun ($JDTT)
{
// ------------------
// Radius of the sun.
$radius = 696000000; // meters
// --------------------------
// Define degrees per radian.
$DegPerRad = 180 / M_PI;
// --------------------------------
// Define meters per AU ±30 (NASA).
$M_per_AU = 149597870691;
/* ---------------------------------------------
Compute the time variable corresponding to JD
and expressed in Julian centuries as reckoned
from J2000.0 (TT Time Scale)
*/
$T = ($JDTT - 2451545.0) / 36525;
/* ---------------------------------------------------
Define light-time constant. This is the light-time
equivalent to 1.0 AU, expressed as a fraction of a
standard day (86400 seconds).
*/
$k = 149597870691.0 / 299792458 / 86400;
// ---------------------------------------
// Compute heliocentric X,Y,Z,R for Earth.
list
(
$hXe,
$hYe,
$hZe,
$hRe
)
= PReg_Split("[ ]", Earth_hXYZR($JDTT));
// -----------------------------------------
// Copy Earth to Sun distance. This initial
// value is the true geometric distance at
// the given moment. No light-time and
// aberration corrections are needed.
$Res = $hRe;
// -------------------------------------------
// Set heliocentric X,Y,Z, R for Sun (origin).
$hXs = $hYs = $hZs = $hRs = 0;
// ---------------------------------
// Compute geocentric X,Y,Z for Sun.
$gXs = $hXs - $hXe;
$gYs = $hYs - $hYe;
$gZs = $hZs - $hZe;
// ----------------------------------
// True distance between Sun and Sun.
$Rps = $hRs;
// --------------------------------------------------
// Compute true distance in AU between Earth and Sun.
$DistAU = SqRt($gXs*$gXs + $gYs*$gYs + $gZs*$gZs);
/* ----------------------------------
Compute starting approximation for
light time between Earth and Sun
as a fraction of a day.
*/
$LTCurrent = $DistAU * $k;
/* -------------------------------
Initialise light-time iteration
loop control variables.
*/
$PrecisionLimit = 0.000000000001;
$LTPrevious = 0.0;
// **************************************************
// BEGIN LIGHT-TIME CORRECTION ITERATION LOOP PROCESS
while (abs($LTCurrent - $LTPrevious) > $PrecisionLimit)
{
$LTPrevious = $LTCurrent;
// --------------------------------------------
// Compute new heliocentric X,Y,Z, R for Earth.
list
(
$hXe,
$hYe,
$hZe,
$hRe
)
= PReg_Split("[ ]", Earth_hXYZR($JDTT - $LTCurrent));
// --------------------------
// New Earth to Sun distance.
$Res = $hRe;
// ------------------------------
// Coordinates of Sun (= origin).
$hXs = $hYs = $hZs = $hRs = 0;
// -------------------------
// New heliocentric distance
// between Sun and Sun.
$Rps = $hRs;
// -------------------------------------
// Compute new geocentric X,Y,Z for Sun.
$gXs = $hXs - $hXe;
$gYs = $hYs - $hYe;
$gZs = $hZs - $hZe;
// -------------------------------------------
// Compute new distance between Earth and Sun.
// Rep = Earth distance to planet or body.
$Rep = SqRt($gXs*$gXs + $gYs*$gYs + $gZs*$gZs);
// ------------------------------------
// Compute new LTCurrent approximation, or
// finished if precision limit reached.
$LTCurrent = $Rep * $k;
}
// ******************************************
// DROP THROUGH HERE AND CONTINUE BELOW AFTER
// LIGHT-TIME ITERATION LOOP HAS FINISHED
// ---------------------------------------------------
// Compute raw geocentric ecliptical longitude of Sun.
$EclLngDeg = Rad2Deg(ATan2($gYs, $gXs));
if ($EclLngDeg < 0) {$EclLngDeg += 360;}
// ---------------------------------------
// Compute raw geocentric latitude of Sun.
$EclLatDeg = Rad2Deg(ATan2($gZs, SqRt($gXs*$gXs + $gYs*$gYs)));
// -------------------------------------------------
// Apply FK5 correction to raw ecliptical longitude.
$u = deg2rad($EclLatDeg);
$Lprime = deg2rad($EclLngDeg - 1.397*$T - 0.00031*$T*$T);
$w = $EclLngDeg + (0.03916*(cos($Lprime) + sin($Lprime))*tan($u) - 0.09033)
/ 3600;
// ------------------------------------------------
// Apply FK5 correction to raw ecliptical latitude.
$u = deg2rad($EclLngDeg - 1.397*$T - 0.00031*$T*$T);
$EclLatDeg += (0.03916*(cos($u) - sin($u)) / 3600);
$EclLngDeg = $w;
// -------------------------------------------
// Apply correction for nutation in longitude.
// The newer IAU 2000B nutation series is used.
$EclLngDeg += Delta_Psi_2000B($JDTT);
// ---------------------------------------
// Compute true obliquity of the ecliptic.
// The IAU 2000B nutation series is used.
$eTrue = Epsilon_Mean($JDTT) + Delta_Epsilon_2000B($JDTT);
// -------------------------------------
// Compute the equatorial RA in degrees
// and hours.
$u = deg2rad($EclLngDeg);
$w = deg2rad($EclLatDeg);
$eps = deg2rad($eTrue);
$y = sin($u)*cos($eps) - tan($w)*sin($eps);
$x = cos($u);
$RADeg = Rad2Deg(atan2($y, $x)); if ($RADeg < 0) {$RADeg += 360;}
$RAHrs = $RADeg / 15;
// ----------------------------------------------
// Compute the equatorial declination in degrees.
$w = asin(sin($w)*cos($eps) + cos($w)*sin($u)*sin($eps));
$DeclDeg = Rad2Deg($w);
// -------------------------------------------
// Compute angular diameter of Sun in degrees.
$AngDiamDeg = $DegPerRad * $radius * 2 / $M_per_AU / $Rep;
// ---------------------------------------------------------------------
// Return the RA, declination, distance, angular diameter and ecliptical
// coordinates of the Sun in a plain-text, space delimited data string.
return "$RAHrs $DeclDeg $DistAU $AngDiamDeg $EclLngDeg $EclLatDeg";
} // End of Geocentric_Sun()
// ****************************************************************************
/*
Compute the mean obliquity of the ecliptic in degrees for the
current JD argument corresponding to any given moment.
This ecliptic obliquity function is based on a formula derived
by J. Laskar, Astronomy and Astrophysics, 1968, Vol. 157, p68.
The estimated accuracy of this formula is ±0.01 arc second between
the years 1000 AD and 3000 AD and a few arc seconds after 10,000
years. It is only valid in the range ±10,000 years either way
of J2000.0
Over the long term, it is more accurate than the formula
adopted by the International Astronomical Union (IAU)
for general ephemeris computations.
---------
ARGUMENTS
$JD = General JD argument for any date and time.
------
ERRORS
No error checking is done.
*/
function Epsilon_Mean ($JD)
{
// ----------------------------------------------
// COMPUTE THE TIME IN JULIAN CENTURIES RECKONED
// FROM J2000.0 CORRESPONDING TO THE JD ARGUMENT
// AND THEN DIVIDE BY 100 FOR DECIMILLENNIA.
$t = ($JD - 2451545.0) / 36525 / 100;
// --------------------------------------
// COMPUTE MEAN OBLIQUITY OF THE ECLIPTIC
// EXPRESSED IN ARC SECONDS.
$p = $t*$t;
$eMeanSS = 84381.448 - 4680.93*$t;
$eMeanSS -= 1.55*$p; $p *= $t;
$eMeanSS += 1999.25*$p; $p *= $t;
$eMeanSS -= 51.38*$p; $p *= $t;
$eMeanSS -= 249.67*$p; $p *= $t;
$eMeanSS -= 39.05*$p; $p *= $t;
$eMeanSS += 7.12*$p; $p *= $t;
$eMeanSS += 27.87*$p; $p *= $t;
$eMeanSS += 5.79*$p; $p *= $t;
$eMeanSS += 2.45*$p;
// -----------------------------------------------
// RETURN THE MEAN OBLIQUITY EXPRESSED IN DEGREES.
$eMeanDeg = $eMeanSS / 3600;
return $eMeanDeg;
} // End of Epsilon_Mean()
// ****************************************************************************
/*
************************************************
THIS FUNCTION COMPUTES THE NUTATION IN LONGITUDE
ACCORDING TO THE IAU 2000B NUTATION SERIES. THE
RETURNED RESULT IS IN DECIMAL DEGREES.
THIS SERIES CONSISTS OF 77 TERMS.
*/
function Delta_Psi_2000B ($JD)
{
// ------------------------------------------------------
// Compute time in Julian centuries reckoned from J2000.0
// correspomding to the JD number.
$T = ($JD - 2451545.0) / 36525.0;
// -------------------
// Compute powers of T
$T2 = $T * $T;
$T3 = $T * $T2;
$T4 = $T * $T3;
// -----------------------------------
// Mean anomaly of the Moon in radians
$L = deg2rad((485868.249036 + 1717915923.2178*$T + 31.8792*$T2
+ 0.051635*$T3 - 0.0002447*$T4) / 3600);
// ----------------------------------
// Mean anomaly of the Sun in radians
$Lp = deg2rad((1287104.79305 + 129596581.0481*$T
- 0.5532*$T2 + 0.000136*$T3 - 0.00001149*$T4) / 3600);
// ----------------------------------------------------
// Mean argument of the latitude of the Moon in radians
$F = deg2rad((335779.526232 + 1739527262.8478*$T
- 12.7512*$T2 - 0.001037*$T3 + 0.00000417*$T4) / 3600);
// ---------------------------------------------------
// Mean elongation of the Moon from the Sun in radians
$D = deg2rad((1072260.70369 + 1602961601.2090*$T
- 6.3706*$T2 + 0.006593*$T3 - 0.00003169*$T4) / 3600);
// ----------------------------------------------------------------
// Mean longitude of the mean ascending node of the Moon in radians
$Om = deg2rad((450160.398036 - 6962890.5431*$T
+ 7.4722*$T2 + 0.007702*$T3 - 0.00005939*$T4) / 3600);
// SUM SERIES FOR NUTATION IN LONGITUDE (dPsi) IN ARC SEC * 10E+7
$s = 0;
$s += (-172064161 - 174666*$T)*sin($Om) + 33386*cos($Om);
$s += (-13170906 - 1675*$T)*sin(2*($F - $D + $Om)) - 13696*cos(2*($F - $D + $Om));
$s += (-2276413 - 234*$T)*sin(2*($F + $Om)) + 2796*cos(2*($F + $Om));
$s += (2074554 + 207*$T)*sin(2*$Om) - 698*cos(2*$Om);
$s += (1475877 - 3633*$T)*sin($Lp) + 11817*cos($Lp);
$s += (-516821 + 1226*$T)*sin($Lp + 2*($F - $D + $Om)) - 524*cos($Lp + 2*($F - $D + $Om));
$s += (711159 + 73*$T)*sin($L) - 872*cos($L);
$s += (-387298 - 367*$T)*sin(2*$F + $Om) + 380*cos(2*$F + $Om);
$s += (-301461 - 36*$T)*sin($L + 2*($F + $Om)) + 816*cos($L + 2*($F + $Om));
$s += (215829 - 494*$T)*sin(2*($F - $D + $Om) - $Lp) + 111*cos(2*($F - $D + $Om) - $Lp);
$s += (128227 + 137*$T)*sin(2*($F - $D) + $Om) + 181*cos(2*($F - $D) + $Om);
$s += (123457 + 11*$T)*sin(2*($F + $Om) - $L) + 19*cos(2*($F + $Om) - $L);
$s += (156994 + 10*$T)*sin(2*$D - $L) - 168*cos(2*$D - $L);
$s += (63110 + 63*$T)*sin($L + $Om) + 27*cos($L + $Om);
$s += (-57976 - 63*$T)*sin($Om - $L) - 189*cos($Om - $L);
$s += (-59641 - 11*$T)*sin(2*($F + $D + $Om) - $L) + 149*cos(2*($F + $D + $Om) - $L);
$s += (-51613 - 42*$T)*sin($L + 2*$F + $Om) + 129*cos($L + 2*$F + $Om);
$s += (45893 + 50*$T)*sin(2*($F - $L) + $Om) + 31*cos(2*($F - $L) + $Om);
$s += (63384 + 11*$T)*sin(2*$D) - 150*cos(2*$D);
$s += (-38571 - $T)*sin(2*($F + $D + $Om)) + 158*cos(2*($F + $D + $Om));
$s += 32481*sin(2*($F - $Lp - $D + $Om));
$s -= 47722*sin(2*($D - $L)) + 18*cos(2*($D - $L));
$s += (-31046 - $T)*sin(2*($L + $F + $Om)) + 131*cos(2*($L + $F + $Om));
$s += 28593*sin($L + 2*($F - $D + $Om)) - cos($L + 2*($F - $D + $Om));
$s += (20441 + 21*$T)*sin(2*$F - $L + $Om) + 10*cos(2*$F - $L + $Om);
$s += 29243*sin(2*$L) - 74*cos(2*$L);
$s += 25887*sin(2*$F) - 66*cos(2*$F);
$s += (-14053 - 25*$T)*sin($Lp + $Om) + 79*cos($Lp + $Om);
$s += (15164 + 10*$T)*sin(2*$D - $L + $Om) + 11*cos(2*$D - $L + $Om);
$s += (-15794 + 72*$T)*sin(2*($Lp + $F - $D + $Om)) - 16*cos(2*($Lp + $F - $D + $Om));
$s += 21783*sin(2*($D - $F)) + 13*cos(2*($D - $F));
$s += (-12873 - 10*$T)*sin($L - 2*$D + $Om) - 37*cos($L - 2*$D + $Om);
$s += (-12654 + 11*$T)*sin($Om - $Lp) + 63*cos($Om - $Lp);
$s -= 10204*sin(2*($F + $D) - $L + $Om) - 25*cos(2*($F + $D) - $L + $Om);
$s += (16707 - 85*$T)*sin(2*$Lp) - 10*cos(2*$Lp);
$s -= 7691*sin($L + 2*($F + $D + $Om)) - 44*cos($L + 2*($F + $D + $Om));
$s -= 11024*sin(-2*$L + 2*$F) + 14*cos(2*($F - $L));
$s += (7566 - 21*$T)*sin($Lp + 2*($F + $Om)) - 11*cos($Lp + 2*($F + $Om));
$s += (-6637 - 11*$T)*sin(2*($F + $D) + $Om) + 25*cos(2*($F + $D) + $Om);
$s += (-7141 + 21*$T)*sin(2*($F + $Om) - $Lp) + 8*cos(2*($F + $Om) - $Lp);
$s += (-6302 - 11*$T)*sin(2*$D + $Om) + 2*cos(2*$D + $Om);
$s += (5800 + 10*$T)*sin($L + 2*($F - $D) + $Om) + 2*cos($L + 2*($F - $D) + $Om);
$s += 6443*sin(2*($L + $F - $D + $Om)) - 7*cos(2*($L + $F - $D + $Om));
$s += (-5774 - 11*$T)*sin(2*($D - $L) + $Om) - 15*cos(2*($D - $L) + $Om);
$s -= 5350*sin(2*($L + $F) + $Om) - 21*cos(2*($L + $F) + $Om);
$s += (-4752 - 11*$T)*sin(2*($F - $D) - $Lp + $Om) - 3*cos(2*($F - $D) - $Lp + $Om);
$s += (-4940 - 11*$T)*sin($Om - 2*$D) - 21*cos($Om - 2*$D);
$s += 7350*sin(2*$D - $L - $Lp) - 8*cos(2*$D - $L - $Lp);
$s += 4065*sin(2*($L - $D) + $Om) + 6*cos(2*($L - $D) + $Om);
$s += 6579*sin($L + 2*$D) - 24*cos($L + 2*$D);
$s += 3579*sin($Lp + 2*($F - $D) + $Om) + 5*cos($Lp + 2*($F - $D) + $Om);
$s += 4725*sin($L - $Lp) - 6*cos($L - $Lp);
$s -= 3075*sin(2*($F - $L + $Om)) + 2*cos(2*($F - $L + $Om));
$s -= 2904*sin(3*$L + 2*($F + $Om)) - 15*cos(3*$L + 2*($F + $Om));
$s += 4348*sin(2*$D - $Lp) - 10*cos(2*$D - $Lp);
$s -= 2878*sin($L - $Lp + 2*($F + $Om)) - 8*cos($L - $Lp + 2*($F + $Om));
$s -= 4230*sin($D) - 5*cos($D);
$s -= 2819*sin(2*($F + $D + $Om) - $L - $Lp) - 7*cos(2*($F + $D + $Om) - $L - $Lp);
$s -= 4056*sin(2*$F - $L) - 5*cos(2*$F - $L);
$s -= 2647*sin(2*($F + $D + $Om) - $Lp) - 11*cos(2*($F + $D + $Om) - $Lp);
$s -= 2294*sin($Om - 2*$L) + 10*cos($Om - 2*$L);
$s += 2481*sin($L + $Lp + 2*($F + $Om)) - 7*cos($L + $Lp + 2*($F + $Om));
$s += 2179*sin(2*$L + $Om) - 2*cos(2*$L + $Om);
$s += 3276*sin($Lp - $L + $D) + cos($Lp - $L + $D);
$s -= 3389*sin($L + $Lp) - 5*cos($L + $Lp);
$s += 3339*sin($L + 2*$F) - 13*cos($L + 2*$F);
$s -= 1987*sin(2*($F - $D) - $L + $Om) + 6*cos(2*($F - $D) - $L + $Om);
$s -= 1981*sin($L + 2*$Om);
$s += 4026*sin($D - $L) - 353*cos($D - $L);
$s += 1660*sin($D + 2*($F + $Om)) - 5*cos($D + 2*($F + $Om));
$s -= 1521*sin(2*($F + 2*$D + $Om) - $L) - 9*cos(2*($F + 2*$D + $Om) - $L);
$s += 1314*sin($Lp - $L + $D + $Om);
$s -= 1283*sin(2*($F - $Lp - $D) + $Om);
$s -= 1331*sin($L + 2*($F + $D) + $Om) - 8*cos($L + 2*($F + $D) + $Om);
$s += 1383*sin(2*($F - $L + $D + $Om)) - 2*cos(2*($F - $L + $D + $Om));
$s += 1405*sin(2*$Om - $L) + 4*cos(2*$Om - $L);
$s += 1290*sin($L + $Lp + 2*($F - $D + $Om));
$dPsiDeg = $s / 36000000000;
return $dPsiDeg;
} // End of Delta_Psi_2000B()
// ****************************
// ****************************
/*
************************************************
THIS FUNCTION COMPUTES THE NUTATION IN OBLIQUITY
ACCORDING TO THE IAU 2000B NUTATION SERIES. THE
RETURNED RESULT IS IN DECIMAL DEGREES.
THIS SERIES CONSISTS OF 77 TERMS.
*/
function Delta_Epsilon_2000B ($JD)
{
// ------------------------------------------------------
// Compute time in Julian centuries reckoned from J2000.0
// correspomding to the JD number.
$T = ($JD - 2451545.0) / 36525.0;
// -------------------
// Compute powers of T
$T2 = $T * $T;
$T3 = $T * $T2;
$T4 = $T * $T3;
// -----------------------------------
// Mean anomaly of the Moon in radians
$L = deg2rad((485868.249036 + 1717915923.2178*$T + 31.8792*$T2
+ 0.051635*$T3 - 0.00024470*$T4) / 3600.0);
// ----------------------------------
// Mean anomaly of the Sun in radians
$Lp = deg2rad((1287104.79305 + 129596581.0481*$T
- 0.5532*$T2 + 0.000136*$T3 - 0.00001149*$T4) / 3600.0);
// ----------------------------------------------------
// Mean argument of the latitude of the Moon in radians
$F = deg2rad((335779.526232 + 1739527262.8478*$T
- 12.7512*$T2 - 0.001037*$T3 + 0.00000417*$T4) / 3600.0);
// ---------------------------------------------------
// Mean elongation of the Moon from the Sun in radians
$D = deg2rad((1072260.70369 + 1602961601.2090*$T
- 6.3706*$T2 + 0.006593*$T3 - 0.00003169*$T4) / 3600.0);
// ----------------------------------------------------------------
// Mean longitude of the mean ascending node of the Moon in radians
$Om = deg2rad((450160.398036 - 6962890.5431*$T
+ 7.4722*$T2 + 0.007702*$T3 - 0.00005939*$T4) / 3600.0);
// SUM SERIES FOR NUTATION IN OBLIQUITY (dEps) IN ARC SEC * 10E+7
$s = 0;
$s += (92052331 + 9086*$T)*cos($Om) + 15377*sin($Om);
$s += (5730336 - 3015*$T)*cos(2*($F - $D + $Om)) - 4587*sin(2*($F - $D + $Om));
$s += (978459 - 485*$T)*cos(2*($F + $Om)) + 1374*sin(2*($F + $Om));
$s += (-897492 + 470*$T)*cos(2*$Om) - 291*sin(2*$Om);
$s += (73871 - 184*$T)*cos($Lp) - 1924*sin($Lp);
$s += (224386 - 677*$T)*cos($Lp + 2*($F - $D + $Om)) - 174*sin($Lp + 2*($F - $D + $Om));
$s -= 6750*cos($L) - 358*sin($L);
$s += (200728 + 18*$T)*cos(2*$F + $Om) + 318*sin(2*$F + $Om);
$s += (129025 - 63*$T)*cos($L + 2*($F + $Om)) + 367*sin($L + 2*($F + $Om));
$s += (-95929 + 299*$T)*cos(2*($F - $D + $Om) - $Lp) + 132*sin(2*($F - $D + $Om) - $Lp);
$s += (-68982 - 9*$T)*cos(2*($F - $D) + $Om) + 39*sin(2*($F - $D) + $Om);
$s += (-53311 + 32*$T)*cos(2*($F + $Om) - $L) - 4*sin(2*($F + $Om) - $L);
$s -= 1235*cos(2*$D - $L) - 82*sin(2*$D - $L);
$s -= 33228*cos($L + $Om) + 9*sin($L + $Om);
$s += 31429*cos($Om - $L) - 75*sin($Om - $L);
$s += (25543 - 11*$T)*cos(2*($F + $D + $Om) - $L) + 66*sin(2*($F + $D + $Om) - $L);
$s += 26366*cos($L + 2*$F + $Om) + 78*sin($L + 2*$F + $Om);
$s += (-24236 - 10*$T)*cos(2*($F - $L) + $Om) + 20*sin(2*($F - $L) + $Om);
$s -= 1220*cos(2*$D) - 29*sin(2*$D);
$s += (16452 - 11*$T)*cos(2*($F + $D + $Om)) + 68*sin(2*($F + $D + $Om));
$s -= 13870*cos(2*($F - $Lp - $D + $Om));
$s += 477*cos(2*($D - $L)) - 25*sin(2*($D - $L));
$s += (13238 - 11*$T)*cos(2*($L + $F + $Om)) + 59*sin(2*($L + $F + $Om));
$s += (-12338 + 10*$T)*cos($L + 2*($F - $D + $Om)) - 3*sin($L + 2*($F - $D + $Om));
$s -= 10758*cos(2*$F - $L + $Om) + 3*sin(2*$F - $L + $Om);
$s -= 609*cos(2*$L) - 13*sin(2*$L);
$s -= 550*cos(2*$F) - 11*sin(2*$F);
$s += (8551 - 2*$T)*cos($Lp + $Om) - 45*sin($Lp + $Om);
$s -= 8001*cos(2*$D - $L + $Om) + sin(2*$D - $L + $Om);
$s += (6850 - 42*$T)*cos(2*($Lp + $F - $D + $Om)) - 5*sin(2*($Lp + $F - $D + $Om));
$s -= 167*cos(2*($D - $F)) - 13*sin(2*($D - $F));
$s += 6953*cos($L - 2*$D + $Om) - 14*sin($L - 2*$D + $Om);
$s += 6415*cos($Om - $Lp) + 26*sin($Om - $Lp);
$s += 5222*cos(2*($F + $D) - $L + $Om) + 15*sin(2*($F + $D) - $L + $Om);
$s += (168 - $T)*cos(2*$Lp) + 10*sin(2*$Lp);
$s += 3268*cos($L + 2*($F + $D + $Om)) + 19*sin($L + 2*($F + $D + $Om));
$s += 104*cos(2*($F - $L)) + 2*sin(2*($F - $L));
$s -= 3250*cos($Lp + 2*($F + $Om)) + 5*sin($Lp + 2*($F + $Om));
$s += 3353*cos(2*($F + $D) + $Om) + 14*sin(2*($F + $D) + $Om);
$s += 3070*cos(2*($F + $Om) - $Lp) + 4*sin(2*($F + $Om) - $Lp);
$s += 3272*cos(2*$D + $Om) + 4*sin(2*$D + $Om);
$s -= 3045*cos($L + 2*($F - $D) + $Om) + sin($L + 2*($F - $D) + $Om);
$s -= 2768*cos(2*($L + $F - $D + $Om)) + 4*sin(2*($L + $F - $D + $Om));
$s += 3041*cos(2*($D - $L) + $Om) - 5*sin(2*($D - $L) + $Om);
$s += 2695*cos(2*($L + $F) + $Om) + 12*sin(2*($L + $F) + $Om);
$s += 2719*cos(2*($F - $D) - $Lp + $Om) - 3*sin(2*($F - $D) - $Lp + $Om);
$s += 2720*cos($Om - 2*$D) - 9*sin($Om - 2*$D);
$s -= 51*cos(2*$D - $L - $Lp) - 4*sin(2*$D - $L - $Lp);
$s -= 2206*cos(2*($L - $D) + $Om) - sin(2*($L - $D) + $Om);
$s -= 199*cos($L + 2*$D) - 2*sin($L + 2*$D);
$s -= 1900*cos($Lp + 2*($F - $D) + $Om) - sin($Lp + 2*($F - $D) + $Om);
$s -= 41*cos($L - $Lp) - 3*sin($L - $Lp);
$s += 1313*cos(2*($F - $L + $Om)) - sin(2*($F - $L + $Om));
$s += 1233*cos(3*$L + 2*($F + $Om)) + 7*sin(3*$L + 2*($F + $Om));
$s -= 81*cos(2*$D - $Lp) - 2*sin(2*$D - $Lp);
$s += 1232*cos($L - $Lp + 2*($F + $Om)) + 4*sin($L - $Lp + 2*($F + $Om));
$s -= 20*cos($D) + 2*sin($D);
$s += 1207*cos(2*($F + $D + $Om) - $L - $Lp) + 3*sin(2*($F + $D + $Om) - $L - $Lp);
$s += 40*cos(2*$F - $L) - 2*sin(2*$F - $L);
$s += 1129*cos(2*($F + $D + $Om) - $Lp) + 5*sin(2*($F + $D + $Om) - $Lp);
$s += 1266*cos($Om - 2*$L) - 4*sin($Om - 2*$L);
$s -= 1062*cos($L + $Lp + 2*($F + $Om)) + 3*sin($L + $Lp + 2*($F + $Om));
$s -= 1129*cos(2*$L + $Om) + 2*sin(2*$L + $Om);
$s -= 9*cos($Lp + $D - $L);
$s += 35*cos($L + $Lp) - 2*sin($L + $Lp);
$s -= 107*cos($L + 2*$F) - sin($L + 2*$F);
$s += 1073*cos(2*($F - $D) - $L + $Om) - 2*sin(2*($F - $D) - $L + $Om);
$s += 854*cos($L + 2*$Om);
$s -= 553*cos($D - $L) + 139*sin($D - $L);
$s -= 710*cos(2*($F + $Om) + $D) + 2*sin(2*($F + $Om) + $D);
$s += 647*cos(2*($F + 2*$D + $Om) - $L) + 4*sin(2*($F + 2*$D + $Om) - $L);
$s -= 700*cos($Lp - $L + $D + $Om);
$s += 672*cos(2*($F - $Lp - $D) + $Om);
$s += 663*cos($L + 2*($F + $D) + $Om) + 4*sin($L + 2*($F + $D) + $Om);
$s -= 594*cos(2*($F - $L + $D + $Om)) + 2*sin(2*($F - $L + $D + $Om));
$s -= 610*cos(2*$Om - $L) - 2*sin(2*$Om - $L);
$s -= 556*cos($L + $Lp + 2*($F - $D + $Om));
$dEpsDeg = $s /36000000000.0;
return $dEpsDeg;
} // End of Delta_Epsilon_2000B()
// ****************************************************************************
// ****************************************************************************
/*
******************************************************
EARTH
Heliocentric Coords Module - VSOP 87 Theory - Series C3
Heliocentric rectangular X,Y,Z,R coordinates for the
mean dynamical ecliptic and equinox of the date.
Module Range: 2000 BC to 6000 AD
Originally written in PHP 4.3.11
Jay Tanner - NeoProgrammics
2007-Jun-15-Fri
Ref:
Planetary Theories in Rectangular and Spherical Variables
VSOP87 Solutions
Astronomy & Astrophysics
vol. 202, p309-p315
Pierre Bretagnon, Gerard Francou
1988
AUTHOR : Jay Tanner - Revised: 2025
LANGUAGE : PHP v8.2.12
LICENSE : Public Domain
Jay Tanner
VSOP87@NeoProgrammics.com
******************************************************
*/
function Earth_hXYZR($JDArg)
{
// Compute time in Julian millennia from J2000.0
$t = ($JDArg - 2451545) / 365250;
// Compute the heliocentric coordinates for time ($t)
$hX = Earth_X0($t) + Earth_X1($t) + Earth_X2($t)
+ Earth_X3($t) + Earth_X4($t) + Earth_X5($t);
$hY = Earth_Y0($t) + Earth_Y1($t) + Earth_Y2($t)
+ Earth_Y3($t) + Earth_Y4($t) + Earth_Y5($t);
$hZ = Earth_Z0($t) + Earth_Z1($t) + Earth_Z2($t)
+ Earth_Z3($t) + Earth_Z4($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 $hR";
}
/*
Earth - VSOP87 Series Version C3 - Rectangular (X,Y,Z) Coordinates
X = X-Coordinate in AU (Astronomical Units)
Y = Y-Coordinate in AU
Z = Z-Coordinate in AU
R*R = (X*X + Y*Y + Z*Z)
HELIOCENTRIC DYNAMICAL ECLIPTIC AND EQUINOX OF THE DATE
PHP Language
VSOP87 Functions Source Code
Generated By NeoProgrammics VSOP87 Code Generator
(c) Jay Tanner 2008
Ref:
Planetary Theories in Rectangular and Spherical Variables
VSOP87 Solutions
Astronomy & Astrophysics
vol. 202, p309-p315
Pierre Bretagnon, Gerard Francou
1988
Source code provided under the provisions of
GNU Affero General Public License, version 3.
http://www.fsf.org/licensing/licenses/agpl-3.0.html
*/
function Earth_X0($t) // 1007 terms of order 0
{
$X0 = 0.99986069925*cos(1.75347045757 + 6283.3196674749*$t);
$X0 += 0.02506324281*cos(4.93819429098 + 0.2438174835*$t);
$X0 += 0.00835274807*cos(1.71033525539 + 12566.3955174663*$t);
$X0 += 0.00010466796*cos(1.66721984219 + 18849.4713674577*$t);
$X0 += 0.00003490608*cos(4.44373803231 + 6282.83203250789*$t);
$X0 += 0.00003110838*cos(0.66875189331 + 83997.09113559539*$t);
$X0 += 0.00002561408*cos(0.58588607490 + 529.9347825781*$t);
$X0 += 0.00002142365*cos(1.09204474884 + 1577.0997249643*$t);
$X0 += 0.00001709161*cos(0.49540863237 + 6279.7965491259*$t);
$X0 += 0.00001707934*cos(6.15314019418 + 6286.84278582391*$t);
$X0 += 0.00001442753*cos(3.47210398336 + 2353.1099712553*$t);
$X0 += 0.00001113027*cos(3.69621650479 + 5223.4501023187*$t);
$X0 += 0.00000934484*cos(6.07385378286 + 12036.7045523717*$t);
$X0 += 0.00000899854*cos(3.17607463681 + 10213.5293636945*$t);
$X0 += 0.00000566820*cos(2.15241946891 + 1059.6257476727*$t);
$X0 += 0.00000661858*cos(1.31175222119 + 5753.6287023803*$t);
$X0 += 0.00000739644*cos(4.36662524112 + 398.3928208917*$t);
$X0 += 0.00000681381*cos(2.21815397940 + 4705.9761250271*$t);
$X0 += 0.00000611293*cos(5.38470180335 + 6813.0106325695*$t);
$X0 += 0.00000451129*cos(6.09315891204 + 5885.1706640667*$t);
$X0 += 0.00000451985*cos(1.27931036318 + 6257.0213476751*$t);
$X0 += 0.00000449743*cos(5.36941929064 + 6309.61798727471*$t);
$X0 += 0.00000406291*cos(0.54369369385 + 6681.46867088311*$t);
$X0 += 0.00000541115*cos(0.78670634299 + 775.7664288075*$t);
$X0 += 0.00000546682*cos(1.46109463961 + 14143.7390599141*$t);
$X0 += 0.00000513780*cos(4.43695037790 + 7860.6632099227*$t);
$X0 += 0.00000263916*cos(5.39551752630 + 5507.7970561509*$t);
$X0 += 0.00000217220*cos(4.51265697015 + 11507.0135872771*$t);
$X0 += 0.00000292146*cos(2.51372357301 + 5507.3094211839*$t);
$X0 += 0.00000227915*cos(1.23940916733 + 7058.8422787989*$t);
$X0 += 0.00000226835*cos(3.27356345008 + 4693.75913722409*$t);
$X0 += 0.00000255833*cos(2.26545070197 + 12168.2465140581*$t);
$X0 += 0.00000256157*cos(1.45478864804 + 710.1768660418*$t);
$X0 += 0.00000178679*cos(2.96645630109 + 796.5418242999*$t);
$X0 += 0.00000178303*cos(0.40472561766 + 6283.25235717211*$t);
$X0 += 0.00000178303*cos(6.24380795499 + 6283.3869777777*$t);
$X0 += 0.00000155471*cos(1.62414733243 + 25132.5472174491*$t);
$X0 += 0.00000155246*cos(1.41969109555 + 5487.0216606585*$t);
$X0 += 0.00000207640*cos(5.85326148962 + 11790.8729061423*$t);
$X0 += 0.00000199988*cos(4.07216830110 + 17790.08943726851*$t);
$X0 += 0.00000128970*cos(5.21698329136 + 7079.61767429131*$t);
$X0 += 0.00000128155*cos(4.80258701251 + 3739.0052475915*$t);
$X0 += 0.00000152241*cos(0.86901699174 + 213.5429129215*$t);
$X0 += 0.00000078109*cos(1.84890519772 + 8827.6340873583*$t);
$X0 += 0.00000073503*cos(2.69517697923 + 1589.3167127673*$t);
$X0 += 0.00000093001*cos(3.93777887053 + 9437.5191174035*$t);
$X0 += 0.00000065526*cos(3.65568333160 + 11770.0975106499*$t);
$X0 += 0.00000063240*cos(2.24124127597 + 6262.5442719825*$t);
$X0 += 0.00000062961*cos(4.40729385308 + 6304.0950629673*$t);
$X0 += 0.00000085870*cos(3.02430778985 + 167284.00540514899*$t);
$X0 += 0.00000083233*cos(6.19780778434 + 3340.8562441833*$t);
$X0 += 0.00000062850*cos(2.03823135444 + 7.3573644843*$t);
$X0 += 0.00000079971*cos(2.49335782552 + 6070.0205720369*$t);
$X0 += 0.00000060043*cos(3.39955163445 + 4137.1542509997*$t);
$X0 += 0.00000075613*cos(4.15948190002 + 6496.6187629129*$t);
$X0 += 0.00000053731*cos(1.56268892040 + 1194.6908277081*$t);
$X0 += 0.00000057574*cos(3.96971590315 + 6284.2999885431*$t);
$X0 += 0.00000057574*cos(2.67881766950 + 6282.3393464067*$t);
$X0 += 0.00000072385*cos(4.85114866885 + 10976.83498721549*$t);
$X0 += 0.00000051135*cos(1.31237333336 + 6290.4332144757*$t);
$X0 += 0.00000050604*cos(5.34520074613 + 6276.2061204741*$t);
$X0 += 0.00000049613*cos(2.64370047145 + 6127.8992680407*$t);
$X0 += 0.00000048009*cos(4.00571885519 + 6438.7400669091*$t);
$X0 += 0.00000059233*cos(3.78322753249 + 3154.4432674121*$t);
$X0 += 0.00000048264*cos(4.77126143981 + 801.5771136403*$t);
$X0 += 0.00000047368*cos(6.10696378485 + 3128.6325825793*$t);
$X0 += 0.00000039225*cos(3.25281924495 + 8429.4850839501*$t);
$X0 += 0.00000051307*cos(5.78448747277 + 12353.0964220283*$t);
$X0 += 0.00000050639*cos(2.05215225623 + 11856.462468908*$t);
$X0 += 0.00000039555*cos(4.93022654622 + 5481.4987363511*$t);
$X0 += 0.00000042757*cos(3.64063452002 + 17260.3984721739*$t);
$X0 += 0.00000048941*cos(0.45355151773 + 9225.7830907665*$t);
$X0 += 0.00000048302*cos(0.60366334071 + 2544.07060239989*$t);
$X0 += 0.00000037971*cos(3.04093006964 + 426.8420083595*$t);
$X0 += 0.00000043643*cos(3.14688065147 + 5856.23384163189*$t);
$X0 += 0.00000031830*cos(2.00885127406 + 2145.92159899169*$t);
$X0 += 0.00000033959*cos(1.72230567102 + 7085.1405985987*$t);
$X0 += 0.00000030184*cos(3.96882361878 + 10977.32262218251*$t);
$X0 += 0.00000032562*cos(2.84647033523 + 4164.0681721295*$t);
$X0 += 0.00000038887*cos(5.36022568355 + 13367.7288136231*$t);
$X0 += 0.00000028515*cos(6.10933021457 + 12569.91863581531*$t);
$X0 += 0.00000028873*cos(1.01228967614 + 3930.4535137031*$t);
$X0 += 0.00000036633*cos(2.90798803424 + 18073.9487561337*$t);
$X0 += 0.00000024984*cos(2.17919076736 + 26.0545023163*$t);
$X0 += 0.00000026364*cos(0.54621601823 + 9438.0067523705*$t);
$X0 += 0.00000030326*cos(1.99372292658 + 4535.3032544079*$t);
$X0 += 0.00000028166*cos(0.48127325062 + 12562.8723991173*$t);
$X0 += 0.00000028001*cos(2.82603231075 + 5088.8726572503*$t);
$X0 += 0.00000021157*cos(5.07256589577 + 11371.9485072417*$t);
$X0 += 0.00000023113*cos(0.85996930170 + 5223.93773728571*$t);
$X0 += 0.00000021642*cos(4.63524157818 + 12559.2819704655*$t);
$X0 += 0.00000019448*cos(4.40136974621 + 12565.9078824993*$t);
$X0 += 0.00000026055*cos(0.30340363466 + 71430.45180064559*$t);
$X0 += 0.00000018232*cos(3.41362095130 + 1747.7725955835*$t);
$X0 += 0.00000023248*cos(6.19009992884 + 18319.7804023631*$t);
$X0 += 0.00000022785*cos(1.16821848960 + 5753.14106741329*$t);
$X0 += 0.00000017091*cos(0.58584172932 + 4933.4522578161*$t);
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$X0 += 0.00000000057*cos(0.02714811761 + 10027.65937824569*$t);
$X0 += 0.00000000060*cos(2.20528431296 + 647.25465079831*$t);
$X0 += 0.00000000072*cos(4.16486482248 + 4597.77991000629*$t);
$X0 += 0.00000000059*cos(3.82312915284 + 6279.30891415889*$t);
$X0 += 0.00000000068*cos(2.71579349818 + 3166.66025521511*$t);
$X0 += 0.00000000056*cos(4.67855976016 + 6226.5164053051*$t);
$X0 += 0.00000000056*cos(1.96997381249 + 6340.12292964471*$t);
$X0 += 0.00000000056*cos(2.52728721608 + 12303.3115940935*$t);
$X0 += 0.00000000057*cos(3.09052199581 + 5864.3952685743*$t);
$X0 += 0.00000000057*cos(3.55801157684 + 6702.2440663755*$t);
$X0 += 0.00000000069*cos(1.90302432953 + 23536.3607751645*$t);
$X0 += 0.00000000059*cos(0.79584524101 + 5760.25461441409*$t);
$X0 += 0.00000000065*cos(0.39208551086 + 12139.30969162329*$t);
$X0 += 0.00000000059*cos(3.38503180730 + 67589.3312645407*$t);
$X0 += 0.00000000073*cos(0.51774809611 + 11079.92776143409*$t);
$X0 += 0.00000000076*cos(2.34882980338 + 23227.0824525087*$t);
$X0 += 0.00000000067*cos(2.11713130342 + 4804.4530934105*$t);
$X0 += 0.00000000073*cos(6.00949211634 + 30349.1275902505*$t);
$X0 += 0.00000000074*cos(4.74855693255 + 92747.9329843061*$t);
$X0 += 0.00000000070*cos(1.56579326622 + 12299.7884757445*$t);
$X0 += 0.00000000060*cos(0.37222072501 + 12171.7696324071*$t);
$X0 += 0.00000000059*cos(2.60537764043 + 15.49628866851*$t);
$X0 += 0.00000000074*cos(5.91207332800 + 3684.1342325067*$t);
$X0 += 0.00000000058*cos(3.15618940951 + 6717.0314053517*$t);
$X0 += 0.00000000053*cos(2.11594966811 + 26087.65932409069*$t);
$X0 += 0.00000000059*cos(1.05069506955 + 12164.7233957091*$t);
$X0 += 0.00000000063*cos(3.66132366701 + 5219.5179490556*$t);
$X0 += 0.00000000056*cos(4.02457482788 + 3178.38960805111*$t);
$X0 += 0.00000000063*cos(0.59069175384 + 5227.38225558179*$t);
$X0 += 0.00000000070*cos(3.26289105386 + 19004.4041319249*$t);
$X0 += 0.00000000072*cos(1.05516042130 + 4583.55281600469*$t);
$X0 += 0.00000000052*cos(5.67763480740 + 3627.2636600341*$t);
$X0 += 0.00000000052*cos(4.87358219235 + 6411.2712005095*$t);
$X0 += 0.00000000052*cos(1.77495138030 + 6155.3681344403*$t);
$X0 += 0.00000000054*cos(3.61747287023 + 5849.6079295981*$t);
$X0 += 0.00000000066*cos(4.36702417592 + 5791.16874004909*$t);
$X0 += 0.00000000066*cos(1.22543152233 + 5791.6563750161*$t);
$X0 += 0.00000000051*cos(0.84172627776 + 5113.2437810993*$t);
$X0 += 0.00000000058*cos(4.29307138428 + 30775.7257811265*$t);
$X0 += 0.00000000061*cos(5.44071514919 + 14169.5497447469*$t);
$X0 += 0.00000000054*cos(4.73181482869 + 10454.74520408871*$t);
$X0 += 0.00000000056*cos(2.77114790322 + 23141.8022004081*$t);
$X0 += 0.00000000067*cos(2.31997560907 + 28313.0449871775*$t);
$X0 += 0.00000000056*cos(1.94933767144 + 5244.2930566845*$t);
$X0 += 0.00000000062*cos(2.18007483018 + 5657.6494751625*$t);
$X0 += 0.00000000062*cos(4.46845874247 + 6908.9898597873*$t);
$X0 += 0.00000000050*cos(1.53914825533 + 2574.99527684569*$t);
$X0 += 0.00000000050*cos(1.32272515661 + 536.5606946119*$t);
$X0 += 0.00000000050*cos(1.95397557344 + 6684.9917892321*$t);
$X0 += 0.00000000050*cos(4.69455799921 + 5881.6475457177*$t);
$X0 += 0.00000000049*cos(5.07674655291 + 16310.73522823709*$t);
$X0 += 0.00000000049*cos(5.07674655291 + 16311.2228632041*$t);
$X0 += 0.00000000065*cos(0.63077087865 + 46386.7499258277*$t);
$X0 += 0.00000000069*cos(3.59016732594 + 60530.2451682583*$t);
$X0 += 0.00000000068*cos(6.19031950148 + 96678.14268052569*$t);
$X0 += 0.00000000049*cos(2.44170258748 + 12323.17927852529*$t);
$X0 += 0.00000000050*cos(3.95175048363 + 21954.4014268815*$t);
$X0 += 0.00000000049*cos(0.26987394090 + 4164.5558070965*$t);
$X0 += 0.00000000059*cos(2.11910349639 + 33794.7875410121*$t);
$X0 += 0.00000000050*cos(3.21674377716 + 43739.0461634493*$t);
$X0 += 0.00000000059*cos(4.28455887932 + 3981.73385156551*$t);
$X0 += 0.00000000058*cos(1.59500717257 + 27707.29867681129*$t);
$X0 += 0.00000000051*cos(3.00541030027 + 7669.21494381111*$t);
$X0 += 0.00000000048*cos(4.80655958998 + 3646.59419483791*$t);
$X0 += 0.00000000065*cos(3.20870046710 + 82534.6474380951*$t);
$X0 += 0.00000000056*cos(4.19440679704 + 800.06494264891*$t);
$X0 += 0.00000000057*cos(0.99121344005 + 11609.61872652869*$t);
$X0 += 0.00000000048*cos(5.23363777755 + 26.5421372833*$t);
$X0 += 0.00000000047*cos(1.10988199958 + 30640.1004561165*$t);
$X0 += 0.00000000060*cos(1.97427905695 + 8982.5668518255*$t);
$X0 += 0.00000000049*cos(3.72444308522 + 96563.24283557819*$t);
$X0 += 0.00000000050*cos(5.17708029533 + 17583.9038888313*$t);
$X0 += 0.00000000046*cos(2.75949485809 + 23539.46356884929*$t);
$X0 += 0.00000000048*cos(2.83397317642 + 170.4290531357*$t);
$X0 += 0.00000000055*cos(4.77764015710 + 735.6326960483*$t);
$X0 += 0.00000000054*cos(4.33153690679 + 6680.98103591609*$t);
$X0 += 0.00000000060*cos(1.72047044215 + 44033.8837720559*$t);
$X0 += 0.00000000064*cos(4.40652103235 + 80181.29364935629*$t);
$X0 += 0.00000000059*cos(5.18038765510 + 24279.3508356971*$t);
$X0 += 0.00000000049*cos(5.16566622453 + 5490.5447790075*$t);
$X0 += 0.00000000058*cos(1.24075349030 + 6490.0204047715*$t);
$X0 += 0.00000000058*cos(5.40778008235 + 6076.6189301783*$t);
$X0 += 0.00000000046*cos(6.06699951300 + 18208.1061251085*$t);
$X0 += 0.00000000045*cos(1.62616739636 + 4480.46004178609*$t);
$X0 += 0.00000000055*cos(3.56883579861 + 16097.9237677661*$t);
$X0 += 0.00000000055*cos(0.42724314502 + 16097.43613279909*$t);
$X0 += 0.00000000061*cos(5.10427594640 + 491.9071099423*$t);
$X0 += 0.00000000054*cos(2.79730041476 + 6006.5738956105*$t);
$X0 += 0.00000000054*cos(3.85123315789 + 6560.0654393393*$t);
$X0 += 0.00000000044*cos(3.20288072834 + 5333.65642353809*$t);
$X0 += 0.00000000052*cos(5.42298629738 + 244287.84382471119*$t);
$X0 += 0.00000000044*cos(1.12093494405 + 2301.34199842589*$t);
$X0 += 0.00000000045*cos(2.78871592108 + 33794.2999060451*$t);
$X0 += 0.00000000046*cos(2.27794751316 + 4384.48081456829*$t);
$X0 += 0.00000000048*cos(6.20709507263 + 35579.9350570535*$t);
$X0 += 0.00000000051*cos(0.20647678216 + 18326.8939493639*$t);
$X0 += 0.00000000045*cos(4.21002666289 + 533.45790092711*$t);
$X0 += 0.00000000046*cos(4.72419290173 + 16703.3059509825*$t);
$X0 += 0.00000000047*cos(0.82323755553 + 5209.2230083171*$t);
$X0 += 0.00000000051*cos(2.88192111957 + 38650.4173236825*$t);
$X0 += 0.00000000046*cos(4.04752097938 + 12555.3498172024*$t);
$X0 += 0.00000000052*cos(6.21526623133 + 5992.3468016089*$t);
$X0 += 0.00000000052*cos(0.43326734132 + 6574.2925333409*$t);
$X0 += 0.00000000044*cos(5.37917268925 + 69942.1974183125*$t);
$X0 += 0.00000000049*cos(5.19212576524 + 12146.9108735911*$t);
$X0 += 0.00000000053*cos(3.10372910020 + 39301.8531447125*$t);
$X0 += 0.00000000045*cos(6.22187415000 + 46360.9392409949*$t);
$X0 += 0.00000000043*cos(3.11607958976 + 8402.0835278533*$t);
$X0 += 0.00000000043*cos(1.76871622593 + 44137.1951668575*$t);
$X0 += 0.00000000049*cos(1.97645700808 + 22029.9691371861*$t);
$X0 += 0.00000000044*cos(3.04557845219 + 31441.92138724031*$t);
$X0 += 0.00000000042*cos(1.28858480303 + 9225.29545579949*$t);
$X0 += 0.00000000045*cos(4.79112566977 + 71519.54096076029*$t);
$X0 += 0.00000000051*cos(4.52703512787 + 7762.1862415393*$t);
$X0 += 0.00000000041*cos(0.43156198612 + 3735.48212924251*$t);
$X0 += 0.00000000057*cos(2.81178684757 + 40398.4337367495*$t);
$X0 += 0.00000000047*cos(4.46091937774 + 4707.9862312257*$t);
$X0 += 0.00000000056*cos(0.65497165024 + 28664.0754677489*$t);
$X0 += 0.00000000050*cos(4.15809563419 + 11919.3846841515*$t);
$X0 += 0.00000000047*cos(0.89798744348 + 316428.47249139856*$t);
$X0 += 0.00000000041*cos(4.27548568888 + 27278.7126339243*$t);
$X0 += 0.00000000056*cos(2.85120735939 + 83659.5206898825*$t);
$X0 += 0.00000000048*cos(2.50261741205 + 12662.3747446841*$t);
$X0 += 0.00000000054*cos(0.83831240155 + 16627.12709789369*$t);
$X0 += 0.00000000052*cos(4.41165168727 + 12571.9184417737*$t);
$X0 += 0.00000000043*cos(4.69793524808 + 7322.34627826531*$t);
$X0 += 0.00000000041*cos(3.56154893542 + 664.99986261351*$t);
$X0 += 0.00000000042*cos(1.54738888492 + 5641.9544251257*$t);
$X0 += 0.00000000044*cos(1.44765859641 + 6425.4982945111*$t);
$X0 += 0.00000000044*cos(5.20087497624 + 6141.1410404387*$t);
$X0 += 0.00000000039*cos(0.38205897719 + 22594.2987131955*$t);
$X0 += 0.00000000040*cos(5.88641926833 + 20894.53186172529*$t);
$X0 += 0.00000000044*cos(5.28307931868 + 5540.3296069423*$t);
$X0 += 0.00000000050*cos(5.69294803866 + 17782.48825530069*$t);
$X0 += 0.00000000054*cos(4.69164296803 + 6006.2846737335*$t);
$X0 += 0.00000000054*cos(1.95689060462 + 6560.3546612163*$t);
$X0 += 0.00000000045*cos(5.54499872381 + 142861.14741877468*$t);
$X0 += 0.00000000047*cos(1.12158335918 + 24499.7634781359*$t);
$X0 += 0.00000000043*cos(1.36615498859 + 7026.3097280075*$t);
$X0 += 0.00000000047*cos(1.95434456607 + 955.8435590921*$t);
$X0 += 0.00000000047*cos(4.50829221159 + 24485.5363841343*$t);
$X0 += 0.00000000040*cos(2.60727518415 + 9388.2497268987*$t);
$X0 += 0.00000000043*cos(5.81439105801 + 6359.5857387505*$t);
$X0 += 0.00000000042*cos(3.96208965107 + 8635.69818627969*$t);
$X0 += 0.00000000051*cos(2.46325624829 + 27831.79440179969*$t);
$X0 += 0.00000000042*cos(1.94770311943 + 6334.60000533731*$t);
$X0 += 0.00000000042*cos(4.70083045322 + 6232.03932961249*$t);
$X0 += 0.00000000052*cos(3.53311914292 + 11905.1625906853*$t);
$X0 += 0.00000000040*cos(1.50948151820 + 7076.0945559423*$t);
$X0 += 0.00000000040*cos(0.29378456988 + 5444.3503797245*$t);
$X0 += 0.00000000040*cos(0.07156369559 + 7122.2889552253*$t);
$X0 += 0.00000000038*cos(2.24525725009 + 44933.4931736739*$t);
$X0 += 0.00000000037*cos(0.27418012894 + 5715.6010297445*$t);
$X0 += 0.00000000037*cos(0.09116813653 + 6851.0383052053*$t);
$X0 += 0.00000000042*cos(0.79913949254 + 36147.6536947839*$t);
$X0 += 0.00000000042*cos(2.85822305358 + 6238.1784478383*$t);
$X0 += 0.00000000042*cos(3.79031051907 + 6328.4608871115*$t);
$X0 += 0.00000000040*cos(3.64347872660 + 3214.8925631597*$t);
$X0 += 0.00000000043*cos(0.65521409425 + 23141.3145654411*$t);
$X0 += 0.00000000041*cos(3.95515629208 + 19804.5834740993*$t);
$X0 += 0.00000000038*cos(2.90982798521 + 20.11150191529*$t);
$X0 += 0.00000000050*cos(1.62788860301 + 84334.66158130829*$t);
$X0 += 0.00000000050*cos(2.84763289309 + 60284.16619777939*$t);
return $X0;
}
function Earth_X1($t) // 600 terms of order 1
{
$X1 = 0.00154550744*cos(0.64605836878 + 0.2438174835*$t);
$X1 += 0.00051503383*cos(6.00263199393 + 12566.3955174663*$t);
$X1 += 0.00001290763*cos(5.95941652859 + 18849.4713674577*$t);
$X1 += 0.00000702576*cos(1.75347943445 + 6283.3196674749*$t);
$X1 += 0.00000430422*cos(2.45216492471 + 6282.83203250789*$t);
$X1 += 0.00000212689*cos(1.73380190045 + 6279.7965491259*$t);
$X1 += 0.00000212524*cos(4.91484799365 + 6286.84278582391*$t);
$X1 += 0.00000062308*cos(0.36193297710 + 4705.9761250271*$t);
$X1 += 0.00000059808*cos(3.81187956678 + 6257.0213476751*$t);
$X1 += 0.00000059474*cos(2.83659652893 + 6309.61798727471*$t);
$X1 += 0.00000048914*cos(5.21332670904 + 775.7664288075*$t);
$X1 += 0.00000042814*cos(0.43864033644 + 1059.6257476727*$t);
$X1 += 0.00000046457*cos(0.01089905463 + 7860.6632099227*$t);
$X1 += 0.00000036653*cos(2.19635713914 + 5753.6287023803*$t);
$X1 += 0.00000035649*cos(1.44752011203 + 5885.1706640667*$t);
$X1 += 0.00000035362*cos(4.47215447256 + 6813.0106325695*$t);
$X1 += 0.00000032151*cos(5.19677261546 + 6681.46867088311*$t);
$X1 += 0.00000028763*cos(5.91618988907 + 25132.5472174491*$t);
$X1 += 0.00000028447*cos(1.14976229491 + 6127.8992680407*$t);
$X1 += 0.00000027537*cos(5.49920443604 + 6438.7400669091*$t);
$X1 += 0.00000024819*cos(2.92230738957 + 5487.0216606585*$t);
$X1 += 0.00000020615*cos(3.71821460067 + 7079.61767429131*$t);
$X1 += 0.00000019621*cos(2.88650825392 + 5507.7970561509*$t);
$X1 += 0.00000018378*cos(1.46521342874 + 11790.8729061423*$t);
$X1 += 0.00000016494*cos(6.21543454587 + 11507.0135872771*$t);
$X1 += 0.00000016756*cos(3.81938434057 + 7058.8422787989*$t);
$X1 += 0.00000014558*cos(5.97530104893 + 6290.4332144757*$t);
$X1 += 0.00000014404*cos(0.68122522191 + 6276.2061204741*$t);
$X1 += 0.00000014052*cos(1.45747121073 + 796.5418242999*$t);
$X1 += 0.00000012261*cos(4.15789187748 + 4693.75913722409*$t);
$X1 += 0.00000012758*cos(0.34831751321 + 7.3573644843*$t);
$X1 += 0.00000010086*cos(3.29242550455 + 3739.0052475915*$t);
$X1 += 0.00000009469*cos(4.63920457850 + 6070.0205720369*$t);
$X1 += 0.00000010425*cos(2.38242547117 + 6284.2999885431*$t);
$X1 += 0.00000010425*cos(4.26610810148 + 6282.3393464067*$t);
$X1 += 0.00000009570*cos(1.89427100067 + 4137.1542509997*$t);
$X1 += 0.00000009044*cos(2.00972967096 + 6496.6187629129*$t);
$X1 += 0.00000008544*cos(0.05731253621 + 1194.6908277081*$t);
$X1 += 0.00000008214*cos(1.25401494002 + 1589.3167127673*$t);
$X1 += 0.00000006157*cos(3.35676469316 + 8827.6340873583*$t);
$X1 += 0.00000006271*cos(4.75475820102 + 8429.4850839501*$t);
$X1 += 0.00000005524*cos(5.36941014190 + 4933.4522578161*$t);
$X1 += 0.00000007314*cos(0.49102526454 + 4535.3032544079*$t);
$X1 += 0.00000005157*cos(5.14965163127 + 11770.0975106499*$t);
$X1 += 0.00000006749*cos(4.32513020462 + 5088.8726572503*$t);
$X1 += 0.00000004853*cos(0.62462823219 + 6040.5910635009*$t);
$X1 += 0.00000005304*cos(5.64244320178 + 3154.4432674121*$t);
$X1 += 0.00000004985*cos(4.62777616911 + 12569.91863581531*$t);
$X1 += 0.00000004709*cos(3.96386608147 + 5331.6012612243*$t);
$X1 += 0.00000004601*cos(6.02376124126 + 6526.04827144891*$t);
$X1 += 0.00000004201*cos(1.28125193997 + 7633.1870771337*$t);
$X1 += 0.00000005607*cos(2.55800509408 + 5729.7502646325*$t);
$X1 += 0.00000004257*cos(4.12450123624 + 3930.4535137031*$t);
$X1 += 0.00000004394*cos(0.04709285339 + 12559.2819704655*$t);
$X1 += 0.00000003870*cos(2.68681123019 + 7235.0380737255*$t);
$X1 += 0.00000005154*cos(6.15930214427 + 8031.3360805419*$t);
$X1 += 0.00000005036*cos(4.09009014859 + 6836.8890703173*$t);
$X1 += 0.00000005076*cos(2.30606090748 + 7477.7666776995*$t);
$X1 += 0.00000003593*cos(2.40570544354 + 12565.9078824993*$t);
$X1 += 0.00000003384*cos(5.40354177904 + 10977.32262218251*$t);
$X1 += 0.00000003371*cos(0.28961103245 + 11371.9485072417*$t);
$X1 += 0.00000003536*cos(3.73353119602 + 4164.0681721295*$t);
$X1 += 0.00000004292*cos(4.93786086114 + 1592.8398311163*$t);
$X1 += 0.00000003407*cos(2.40599273330 + 3128.6325825793*$t);
$X1 += 0.00000003152*cos(1.73356525688 + 5223.93773728571*$t);
$X1 += 0.00000002883*cos(4.92077247219 + 1747.7725955835*$t);
$X1 += 0.00000002751*cos(5.24449444697 + 7342.7015976641*$t);
$X1 += 0.00000003323*cos(1.91880015934 + 801.5771136403*$t);
$X1 += 0.00000002999*cos(2.25355241223 + 8636.18582124671*$t);
$X1 += 0.00000002496*cos(3.52078273708 + 2145.92159899169*$t);
$X1 += 0.00000003358*cos(4.25271343539 + 155.17658195069*$t);
$X1 += 0.00000002297*cos(4.53559364224 + 17260.3984721739*$t);
$X1 += 0.00000002047*cos(3.53660263792 + 1990.9888345245*$t);
$X1 += 0.00000002778*cos(1.46152428305 + 5481.4987363511*$t);
$X1 += 0.00000002025*cos(1.44003078455 + 951.4745887671*$t);
$X1 += 0.00000002663*cos(5.71398175957 + 26.0545023163*$t);
$X1 += 0.00000002009*cos(5.73390835065 + 4690.7236538421*$t);
$X1 += 0.00000002148*cos(1.89688144273 + 537.0483295789*$t);
$X1 += 0.00000001853*cos(2.84762029989 + 553.32558535889*$t);
$X1 += 0.00000002478*cos(0.03933370984 + 1349.62359217529*$t);
$X1 += 0.00000002023*cos(2.39095052485 + 522.8212355773*$t);
$X1 += 0.00000001735*cos(2.91944410412 + 529.44714761109*$t);
$X1 += 0.00000002417*cos(5.16772880951 + 7085.1405985987*$t);
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$X1 += 0.00000000020*cos(2.07630932980 + 34115.3578867581*$t);
$X1 += 0.00000000020*cos(1.72148703277 + 21548.7185518083*$t);
$X1 += 0.00000000020*cos(3.68576430300 + 17654.5367222661*$t);
$X1 += 0.00000000025*cos(3.53209868087 + 55798.7021758819*$t);
$X1 += 0.00000000020*cos(0.81961551511 + 20597.4877805247*$t);
$X1 += 0.00000000020*cos(2.60684350676 + 18875.76968725751*$t);
$X1 += 0.00000000022*cos(0.44774356245 + 1588.82907780029*$t);
$X1 += 0.00000000024*cos(1.20852424503 + 9411.7084325707*$t);
$X1 += 0.00000000019*cos(5.85945140949 + 536.5606946119*$t);
$X1 += 0.00000000020*cos(4.99560905506 + 6187.3404402571*$t);
$X1 += 0.00000000020*cos(1.65292451759 + 6379.2988946927*$t);
$X1 += 0.00000000022*cos(4.44471803531 + 18326.8939493639*$t);
$X1 += 0.00000000022*cos(2.18348213630 + 6233.5626420031*$t);
$X1 += 0.00000000022*cos(4.46505143635 + 6333.0766929467*$t);
$X1 += 0.00000000018*cos(2.03036294822 + 5972.4788686065*$t);
$X1 += 0.00000000018*cos(4.61817062443 + 6594.1604663433*$t);
$X1 += 0.00000000019*cos(4.28397604583 + 6948.0757126049*$t);
$X1 += 0.00000000019*cos(2.36455752682 + 5618.5636223449*$t);
$X1 += 0.00000000019*cos(0.18461366541 + 83974.07917321339*$t);
$X1 += 0.00000000019*cos(4.29574443999 + 84020.10309797739*$t);
$X1 += 0.00000000020*cos(3.84957027230 + 50316.9596220473*$t);
$X1 += 0.00000000020*cos(2.85391796921 + 9070.3626913323*$t);
return $X1*$t;
}
function Earth_X2($t) // 248 terms of order 2
{
$X2 = 0.00052911498*cos(3.32403354915 + 6283.3196674749*$t);
$X2 += 0.00006074441*cos(2.05485843872 + 0.2438174835*$t);
$X2 += 0.00002406871*cos(4.23086027149 + 12566.3955174663*$t);
$X2 += 0.00000096033*cos(4.14485769516 + 18849.4713674577*$t);
$X2 += 0.00000029888*cos(0.73436192593 + 6282.83203250789*$t);
$X2 += 0.00000014021*cos(3.21121684298 + 6279.7965491259*$t);
$X2 += 0.00000013375*cos(3.31400005464 + 6286.84278582391*$t);
$X2 += 0.00000008148*cos(2.19949162987 + 6309.61798727471*$t);
$X2 += 0.00000008195*cos(4.38954108022 + 6257.0213476751*$t);
$X2 += 0.00000008001*cos(5.91956929382 + 6127.8992680407*$t);
$X2 += 0.00000007754*cos(0.72231700953 + 6438.7400669091*$t);
$X2 += 0.00000007223*cos(5.38114271434 + 83997.09113559539*$t);
$X2 += 0.00000004616*cos(6.16703227370 + 710.1768660418*$t);
$X2 += 0.00000003060*cos(4.83964573312 + 4705.9761250271*$t);
$X2 += 0.00000003717*cos(2.45040909403 + 5507.7970561509*$t);
$X2 += 0.00000002991*cos(4.05993241608 + 25132.5472174491*$t);
$X2 += 0.00000003235*cos(4.10584554352 + 7058.8422787989*$t);
$X2 += 0.00000002393*cos(3.40776365917 + 775.7664288075*$t);
$X2 += 0.00000002034*cos(4.34141229883 + 6290.4332144757*$t);
$X2 += 0.00000002028*cos(2.28023581144 + 6276.2061204741*$t);
$X2 += 0.00000002064*cos(1.58527926677 + 7860.6632099227*$t);
$X2 += 0.00000001914*cos(4.42314112548 + 5487.0216606585*$t);
$X2 += 0.00000001770*cos(5.05862783743 + 1059.6257476727*$t);
$X2 += 0.00000001761*cos(3.37902852940 + 5753.6287023803*$t);
$X2 += 0.00000001558*cos(2.13660228192 + 7079.61767429131*$t);
$X2 += 0.00000001551*cos(2.12932375831 + 6040.5910635009*$t);
$X2 += 0.00000001436*cos(2.85243683562 + 5885.1706640667*$t);
$X2 += 0.00000001469*cos(4.51404554645 + 6526.04827144891*$t);
$X2 += 0.00000001319*cos(3.46234944603 + 6681.46867088311*$t);
$X2 += 0.00000001180*cos(2.99170595830 + 6813.0106325695*$t);
$X2 += 0.00000001337*cos(1.03982518814 + 5729.7502646325*$t);
$X2 += 0.00000001039*cos(5.82323058792 + 6282.3393464067*$t);
$X2 += 0.00000001313*cos(2.16977183919 + 529.9347825781*$t);
$X2 += 0.00000001041*cos(0.76562479642 + 6284.2999885431*$t);
$X2 += 0.00000001202*cos(5.59909179750 + 6836.8890703173*$t);
$X2 += 0.00000000904*cos(2.42848578586 + 5331.6012612243*$t);
$X2 += 0.00000000870*cos(3.83740101245 + 4933.4522578161*$t);
$X2 += 0.00000001149*cos(4.59530313333 + 167284.00540514899*$t);
$X2 += 0.00000001069*cos(5.80442130983 + 1577.0997249643*$t);
$X2 += 0.00000000772*cos(4.23369730112 + 7235.0380737255*$t);
$X2 += 0.00000000846*cos(2.93878609085 + 11790.8729061423*$t);
$X2 += 0.00000000742*cos(0.30768536261 + 4137.1542509997*$t);
$X2 += 0.00000000966*cos(3.62307276164 + 11856.462468908*$t);
$X2 += 0.00000000664*cos(2.78855764568 + 7633.1870771337*$t);
$X2 += 0.00000000662*cos(4.76048207091 + 1194.6908277081*$t);
$X2 += 0.00000000659*cos(1.23774551244 + 11507.0135872771*$t);
$X2 += 0.00000000853*cos(5.22418483353 + 4535.3032544079*$t);
$X2 += 0.00000000823*cos(5.77365627974 + 155.17658195069*$t);
$X2 += 0.00000000783*cos(5.87375907691 + 5088.8726572503*$t);
$X2 += 0.00000000785*cos(5.03738396313 + 2353.1099712553*$t);
$X2 += 0.00000000694*cos(1.93706172082 + 801.5771136403*$t);
$X2 += 0.00000000566*cos(6.00002295544 + 796.5418242999*$t);
$X2 += 0.00000000684*cos(2.68347359202 + 3128.6325825793*$t);
$X2 += 0.00000000499*cos(2.99674498554 + 12569.91863581531*$t);
$X2 += 0.00000000596*cos(1.38539217884 + 8031.3360805419*$t);
$X2 += 0.00000000486*cos(6.11316978391 + 1589.3167127673*$t);
$X2 += 0.00000000483*cos(6.25283705744 + 8429.4850839501*$t);
$X2 += 0.00000000441*cos(0.27873568624 + 6496.6187629129*$t);
$X2 += 0.00000000412*cos(5.58840963851 + 4693.75913722409*$t);
$X2 += 0.00000000561*cos(0.75091675093 + 7477.7666776995*$t);
$X2 += 0.00000000390*cos(6.20968064366 + 6070.0205720369*$t);
$X2 += 0.00000000405*cos(1.55299195368 + 3739.0052475915*$t);
$X2 += 0.00000000501*cos(3.39229516665 + 1592.8398311163*$t);
$X2 += 0.00000000392*cos(5.39455294636 + 26.0545023163*$t);
$X2 += 0.00000000369*cos(4.36331143713 + 553.32558535889*$t);
$X2 += 0.00000000483*cos(1.36538995021 + 12036.7045523717*$t);
$X2 += 0.00000000489*cos(2.13588971106 + 5223.4501023187*$t);
$X2 += 0.00000000481*cos(4.74275484789 + 10213.5293636945*$t);
$X2 += 0.00000000448*cos(0.85608336591 + 156137.71980228279*$t);
$X2 += 0.00000000321*cos(2.96911879180 + 951.4745887671*$t);
$X2 += 0.00000000320*cos(2.00218171333 + 1990.9888345245*$t);
$X2 += 0.00000000361*cos(0.59519501420 + 12565.9078824993*$t);
$X2 += 0.00000000361*cos(0.08584353459 + 12721.8159169005*$t);
$X2 += 0.00000000412*cos(5.91338851626 + 398.3928208917*$t);
$X2 += 0.00000000304*cos(0.96839213314 + 4690.7236538421*$t);
$X2 += 0.00000000356*cos(1.28855678128 + 5481.4987363511*$t);
$X2 += 0.00000000283*cos(2.23992178340 + 242.97242145751*$t);
$X2 += 0.00000000362*cos(3.88633843420 + 9438.0067523705*$t);
$X2 += 0.00000000248*cos(4.75322854174 + 8827.6340873583*$t);
$X2 += 0.00000000252*cos(1.16164987849 + 3154.4432674121*$t);
$X2 += 0.00000000257*cos(1.79452152688 + 11371.9485072417*$t);
$X2 += 0.00000000327*cos(3.02081233401 + 14143.7390599141*$t);
$X2 += 0.00000000230*cos(0.23367695814 + 1747.7725955835*$t);
$X2 += 0.00000000289*cos(5.24697142787 + 7085.1405985987*$t);
$X2 += 0.00000000297*cos(1.59965866765 + 1349.62359217529*$t);
$X2 += 0.00000000209*cos(0.27341674720 + 11770.0975106499*$t);
$X2 += 0.00000000207*cos(4.92862210539 + 4164.0681721295*$t);
$X2 += 0.00000000188*cos(5.64673454004 + 7875.91568110771*$t);
$X2 += 0.00000000189*cos(0.60545229996 + 2389.1378379327*$t);
$X2 += 0.00000000194*cos(0.41046959310 + 10977.32262218251*$t);
$X2 += 0.00000000176*cos(4.08570919572 + 7342.7015976641*$t);
$X2 += 0.00000000164*cos(2.79150408226 + 5223.93773728571*$t);
$X2 += 0.00000000205*cos(3.21370431881 + 10973.7995038335*$t);
$X2 += 0.00000000205*cos(2.25101785528 + 13368.2164485901*$t);
$X2 += 0.00000000139*cos(4.61869477858 + 10575.6505004253*$t);
$X2 += 0.00000000155*cos(5.81412821499 + 12410.9751180321*$t);
$X2 += 0.00000000152*cos(0.10500467147 + 3930.4535137031*$t);
$X2 += 0.00000000129*cos(5.52193535090 + 397.9051859247*$t);
$X2 += 0.00000000127*cos(0.96654930095 + 12592.6938372661*$t);
$X2 += 0.00000000132*cos(0.16052766322 + 8636.18582124671*$t);
$X2 += 0.00000000122*cos(4.78358483655 + 13119.9649203087*$t);
$X2 += 0.00000000163*cos(0.93280092706 + 5507.3094211839*$t);
$X2 += 0.00000000114*cos(5.70431693679 + 17260.3984721739*$t);
$X2 += 0.00000000118*cos(2.37854817453 + 4292.5746504339*$t);
$X2 += 0.00000000148*cos(5.63695738547 + 17790.08943726851*$t);
$X2 += 0.00000000123*cos(3.75785910050 + 12562.8723991173*$t);
$X2 += 0.00000000103*cos(3.36994741884 + 13518.1139237169*$t);
$X2 += 0.00000000138*cos(3.83865460083 + 12168.2465140581*$t);
$X2 += 0.00000000107*cos(4.33977826153 + 10989.0519750185*$t);
$X2 += 0.00000000104*cos(5.27997888785 + 2145.92159899169*$t);
$X2 += 0.00000000096*cos(1.97792917854 + 6283.25235717211*$t);
$X2 += 0.00000000099*cos(2.27831564394 + 13096.0864825609*$t);
$X2 += 0.00000000096*cos(1.53382620869 + 6283.3869777777*$t);
$X2 += 0.00000000084*cos(5.20596620689 + 16730.70750707931*$t);
$X2 += 0.00000000111*cos(3.96322491245 + 12540.0971976665*$t);
$X2 += 0.00000000087*cos(6.02515097465 + 10177.5014970171*$t);
$X2 += 0.00000000078*cos(4.18422621711 + 12323.6669134923*$t);
$X2 += 0.00000000076*cos(5.70862044549 + 6709.91785835091*$t);
$X2 += 0.00000000105*cos(3.53845405180 + 5642.4420600927*$t);
$X2 += 0.00000000073*cos(0.89693480363 + 5856.7214765989*$t);
$X2 += 0.00000000102*cos(0.66758153957 + 250570.91967470259*$t);
$X2 += 0.00000000070*cos(5.22505818809 + 5753.14106741329*$t);
$X2 += 0.00000000071*cos(0.56166089035 + 14314.4119305333*$t);
$X2 += 0.00000000092*cos(1.96485842296 + 13916.2629271251*$t);
$X2 += 0.00000000070*cos(2.53450052921 + 7084.6529636317*$t);
$X2 += 0.00000000091*cos(3.10960565577 + 6924.1972748571*$t);
$X2 += 0.00000000083*cos(3.98989749432 + 31415.6230674405*$t);
$X2 += 0.00000000088*cos(5.01539409795 + 71430.45180064559*$t);
$X2 += 0.00000000074*cos(1.96538390591 + 529.44714761109*$t);
$X2 += 0.00000000085*cos(5.97852929798 + 95143.37673846159*$t);
$X2 += 0.00000000061*cos(4.23114381660 + 8274.0646845159*$t);
$X2 += 0.00000000060*cos(5.52155170015 + 16496.6052136859*$t);
$X2 += 0.00000000058*cos(1.47891111226 + 5642.93474619389*$t);
$X2 += 0.00000000078*cos(2.41141378465 + 213.5429129215*$t);
$X2 += 0.00000000059*cos(4.67526538731 + 640.1411037975*$t);
$X2 += 0.00000000057*cos(2.06129454632 + 4690.23601887509*$t);
$X2 += 0.00000000056*cos(3.80170948025 + 13341.9181287903*$t);
$X2 += 0.00000000065*cos(3.38872777921 + 4731.7868098599*$t);
$X2 += 0.00000000051*cos(4.81168622601 + 3893.93801205869*$t);
$X2 += 0.00000000050*cos(4.17369676080 + 12573.5090644671*$t);
$X2 += 0.00000000050*cos(4.41669813786 + 3634.37720703489*$t);
$X2 += 0.00000000049*cos(2.27712508812 + 18319.7804023631*$t);
$X2 += 0.00000000066*cos(5.49585584500 + 2787.2868413409*$t);
$X2 += 0.00000000049*cos(1.99905022377 + 13362.6935242827*$t);
$X2 += 0.00000000048*cos(3.76233131596 + 12964.5445208745*$t);
$X2 += 0.00000000053*cos(4.12374270394 + 14919.2616712381*$t);
$X2 += 0.00000000058*cos(1.23083144160 + 1577.5873599313*$t);
$X2 += 0.00000000052*cos(1.27828874996 + 15721.0826023619*$t);
$X2 += 0.00000000061*cos(3.42876383277 + 4292.0870154669*$t);
$X2 += 0.00000000044*cos(0.31046230867 + 24073.1652872599*$t);
$X2 += 0.00000000044*cos(0.38954461131 + 10447.14402212089*$t);
$X2 += 0.00000000042*cos(4.09986255075 + 20426.8149099055*$t);
$X2 += 0.00000000059*cos(1.01599200374 + 84672.23202702119*$t);
$X2 += 0.00000000051*cos(5.38279738858 + 6370.62787201471*$t);
$X2 += 0.00000000051*cos(1.26573618407 + 6196.0114629351*$t);
$X2 += 0.00000000046*cos(0.52171400874 + 2119.00767786191*$t);
$X2 += 0.00000000041*cos(4.09327874029 + 3185.43584474911*$t);
$X2 += 0.00000000056*cos(3.27189314076 + 10976.83498721549*$t);
$X2 += 0.00000000051*cos(2.37524851068 + 9437.5191174035*$t);
$X2 += 0.00000000049*cos(3.21159567950 + 239424.63407183639*$t);
$X2 += 0.00000000036*cos(6.20393463674 + 3495.78900865049*$t);
$X2 += 0.00000000044*cos(3.69396549327 + 18139.5383188994*$t);
$X2 += 0.00000000035*cos(3.61386877088 + 3929.96587873609*$t);
$X2 += 0.00000000044*cos(1.66014811397 + 8661.9965060795*$t);
$X2 += 0.00000000046*cos(3.78615165617 + 3894.4256470257*$t);
$X2 += 0.00000000034*cos(3.81444510796 + 6262.5442719825*$t);
$X2 += 0.00000000034*cos(5.98049768477 + 6304.0950629673*$t);
$X2 += 0.00000000035*cos(3.58408872678 + 18875.2820522905*$t);
$X2 += 0.00000000035*cos(6.09075949155 + 10420.23010099111*$t);
$X2 += 0.00000000032*cos(0.62535692558 + 23013.7833570707*$t);
$X2 += 0.00000000034*cos(3.61147349841 + 7.3573644843*$t);
$X2 += 0.00000000045*cos(1.48783646485 + 3340.8562441833*$t);
$X2 += 0.00000000035*cos(0.38590076970 + 10213.0417287275*$t);
$X2 += 0.00000000031*cos(5.38472872675 + 14712.5609339415*$t);
$X2 += 0.00000000030*cos(4.39715700541 + 12809.12412144031*$t);
$X2 += 0.00000000039*cos(1.14782571257 + 9779.3524936089*$t);
$X2 += 0.00000000041*cos(5.61324415849 + 82576.73740351178*$t);
$X2 += 0.00000000031*cos(0.76672410297 + 22779.6810636773*$t);
$X2 += 0.00000000028*cos(4.07975589699 + 2942.7072407751*$t);
$X2 += 0.00000000028*cos(2.36060849192 + 5429.63565075589*$t);
$X2 += 0.00000000027*cos(4.04275590321 + 11014.8626598513*$t);
$X2 += 0.00000000027*cos(2.11023646997 + 9623.9320941747*$t);
$X2 += 0.00000000025*cos(1.72579553961 + 18209.5740811437*$t);
$X2 += 0.00000000026*cos(2.55064187749 + 9381.2034902007*$t);
$X2 += 0.00000000025*cos(2.68812943588 + 3583.5848481573*$t);
$X2 += 0.00000000030*cos(5.98905764002 + 10447.6316570879*$t);
$X2 += 0.00000000032*cos(4.08880306095 + 796.0541893329*$t);
$X2 += 0.00000000023*cos(6.09814489767 + 9917.45305702629*$t);
$X2 += 0.00000000026*cos(0.90493478768 + 12012.8261146239*$t);
$X2 += 0.00000000024*cos(1.88327707702 + 14143.2514249471*$t);
$X2 += 0.00000000023*cos(2.26727226510 + 26709.8907598969*$t);
$X2 += 0.00000000021*cos(3.86895197800 + 7632.6994421667*$t);
$X2 += 0.00000000021*cos(2.37138453193 + 17256.8753538249*$t);
$X2 += 0.00000000028*cos(1.07450535792 + 12353.0964220283*$t);
$X2 += 0.00000000022*cos(4.83463880427 + 77714.01528560399*$t);
$X2 += 0.00000000021*cos(5.98744320172 + 6993.2527160332*$t);
$X2 += 0.00000000020*cos(0.31265663265 + 6836.40143535029*$t);
$X2 += 0.00000000020*cos(5.44332565028 + 1748.2602305505*$t);
$X2 += 0.00000000026*cos(2.02675372626 + 9225.7830907665*$t);
$X2 += 0.00000000023*cos(0.80832702606 + 149854.64395229139*$t);
$X2 += 0.00000000026*cos(5.31358634432 + 2544.07060239989*$t);
$X2 += 0.00000000018*cos(2.28255799994 + 11614.6771112157*$t);
$X2 += 0.00000000020*cos(4.61413285151 + 426.8420083595*$t);
$X2 += 0.00000000019*cos(3.66100662326 + 30640.1004561165*$t);
$X2 += 0.00000000018*cos(4.77794649120 + 155.6642169177*$t);
$X2 += 0.00000000018*cos(1.89582517195 + 11926.4982311523*$t);
$X2 += 0.00000000022*cos(3.74943338657 + 17298.4261448097*$t);
$X2 += 0.00000000019*cos(3.25511318252 + 18073.46112116669*$t);
$X2 += 0.00000000020*cos(2.60030261119 + 19651.2922985815*$t);
$X2 += 0.00000000024*cos(1.57388276311 + 5856.23384163189*$t);
$X2 += 0.00000000023*cos(4.78368329384 + 72850.80553272919*$t);
$X2 += 0.00000000017*cos(3.95703430839 + 8983.0544867925*$t);
$X2 += 0.00000000016*cos(5.17069195690 + 16460.5773470085*$t);
$X2 += 0.00000000016*cos(1.20099644560 + 17259.91083720689*$t);
$X2 += 0.00000000021*cos(3.77366558760 + 16858.7263504167*$t);
$X2 += 0.00000000020*cos(0.39427566601 + 23543.4743221653*$t);
$X2 += 0.00000000021*cos(3.79445696120 + 13367.7288136231*$t);
$X2 += 0.00000000020*cos(4.04662298246 + 2146.4092339587*$t);
$X2 += 0.00000000014*cos(0.14269366851 + 22484.0923919761*$t);
$X2 += 0.00000000014*cos(4.66600220934 + 16200.52890701769*$t);
$X2 += 0.00000000015*cos(4.21847977142 + 20199.3387771165*$t);
$X2 += 0.00000000019*cos(2.81420484440 + 8672.21368792411*$t);
$X2 += 0.00000000019*cos(4.46915157584 + 18073.9487561337*$t);
$X2 += 0.00000000013*cos(4.71429939378 + 16201.0165419847*$t);
$X2 += 0.00000000017*cos(1.38925168648 + 7860.17557495569*$t);
$X2 += 0.00000000013*cos(4.69427401677 + 18451.3223640495*$t);
$X2 += 0.00000000016*cos(3.33196861521 + 5572.8989839496*$t);
$X2 += 0.00000000012*cos(2.70989366066 + 17996.2749857057*$t);
$X2 += 0.00000000012*cos(0.72221452149 + 19403.0407703001*$t);
$X2 += 0.00000000012*cos(5.53894834507 + 14945.0723560709*$t);
$X2 += 0.00000000015*cos(2.04879024946 + 12559.2819704655*$t);
$X2 += 0.00000000012*cos(4.37879205675 + 10818.3791043993*$t);
$X2 += 0.00000000015*cos(0.57625721169 + 12567.37583853451*$t);
$X2 += 0.00000000011*cos(1.78471307843 + 28767.1682419675*$t);
$X2 += 0.00000000013*cos(1.09547571668 + 90280.16698558679*$t);
$X2 += 0.00000000011*cos(5.02230424673 + 22805.4917485101*$t);
$X2 += 0.00000000011*cos(2.24605985689 + 35372.1310834599*$t);
$X2 += 0.00000000010*cos(6.26009139838 + 11506.52595231009*$t);
$X2 += 0.00000000014*cos(1.93802583909 + 21228.63584102931*$t);
$X2 += 0.00000000010*cos(0.13064402023 + 12779.6946129043*$t);
$X2 += 0.00000000010*cos(6.05309072952 + 23141.8022004081*$t);
$X2 += 0.00000000010*cos(1.18002886182 + 1350.1112271423*$t);
$X2 += 0.00000000010*cos(2.50762435685 + 10575.1628654583*$t);
$X2 += 0.00000000010*cos(2.55643759758 + 22345.5041935917*$t);
$X2 += 0.00000000010*cos(5.33273079625 + 9778.8648586419*$t);
$X2 += 0.00000000009*cos(1.49151911226 + 29826.5501721567*$t);
$X2 += 0.00000000010*cos(4.24000912367 + 23581.5019948011*$t);
$X2 += 0.00000000011*cos(0.39610887139 + 25158.8455372489*$t);
return $X2*$t*$t;
}
function Earth_X3($t) // 46 terms of order 3
{
$X3 = 0.00000232790*cos(3.40634928966 + 0.2438174835*$t);
$X3 += 0.00000076843*cos(2.52439403387 + 12566.3955174663*$t);
$X3 += 0.00000035331*cos(3.34616699853 + 6283.3196674749*$t);
$X3 += 0.00000005282*cos(2.40489818589 + 18849.4713674577*$t);
$X3 += 0.00000001631*cos(5.43859760597 + 6282.83203250789*$t);
$X3 += 0.00000001483*cos(2.22678849266 + 6438.7400669091*$t);
$X3 += 0.00000001479*cos(4.40151760084 + 6127.8992680407*$t);
$X3 += 0.00000000652*cos(4.70876083993 + 6279.7965491259*$t);
$X3 += 0.00000000656*cos(1.58695055624 + 6286.84278582391*$t);
$X3 += 0.00000000317*cos(3.00237328519 + 6526.04827144891*$t);
$X3 += 0.00000000318*cos(3.63024148359 + 6040.5910635009*$t);
$X3 += 0.00000000227*cos(2.27961613476 + 25132.5472174491*$t);
$X3 += 0.00000000201*cos(0.81376672334 + 6836.8890703173*$t);
$X3 += 0.00000000201*cos(5.80642900510 + 5729.7502646325*$t);
$X3 += 0.00000000036*cos(1.33765000112 + 12569.91863581531*$t);
$X3 += 0.00000000034*cos(1.93992455025 + 4705.9761250271*$t);
$X3 += 0.00000000033*cos(4.22745351005 + 12410.9751180321*$t);
$X3 += 0.00000000032*cos(5.38348719867 + 6257.0213476751*$t);
$X3 += 0.00000000032*cos(4.41212819179 + 6309.61798727471*$t);
$X3 += 0.00000000026*cos(0.50334838608 + 775.7664288075*$t);
$X3 += 0.00000000023*cos(2.01776542272 + 1059.6257476727*$t);
$X3 += 0.00000000025*cos(1.58405990040 + 7860.6632099227*$t);
$X3 += 0.00000000027*cos(5.17969059866 + 12565.9078824993*$t);
$X3 += 0.00000000020*cos(3.76292921295 + 5753.6287023803*$t);
$X3 += 0.00000000019*cos(3.01515389134 + 5885.1706640667*$t);
$X3 += 0.00000000019*cos(6.05056350877 + 6813.0106325695*$t);
$X3 += 0.00000000018*cos(2.29290644779 + 12721.8159169005*$t);
$X3 += 0.00000000017*cos(0.49235818139 + 6681.46867088311*$t);
$X3 += 0.00000000013*cos(4.49557806784 + 5487.0216606585*$t);
$X3 += 0.00000000011*cos(5.29141894629 + 7079.61767429131*$t);
$X3 += 0.00000000010*cos(4.46246654504 + 5507.7970561509*$t);
$X3 += 0.00000000010*cos(3.03842434664 + 11790.8729061423*$t);
$X3 += 0.00000000009*cos(1.50545167256 + 11507.0135872771*$t);
$X3 += 0.00000000011*cos(6.25880735981 + 12592.6938372661*$t);
$X3 += 0.00000000009*cos(5.39258795934 + 7058.8422787989*$t);
$X3 += 0.00000000008*cos(1.26531983919 + 6290.4332144757*$t);
$X3 += 0.00000000008*cos(2.25393064493 + 6276.2061204741*$t);
$X3 += 0.00000000008*cos(3.03070423945 + 796.5418242999*$t);
$X3 += 0.00000000007*cos(2.58386169059 + 4693.75913722409*$t);
$X3 += 0.00000000007*cos(1.92157668691 + 7.3573644843*$t);
$X3 += 0.00000000005*cos(4.86563371701 + 3739.0052475915*$t);
$X3 += 0.00000000005*cos(6.21240311845 + 6070.0205720369*$t);
$X3 += 0.00000000006*cos(3.95562930301 + 6284.2999885431*$t);
$X3 += 0.00000000006*cos(5.83931193332 + 6282.3393464067*$t);
$X3 += 0.00000000005*cos(3.46747665337 + 4137.1542509997*$t);
$X3 += 0.00000000005*cos(3.58293336989 + 6496.6187629129*$t);
return $X3*$t*$t*$t;
}
function Earth_X4($t) // 20 terms of order 4
{
$X4 = 0.00000114918*cos(0.06053023506 + 6283.3196674749*$t);
$X4 += 0.00000006817*cos(4.47624663983 + 0.2438174835*$t);
$X4 += 0.00000003158*cos(0.47910545815 + 12566.3955174663*$t);
$X4 += 0.00000000211*cos(3.72351646714 + 6438.7400669091*$t);
$X4 += 0.00000000210*cos(2.88489921647 + 6127.8992680407*$t);
$X4 += 0.00000000253*cos(0.64665875683 + 18849.4713674577*$t);
$X4 += 0.00000000073*cos(3.92376796583 + 6282.83203250789*$t);
$X4 += 0.00000000042*cos(4.60322795936 + 710.1768660418*$t);
$X4 += 0.00000000023*cos(6.04513529243 + 6279.7965491259*$t);
$X4 += 0.00000000022*cos(6.04140763882 + 6286.84278582391*$t);
$X4 += 0.00000000012*cos(0.51640078868 + 25132.5472174491*$t);
$X4 += 0.00000000009*cos(4.21008055560 + 83997.09113559539*$t);
$X4 += 0.00000000009*cos(5.19392488383 + 11856.462468908*$t);
$X4 += 0.00000000008*cos(6.16587249238 + 167284.00540514899*$t);
$X4 += 0.00000000005*cos(5.97913996910 + 6257.0213476751*$t);
$X4 += 0.00000000005*cos(3.78878463461 + 6309.61798727471*$t);
$X4 += 0.00000000005*cos(2.68915538708 + 12410.9751180321*$t);
$X4 += 0.00000000005*cos(5.56850457487 + 156137.71980228279*$t);
$X4 += 0.00000000004*cos(3.40118346072 + 12565.9078824993*$t);
$X4 += 0.00000000003*cos(5.17221494066 + 529.9347825781*$t);
return $X4*$t*$t*$t*$t;
}
function Earth_X5($t) // 7 terms of order 5
{
$X5 = 0.00000000877*cos(0.16136296068 + 6283.3196674749*$t);
$X5 += 0.00000000305*cos(5.62973274927 + 0.2438174835*$t);
$X5 += 0.00000000101*cos(4.88076699149 + 12566.3955174663*$t);
$X5 += 0.00000000025*cos(5.30593958386 + 6438.7400669091*$t);
$X5 += 0.00000000025*cos(1.27879113841 + 6127.8992680407*$t);
$X5 += 0.00000000010*cos(5.11399286577 + 18849.4713674577*$t);
$X5 += 0.00000000003*cos(2.56205735968 + 6282.83203250789*$t);
return $X5*$t*$t*$t*$t*$t;
}
function Earth_Y0($t) // 1007 terms of order 0
{
$Y0 = 0.99986069925*cos(0.18267413078 + 6283.3196674749*$t);
$Y0 += 0.02506324281*cos(3.36739796418 + 0.2438174835*$t);
$Y0 += 0.00835274807*cos(0.13953892859 + 12566.3955174663*$t);
$Y0 += 0.00010466796*cos(0.09642351540 + 18849.4713674577*$t);
$Y0 += 0.00003490608*cos(6.01453435910 + 6282.83203250789*$t);
$Y0 += 0.00003110838*cos(5.38114087369 + 83997.09113559539*$t);
$Y0 += 0.00002561408*cos(5.29827505528 + 529.9347825781*$t);
$Y0 += 0.00002142365*cos(2.66284107563 + 1577.0997249643*$t);
$Y0 += 0.00001709161*cos(5.20779761275 + 6279.7965491259*$t);
$Y0 += 0.00001707934*cos(4.58234386738 + 6286.84278582391*$t);
$Y0 += 0.00001442753*cos(1.90130765657 + 2353.1099712553*$t);
$Y0 += 0.00001113027*cos(5.26701283158 + 5223.4501023187*$t);
$Y0 += 0.00000934484*cos(4.50305745607 + 12036.7045523717*$t);
$Y0 += 0.00000899854*cos(1.60527831001 + 10213.5293636945*$t);
$Y0 += 0.00000566820*cos(0.58162314212 + 1059.6257476727*$t);
$Y0 += 0.00000661858*cos(6.02414120157 + 5753.6287023803*$t);
$Y0 += 0.00000739644*cos(2.79582891432 + 398.3928208917*$t);
$Y0 += 0.00000681381*cos(0.64735765260 + 4705.9761250271*$t);
$Y0 += 0.00000611293*cos(3.81390547656 + 6813.0106325695*$t);
$Y0 += 0.00000451129*cos(4.52236258525 + 5885.1706640667*$t);
$Y0 += 0.00000451985*cos(5.99169934357 + 6257.0213476751*$t);
$Y0 += 0.00000449743*cos(3.79862296384 + 6309.61798727471*$t);
$Y0 += 0.00000406291*cos(5.25608267423 + 6681.46867088311*$t);
$Y0 += 0.00000541115*cos(5.49909532338 + 775.7664288075*$t);
$Y0 += 0.00000546682*cos(6.17348361999 + 14143.7390599141*$t);
$Y0 += 0.00000513780*cos(2.86615405111 + 7860.6632099227*$t);
$Y0 += 0.00000263916*cos(3.82472119950 + 5507.7970561509*$t);
$Y0 += 0.00000217220*cos(2.94186064336 + 11507.0135872771*$t);
$Y0 += 0.00000292146*cos(4.08451989980 + 5507.3094211839*$t);
$Y0 += 0.00000227915*cos(5.95179814771 + 7058.8422787989*$t);
$Y0 += 0.00000226835*cos(4.84435977688 + 4693.75913722409*$t);
$Y0 += 0.00000255833*cos(0.69465437518 + 12168.2465140581*$t);
$Y0 += 0.00000256157*cos(6.16717762843 + 710.1768660418*$t);
$Y0 += 0.00000178679*cos(1.39565997429 + 796.5418242999*$t);
$Y0 += 0.00000178303*cos(5.11711459804 + 6283.25235717211*$t);
$Y0 += 0.00000178303*cos(4.67301162820 + 6283.3869777777*$t);
$Y0 += 0.00000155471*cos(0.05335100564 + 25132.5472174491*$t);
$Y0 += 0.00000155246*cos(6.13208007594 + 5487.0216606585*$t);
$Y0 += 0.00000207640*cos(4.28246516283 + 11790.8729061423*$t);
$Y0 += 0.00000199988*cos(2.50137197430 + 17790.08943726851*$t);
$Y0 += 0.00000128970*cos(3.64618696457 + 7079.61767429131*$t);
$Y0 += 0.00000128155*cos(3.23179068571 + 3739.0052475915*$t);
$Y0 += 0.00000152241*cos(5.58140597212 + 213.5429129215*$t);
$Y0 += 0.00000078109*cos(0.27810887092 + 8827.6340873583*$t);
$Y0 += 0.00000073503*cos(1.12438065243 + 1589.3167127673*$t);
$Y0 += 0.00000093001*cos(5.50857519732 + 9437.5191174035*$t);
$Y0 += 0.00000065526*cos(2.08488700481 + 11770.0975106499*$t);
$Y0 += 0.00000063240*cos(0.67044494917 + 6262.5442719825*$t);
$Y0 += 0.00000062961*cos(2.83649752628 + 6304.0950629673*$t);
$Y0 += 0.00000085870*cos(1.45351146305 + 167284.00540514899*$t);
$Y0 += 0.00000083233*cos(4.62701145755 + 3340.8562441833*$t);
$Y0 += 0.00000062850*cos(0.46743502764 + 7.3573644843*$t);
$Y0 += 0.00000079971*cos(0.92256149872 + 6070.0205720369*$t);
$Y0 += 0.00000060043*cos(1.82875530765 + 4137.1542509997*$t);
$Y0 += 0.00000075613*cos(2.58868557323 + 6496.6187629129*$t);
$Y0 += 0.00000053731*cos(6.27507790078 + 1194.6908277081*$t);
$Y0 += 0.00000057574*cos(2.39891957636 + 6284.2999885431*$t);
$Y0 += 0.00000057574*cos(1.10802134270 + 6282.3393464067*$t);
$Y0 += 0.00000072385*cos(0.13875968847 + 10976.83498721549*$t);
$Y0 += 0.00000051135*cos(6.02476231374 + 6290.4332144757*$t);
$Y0 += 0.00000050604*cos(3.77440441934 + 6276.2061204741*$t);
$Y0 += 0.00000049613*cos(1.07290414466 + 6127.8992680407*$t);
$Y0 += 0.00000048009*cos(2.43492252840 + 6438.7400669091*$t);
$Y0 += 0.00000059233*cos(5.35402385929 + 3154.4432674121*$t);
$Y0 += 0.00000048264*cos(0.05887245943 + 801.5771136403*$t);
$Y0 += 0.00000047368*cos(4.53616745806 + 3128.6325825793*$t);
$Y0 += 0.00000039225*cos(1.68202291816 + 8429.4850839501*$t);
$Y0 += 0.00000051307*cos(4.21369114598 + 12353.0964220283*$t);
$Y0 += 0.00000050639*cos(0.48135592944 + 11856.462468908*$t);
$Y0 += 0.00000039555*cos(3.35943021943 + 5481.4987363511*$t);
$Y0 += 0.00000042757*cos(2.06983819322 + 17260.3984721739*$t);
$Y0 += 0.00000048941*cos(5.16594049812 + 9225.7830907665*$t);
$Y0 += 0.00000048302*cos(2.17445966751 + 2544.07060239989*$t);
$Y0 += 0.00000037971*cos(1.47013374285 + 426.8420083595*$t);
$Y0 += 0.00000043643*cos(4.71767697827 + 5856.23384163189*$t);
$Y0 += 0.00000031830*cos(3.57964760085 + 2145.92159899169*$t);
$Y0 += 0.00000033959*cos(0.15150934422 + 7085.1405985987*$t);
$Y0 += 0.00000030184*cos(2.39802729198 + 10977.32262218251*$t);
$Y0 += 0.00000032562*cos(4.41726666203 + 4164.0681721295*$t);
$Y0 += 0.00000038887*cos(0.64783670316 + 13367.7288136231*$t);
$Y0 += 0.00000028515*cos(4.53853388778 + 12569.91863581531*$t);
$Y0 += 0.00000028873*cos(5.72467865653 + 3930.4535137031*$t);
$Y0 += 0.00000036633*cos(1.33719170745 + 18073.9487561337*$t);
$Y0 += 0.00000024984*cos(3.74998709416 + 26.0545023163*$t);
$Y0 += 0.00000026364*cos(5.25860499861 + 9438.0067523705*$t);
$Y0 += 0.00000030326*cos(0.42292659979 + 4535.3032544079*$t);
$Y0 += 0.00000028166*cos(5.19366223100 + 12562.8723991173*$t);
$Y0 += 0.00000028001*cos(1.25523598395 + 5088.8726572503*$t);
$Y0 += 0.00000021157*cos(3.50176956898 + 11371.9485072417*$t);
$Y0 += 0.00000023113*cos(5.57235828208 + 5223.93773728571*$t);
$Y0 += 0.00000021642*cos(3.06444525139 + 12559.2819704655*$t);
$Y0 += 0.00000019448*cos(5.97216607301 + 12565.9078824993*$t);
$Y0 += 0.00000026055*cos(1.87419996146 + 71430.45180064559*$t);
$Y0 += 0.00000018232*cos(4.98441727809 + 1747.7725955835*$t);
$Y0 += 0.00000023248*cos(4.61930360205 + 18319.7804023631*$t);
$Y0 += 0.00000022785*cos(2.73901481639 + 5753.14106741329*$t);
$Y0 += 0.00000017091*cos(5.29823070971 + 4933.4522578161*$t);
$Y0 += 0.00000019399*cos(6.00268090156 + 10447.14402212089*$t);
$Y0 += 0.00000021067*cos(2.22953967314 + 7477.7666776995*$t);
$Y0 += 0.00000021310*cos(3.08840298987 + 8031.3360805419*$t);
$Y0 += 0.00000014189*cos(6.02227444325 + 2942.7072407751*$t);
$Y0 += 0.00000013864*cos(3.02270988640 + 8636.18582124671*$t);
$Y0 += 0.00000018884*cos(0.85614785764 + 156137.71980228279*$t);
$Y0 += 0.00000017875*cos(4.86899529635 + 1592.8398311163*$t);
$Y0 += 0.00000018602*cos(2.07103958699 + 17297.9385098427*$t);
$Y0 += 0.00000013605*cos(3.62641283985 + 13096.0864825609*$t);
$Y0 += 0.00000015064*cos(1.55068405670 + 16496.6052136859*$t);
$Y0 += 0.00000012969*cos(4.49412072551 + 7633.1870771337*$t);
$Y0 += 0.00000014403*cos(6.14964820819 + 20426.8149099055*$t);
$Y0 += 0.00000013311*cos(2.03652540541 + 12139.7973265903*$t);
$Y0 += 0.00000013645*cos(3.57902352159 + 13368.2164485901*$t);
$Y0 += 0.00000011583*cos(3.88983863974 + 5331.6012612243*$t);
$Y0 += 0.00000011405*cos(5.97095658034 + 529.44714761109*$t);
$Y0 += 0.00000015057*cos(0.50195173390 + 7084.6529636317*$t);
$Y0 += 0.00000014330*cos(4.45695507640 + 7342.7015976641*$t);
$Y0 += 0.00000012375*cos(1.53862290035 + 6279.72923882311*$t);
$Y0 += 0.00000012366*cos(1.96831814313 + 6286.9100961267*$t);
$Y0 += 0.00000010016*cos(3.81622500644 + 397.9051859247*$t);
$Y0 += 0.00000012435*cos(5.77865382585 + 15110.7099373497*$t);
$Y0 += 0.00000009513*cos(5.90294963286 + 7235.0380737255*$t);
$Y0 += 0.00000010997*cos(0.62118771904 + 10989.0519750185*$t);
$Y0 += 0.00000011583*cos(2.48171191864 + 5729.7502646325*$t);
$Y0 += 0.00000009034*cos(3.85796197835 + 9623.9320941747*$t);
$Y0 += 0.00000011842*cos(2.59877813496 + 15721.0826023619*$t);
$Y0 += 0.00000008869*cos(3.47611287212 + 6148.2545874395*$t);
$Y0 += 0.00000008614*cos(0.03081566771 + 6418.38474751031*$t);
$Y0 += 0.00000010312*cos(1.02710009735 + 6836.8890703173*$t);
$Y0 += 0.00000008411*cos(0.87289239606 + 14712.5609339415*$t);
$Y0 += 0.00000007911*cos(1.58349090213 + 2119.00767786191*$t);
$Y0 += 0.00000010379*cos(0.10632075985 + 1349.62359217529*$t);
$Y0 += 0.00000010374*cos(3.97648848184 + 5486.53402569149*$t);
$Y0 += 0.00000010480*cos(1.38209289015 + 5999.4603486097*$t);
$Y0 += 0.00000007404*cos(3.84339417190 + 6040.5910635009*$t);
$Y0 += 0.00000007357*cos(5.40136984638 + 5088.3850222833*$t);
$Y0 += 0.00000009820*cos(2.12476608355 + 6567.1789863401*$t);
$Y0 += 0.00000007018*cos(5.94659139192 + 6526.04827144891*$t);
$Y0 += 0.00000009668*cos(3.49318502073 + 21228.1482060623*$t);
$Y0 += 0.00000007545*cos(5.94843445846 + 12540.0971976665*$t);
$Y0 += 0.00000007202*cos(4.31311905021 + 6245.2919948391*$t);
$Y0 += 0.00000007144*cos(5.47703554612 + 6321.3473401107*$t);
$Y0 += 0.00000008883*cos(5.46710407546 + 5642.93474619389*$t);
$Y0 += 0.00000006626*cos(5.41362465894 + 5327.7199258663*$t);
$Y0 += 0.00000007015*cos(5.70701993379 + 7860.17557495569*$t);
$Y0 += 0.00000006159*cos(5.65831198505 + 12964.5445208745*$t);
$Y0 += 0.00000007413*cos(3.46419092567 + 23543.4743221653*$t);
$Y0 += 0.00000006355*cos(3.46461466453 + 1990.9888345245*$t);
$Y0 += 0.00000007286*cos(2.01139981548 + 537.0483295789*$t);
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$Y0 += 0.00000000049*cos(0.36435757253 + 16310.73522823709*$t);
$Y0 += 0.00000000049*cos(3.50595022612 + 16311.2228632041*$t);
$Y0 += 0.00000000065*cos(2.20156720545 + 46386.7499258277*$t);
$Y0 += 0.00000000069*cos(5.16096365273 + 60530.2451682583*$t);
$Y0 += 0.00000000068*cos(4.61952317468 + 96678.14268052569*$t);
$Y0 += 0.00000000049*cos(4.01249891427 + 12323.17927852529*$t);
$Y0 += 0.00000000050*cos(2.38095415684 + 21954.4014268815*$t);
$Y0 += 0.00000000049*cos(4.98226292129 + 4164.5558070965*$t);
$Y0 += 0.00000000059*cos(0.54830716960 + 33794.7875410121*$t);
$Y0 += 0.00000000050*cos(1.64594745036 + 43739.0461634493*$t);
$Y0 += 0.00000000059*cos(2.71376255252 + 3981.73385156551*$t);
$Y0 += 0.00000000058*cos(3.16580349936 + 27707.29867681129*$t);
$Y0 += 0.00000000051*cos(1.43461397348 + 7669.21494381111*$t);
$Y0 += 0.00000000048*cos(3.23576326319 + 3646.59419483791*$t);
$Y0 += 0.00000000065*cos(1.63790414031 + 82534.6474380951*$t);
$Y0 += 0.00000000056*cos(2.62361047024 + 800.06494264891*$t);
$Y0 += 0.00000000057*cos(2.56200976684 + 11609.61872652869*$t);
$Y0 += 0.00000000048*cos(3.66284145075 + 26.5421372833*$t);
$Y0 += 0.00000000047*cos(5.82227097996 + 30640.1004561165*$t);
$Y0 += 0.00000000060*cos(3.54507538375 + 8982.5668518255*$t);
$Y0 += 0.00000000049*cos(2.15364675842 + 96563.24283557819*$t);
$Y0 += 0.00000000050*cos(3.60628396854 + 17583.9038888313*$t);
$Y0 += 0.00000000046*cos(4.33029118489 + 23539.46356884929*$t);
$Y0 += 0.00000000048*cos(4.40476950322 + 170.4290531357*$t);
$Y0 += 0.00000000055*cos(0.06525117672 + 735.6326960483*$t);
$Y0 += 0.00000000054*cos(5.90233323358 + 6680.98103591609*$t);
$Y0 += 0.00000000060*cos(3.29126676894 + 44033.8837720559*$t);
$Y0 += 0.00000000064*cos(5.97731735914 + 80181.29364935629*$t);
$Y0 += 0.00000000059*cos(3.60959132830 + 24279.3508356971*$t);
$Y0 += 0.00000000049*cos(3.59486989773 + 5490.5447790075*$t);
$Y0 += 0.00000000058*cos(5.95314247069 + 6490.0204047715*$t);
$Y0 += 0.00000000058*cos(3.83698375555 + 6076.6189301783*$t);
$Y0 += 0.00000000046*cos(1.35461053261 + 18208.1061251085*$t);
$Y0 += 0.00000000045*cos(3.19696372316 + 4480.46004178609*$t);
$Y0 += 0.00000000055*cos(1.99803947181 + 16097.9237677661*$t);
$Y0 += 0.00000000055*cos(1.99803947181 + 16097.43613279909*$t);
$Y0 += 0.00000000061*cos(3.53347961961 + 491.9071099423*$t);
$Y0 += 0.00000000054*cos(1.22650408797 + 6006.5738956105*$t);
$Y0 += 0.00000000054*cos(2.28043683109 + 6560.0654393393*$t);
$Y0 += 0.00000000044*cos(4.77367705513 + 5333.65642353809*$t);
$Y0 += 0.00000000052*cos(3.85218997059 + 244287.84382471119*$t);
$Y0 += 0.00000000044*cos(2.69173127084 + 2301.34199842589*$t);
$Y0 += 0.00000000045*cos(4.35951224787 + 33794.2999060451*$t);
$Y0 += 0.00000000046*cos(3.84874383995 + 4384.48081456829*$t);
$Y0 += 0.00000000048*cos(4.63629874583 + 35579.9350570535*$t);
$Y0 += 0.00000000051*cos(4.91886576255 + 18326.8939493639*$t);
$Y0 += 0.00000000045*cos(2.63923033609 + 533.45790092711*$t);
$Y0 += 0.00000000046*cos(3.15339657493 + 16703.3059509825*$t);
$Y0 += 0.00000000047*cos(2.39403388232 + 5209.2230083171*$t);
$Y0 += 0.00000000051*cos(1.31112479278 + 38650.4173236825*$t);
$Y0 += 0.00000000046*cos(2.47672465258 + 12555.3498172024*$t);
$Y0 += 0.00000000052*cos(4.64446990453 + 5992.3468016089*$t);
$Y0 += 0.00000000052*cos(5.14565632171 + 6574.2925333409*$t);
$Y0 += 0.00000000044*cos(3.80837636245 + 69942.1974183125*$t);
$Y0 += 0.00000000049*cos(3.62132943845 + 12146.9108735911*$t);
$Y0 += 0.00000000053*cos(4.67452542700 + 39301.8531447125*$t);
$Y0 += 0.00000000045*cos(4.65107782321 + 46360.9392409949*$t);
$Y0 += 0.00000000043*cos(1.54528326296 + 8402.0835278533*$t);
$Y0 += 0.00000000043*cos(0.19791989913 + 44137.1951668575*$t);
$Y0 += 0.00000000049*cos(3.54725333487 + 22029.9691371861*$t);
$Y0 += 0.00000000044*cos(1.47478212539 + 31441.92138724031*$t);
$Y0 += 0.00000000042*cos(2.85938112982 + 9225.29545579949*$t);
$Y0 += 0.00000000045*cos(3.22032934298 + 71519.54096076029*$t);
$Y0 += 0.00000000051*cos(2.95623880108 + 7762.1862415393*$t);
$Y0 += 0.00000000041*cos(5.14395096650 + 3735.48212924251*$t);
$Y0 += 0.00000000057*cos(1.24099052077 + 40398.4337367495*$t);
$Y0 += 0.00000000047*cos(6.03171570454 + 4707.9862312257*$t);
$Y0 += 0.00000000056*cos(5.36736063063 + 28664.0754677489*$t);
$Y0 += 0.00000000050*cos(2.58729930740 + 11919.3846841515*$t);
$Y0 += 0.00000000047*cos(5.61037642387 + 316428.47249139856*$t);
$Y0 += 0.00000000041*cos(2.70468936208 + 27278.7126339243*$t);
$Y0 += 0.00000000056*cos(1.28041103259 + 83659.5206898825*$t);
$Y0 += 0.00000000048*cos(0.93182108526 + 12662.3747446841*$t);
$Y0 += 0.00000000054*cos(2.40910872834 + 16627.12709789369*$t);
$Y0 += 0.00000000052*cos(2.84085536047 + 12571.9184417737*$t);
$Y0 += 0.00000000043*cos(3.12713892129 + 7322.34627826531*$t);
$Y0 += 0.00000000041*cos(1.99075260862 + 664.99986261351*$t);
$Y0 += 0.00000000042*cos(3.11818521171 + 5641.9544251257*$t);
$Y0 += 0.00000000044*cos(6.16004757680 + 6425.4982945111*$t);
$Y0 += 0.00000000044*cos(3.63007864944 + 6141.1410404387*$t);
$Y0 += 0.00000000039*cos(5.09444795757 + 22594.2987131955*$t);
$Y0 += 0.00000000040*cos(1.17403028794 + 20894.53186172529*$t);
$Y0 += 0.00000000044*cos(3.71228299188 + 5540.3296069423*$t);
$Y0 += 0.00000000050*cos(0.98055905828 + 17782.48825530069*$t);
$Y0 += 0.00000000054*cos(3.12084664124 + 6006.2846737335*$t);
$Y0 += 0.00000000054*cos(0.38609427782 + 6560.3546612163*$t);
$Y0 += 0.00000000045*cos(0.83260974343 + 142861.14741877468*$t);
$Y0 += 0.00000000047*cos(5.83397233956 + 24499.7634781359*$t);
$Y0 += 0.00000000043*cos(6.07854396898 + 7026.3097280075*$t);
$Y0 += 0.00000000047*cos(0.38354823927 + 955.8435590921*$t);
$Y0 += 0.00000000047*cos(2.93749588479 + 24485.5363841343*$t);
$Y0 += 0.00000000040*cos(1.03647885736 + 9388.2497268987*$t);
$Y0 += 0.00000000043*cos(4.24359473122 + 6359.5857387505*$t);
$Y0 += 0.00000000042*cos(5.53288597787 + 8635.69818627969*$t);
$Y0 += 0.00000000051*cos(4.03405257508 + 27831.79440179969*$t);
$Y0 += 0.00000000042*cos(0.37690679264 + 6334.60000533731*$t);
$Y0 += 0.00000000042*cos(3.13003412642 + 6232.03932961249*$t);
$Y0 += 0.00000000052*cos(1.96232281613 + 11905.1625906853*$t);
$Y0 += 0.00000000040*cos(6.22187049858 + 7076.0945559423*$t);
$Y0 += 0.00000000040*cos(5.00617355027 + 5444.3503797245*$t);
$Y0 += 0.00000000040*cos(4.78395267597 + 7122.2889552253*$t);
$Y0 += 0.00000000038*cos(0.67446092329 + 44933.4931736739*$t);
$Y0 += 0.00000000037*cos(4.98656910933 + 5715.6010297445*$t);
$Y0 += 0.00000000037*cos(4.80355711691 + 6851.0383052053*$t);
$Y0 += 0.00000000042*cos(5.51152847292 + 36147.6536947839*$t);
$Y0 += 0.00000000042*cos(1.28742672679 + 6238.1784478383*$t);
$Y0 += 0.00000000042*cos(2.21951419227 + 6328.4608871115*$t);
$Y0 += 0.00000000040*cos(5.21427505339 + 3214.8925631597*$t);
$Y0 += 0.00000000043*cos(2.22601042104 + 23141.3145654411*$t);
$Y0 += 0.00000000041*cos(5.52595261887 + 19804.5834740993*$t);
$Y0 += 0.00000000038*cos(4.48062431201 + 20.11150191529*$t);
$Y0 += 0.00000000050*cos(0.05709227621 + 84334.66158130829*$t);
$Y0 += 0.00000000050*cos(4.41842921988 + 60284.16619777939*$t);
return $Y0;
}
function Earth_Y1($t) // 600 terms of order 1
{
$Y1 = 0.00154550744*cos(5.35844734917 + 0.2438174835*$t);
$Y1 += 0.00051503383*cos(4.43183566713 + 12566.3955174663*$t);
$Y1 += 0.00001290763*cos(4.38862020180 + 18849.4713674577*$t);
$Y1 += 0.00000702576*cos(0.18268310766 + 6283.3196674749*$t);
$Y1 += 0.00000430422*cos(4.02296125150 + 6282.83203250789*$t);
$Y1 += 0.00000212689*cos(0.16300557365 + 6279.7965491259*$t);
$Y1 += 0.00000212524*cos(3.34405166686 + 6286.84278582391*$t);
$Y1 += 0.00000062308*cos(5.07432195748 + 4705.9761250271*$t);
$Y1 += 0.00000059808*cos(2.24108323998 + 6257.0213476751*$t);
$Y1 += 0.00000059474*cos(1.26580020213 + 6309.61798727471*$t);
$Y1 += 0.00000048914*cos(3.64253038225 + 775.7664288075*$t);
$Y1 += 0.00000042814*cos(5.15102931682 + 1059.6257476727*$t);
$Y1 += 0.00000046457*cos(4.72328803502 + 7860.6632099227*$t);
$Y1 += 0.00000036653*cos(0.62556081234 + 5753.6287023803*$t);
$Y1 += 0.00000035649*cos(6.15990909241 + 5885.1706640667*$t);
$Y1 += 0.00000035362*cos(2.90135814576 + 6813.0106325695*$t);
$Y1 += 0.00000032151*cos(3.62597628866 + 6681.46867088311*$t);
$Y1 += 0.00000028763*cos(4.34539356227 + 25132.5472174491*$t);
$Y1 += 0.00000028447*cos(5.86215127530 + 6127.8992680407*$t);
$Y1 += 0.00000027537*cos(3.92840810925 + 6438.7400669091*$t);
$Y1 += 0.00000024819*cos(1.35151106278 + 5487.0216606585*$t);
$Y1 += 0.00000020615*cos(2.14741827387 + 7079.61767429131*$t);
$Y1 += 0.00000019621*cos(1.31571192713 + 5507.7970561509*$t);
$Y1 += 0.00000018378*cos(6.17760240913 + 11790.8729061423*$t);
$Y1 += 0.00000016494*cos(4.64463821908 + 11507.0135872771*$t);
$Y1 += 0.00000016756*cos(2.24858801378 + 7058.8422787989*$t);
$Y1 += 0.00000014558*cos(4.40450472214 + 6290.4332144757*$t);
$Y1 += 0.00000014404*cos(5.39361420229 + 6276.2061204741*$t);
$Y1 += 0.00000014052*cos(6.16986019111 + 796.5418242999*$t);
$Y1 += 0.00000012261*cos(5.72868820428 + 4693.75913722409*$t);
$Y1 += 0.00000012758*cos(5.06070649359 + 7.3573644843*$t);
$Y1 += 0.00000010086*cos(1.72162917776 + 3739.0052475915*$t);
$Y1 += 0.00000009469*cos(3.06840825171 + 6070.0205720369*$t);
$Y1 += 0.00000010425*cos(0.81162914438 + 6284.2999885431*$t);
$Y1 += 0.00000010425*cos(2.69531177468 + 6282.3393464067*$t);
$Y1 += 0.00000009570*cos(0.32347467387 + 4137.1542509997*$t);
$Y1 += 0.00000009044*cos(0.43893334417 + 6496.6187629129*$t);
$Y1 += 0.00000008544*cos(4.76970151659 + 1194.6908277081*$t);
$Y1 += 0.00000008214*cos(5.96640392040 + 1589.3167127673*$t);
$Y1 += 0.00000006157*cos(1.78596836636 + 8827.6340873583*$t);
$Y1 += 0.00000006271*cos(3.18396187423 + 8429.4850839501*$t);
$Y1 += 0.00000005524*cos(3.79861381511 + 4933.4522578161*$t);
$Y1 += 0.00000007314*cos(5.20341424492 + 4535.3032544079*$t);
$Y1 += 0.00000005157*cos(3.57885530448 + 11770.0975106499*$t);
$Y1 += 0.00000006749*cos(2.75433387783 + 5088.8726572503*$t);
$Y1 += 0.00000004853*cos(5.33701721257 + 6040.5910635009*$t);
$Y1 += 0.00000005304*cos(0.93005422139 + 3154.4432674121*$t);
$Y1 += 0.00000004985*cos(3.05697984231 + 12569.91863581531*$t);
$Y1 += 0.00000004709*cos(2.39306975468 + 5331.6012612243*$t);
$Y1 += 0.00000004601*cos(4.45296491447 + 6526.04827144891*$t);
$Y1 += 0.00000004201*cos(5.99364092036 + 7633.1870771337*$t);
$Y1 += 0.00000005607*cos(0.98720876729 + 5729.7502646325*$t);
$Y1 += 0.00000004257*cos(2.55370490945 + 3930.4535137031*$t);
$Y1 += 0.00000004394*cos(4.75948183378 + 12559.2819704655*$t);
$Y1 += 0.00000003870*cos(1.11601490340 + 7235.0380737255*$t);
$Y1 += 0.00000005154*cos(4.58850581748 + 8031.3360805419*$t);
$Y1 += 0.00000005036*cos(2.51929382179 + 6836.8890703173*$t);
$Y1 += 0.00000005076*cos(0.73526458069 + 7477.7666776995*$t);
$Y1 += 0.00000003593*cos(3.97650177033 + 12565.9078824993*$t);
$Y1 += 0.00000003384*cos(3.83274545225 + 10977.32262218251*$t);
$Y1 += 0.00000003371*cos(5.00200001284 + 11371.9485072417*$t);
$Y1 += 0.00000003536*cos(5.30432752281 + 4164.0681721295*$t);
$Y1 += 0.00000004292*cos(3.36706453434 + 1592.8398311163*$t);
$Y1 += 0.00000003407*cos(0.83519640650 + 3128.6325825793*$t);
$Y1 += 0.00000003152*cos(0.16276893009 + 5223.93773728571*$t);
$Y1 += 0.00000002883*cos(0.20838349180 + 1747.7725955835*$t);
$Y1 += 0.00000002751*cos(3.67369812017 + 7342.7015976641*$t);
$Y1 += 0.00000003323*cos(3.48959648614 + 801.5771136403*$t);
$Y1 += 0.00000002999*cos(0.68275608544 + 8636.18582124671*$t);
$Y1 += 0.00000002496*cos(5.09157906387 + 2145.92159899169*$t);
$Y1 += 0.00000003358*cos(5.82350976219 + 155.17658195069*$t);
$Y1 += 0.00000002297*cos(2.96479731544 + 17260.3984721739*$t);
$Y1 += 0.00000002047*cos(1.96580631113 + 1990.9888345245*$t);
$Y1 += 0.00000002778*cos(6.17391326343 + 5481.4987363511*$t);
$Y1 += 0.00000002025*cos(3.01082711135 + 951.4745887671*$t);
$Y1 += 0.00000002663*cos(1.00159277919 + 26.0545023163*$t);
$Y1 += 0.00000002009*cos(4.16311202386 + 4690.7236538421*$t);
$Y1 += 0.00000002148*cos(0.32608511593 + 537.0483295789*$t);
$Y1 += 0.00000001853*cos(4.41841662668 + 553.32558535889*$t);
$Y1 += 0.00000002478*cos(1.61013003664 + 1349.62359217529*$t);
$Y1 += 0.00000002023*cos(0.82015419806 + 522.8212355773*$t);
$Y1 += 0.00000001735*cos(4.49024043092 + 529.44714761109*$t);
$Y1 += 0.00000002417*cos(3.59693248271 + 7085.1405985987*$t);
$Y1 += 0.00000001809*cos(2.35536809783 + 397.9051859247*$t);
$Y1 += 0.00000001893*cos(2.65666986732 + 9438.0067523705*$t);
$Y1 += 0.00000001708*cos(5.00361322564 + 10989.0519750185*$t);
$Y1 += 0.00000001898*cos(3.91087003459 + 5216.33655531789*$t);
$Y1 += 0.00000001820*cos(3.44808607160 + 5230.5636493195*$t);
$Y1 += 0.00000001541*cos(5.81316348536 + 426.8420083595*$t);
$Y1 += 0.00000001555*cos(2.09924495059 + 13096.0864825609*$t);
$Y1 += 0.00000001779*cos(0.23737949225 + 12562.8723991173*$t);
$Y1 += 0.00000001448*cos(1.75844475078 + 5753.14106741329*$t);
$Y1 += 0.00000001450*cos(5.71201368260 + 6262.96434807611*$t);
$Y1 += 0.00000001450*cos(4.07811254364 + 6303.6749868737*$t);
$Y1 += 0.00000001822*cos(0.13446699374 + 10973.7995038335*$t);
$Y1 += 0.00000001372*cos(5.60520656116 + 7875.91568110771*$t);
$Y1 += 0.00000001375*cos(2.34041210234 + 7084.6529636317*$t);
$Y1 += 0.00000001400*cos(3.28144398068 + 12721.8159169005*$t);
$Y1 += 0.00000001247*cos(0.29225580262 + 2119.00767786191*$t);
$Y1 += 0.00000001231*cos(2.53164637932 + 18319.7804023631*$t);
$Y1 += 0.00000001141*cos(1.92161882496 + 1066.7392946735*$t);
$Y1 += 0.00000001138*cos(1.23855949465 + 2942.7072407751*$t);
$Y1 += 0.00000001047*cos(1.31663136695 + 5642.93474619389*$t);
$Y1 += 0.00000001058*cos(2.19001683016 + 242.97242145751*$t);
$Y1 += 0.00000001025*cos(0.60899466577 + 10447.14402212089*$t);
$Y1 += 0.00000000973*cos(4.95398300734 + 640.1411037975*$t);
$Y1 += 0.00000001114*cos(4.36978275435 + 15721.0826023619*$t);
$Y1 += 0.00000000963*cos(0.56100772029 + 2389.1378379327*$t);
$Y1 += 0.00000000941*cos(4.21626686326 + 20426.8149099055*$t);
$Y1 += 0.00000001068*cos(5.08632600308 + 529.9347825781*$t);
$Y1 += 0.00000000929*cos(1.54055499699 + 10575.6505004253*$t);
$Y1 += 0.00000000899*cos(5.79114005938 + 16496.6052136859*$t);
$Y1 += 0.00000000889*cos(5.01192484889 + 6277.7967431675*$t);
$Y1 += 0.00000000889*cos(4.77820137734 + 6288.8425917823*$t);
$Y1 += 0.00000001018*cos(2.66299766067 + 12540.0971976665*$t);
$Y1 += 0.00000001060*cos(5.76865363011 + 5760.7422493811*$t);
$Y1 += 0.00000001017*cos(4.02093017183 + 6805.89708556871*$t);
$Y1 += 0.00000000797*cos(3.79336643920 + 14314.4119305333*$t);
$Y1 += 0.00000000795*cos(0.10742263482 + 6286.6060248927*$t);
$Y1 += 0.00000000795*cos(3.39951828424 + 6280.0333100571*$t);
$Y1 += 0.00000000800*cos(3.18366130818 + 12029.5910053709*$t);
$Y1 += 0.00000000719*cos(2.29666441302 + 9623.9320941747*$t);
$Y1 += 0.00000000698*cos(4.94363251872 + 6148.2545874395*$t);
$Y1 += 0.00000000686*cos(3.79368723538 + 5856.7214765989*$t);
$Y1 += 0.00000000673*cos(3.99105175160 + 12964.5445208745*$t);
$Y1 += 0.00000000902*cos(0.69698416448 + 13368.2164485901*$t);
$Y1 += 0.00000000678*cos(4.84647193821 + 6418.38474751031*$t);
$Y1 += 0.00000000671*cos(6.00179402654 + 6709.91785835091*$t);
$Y1 += 0.00000000744*cos(2.68741072621 + 12043.8180993725*$t);
$Y1 += 0.00000000706*cos(2.51950741945 + 16730.70750707931*$t);
$Y1 += 0.00000000661*cos(2.42216375426 + 14712.5609339415*$t);
$Y1 += 0.00000000633*cos(5.58153853935 + 4292.5746504339*$t);
$Y1 += 0.00000000621*cos(1.74121096386 + 13119.9649203087*$t);
$Y1 += 0.00000000638*cos(2.04188798982 + 4690.23601887509*$t);
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$Y1 += 0.00000000049*cos(3.35593265214 + 21393.7857873411*$t);
$Y1 += 0.00000000049*cos(4.47248238697 + 5547.4431539431*$t);
$Y1 += 0.00000000049*cos(5.31764383927 + 7019.19618100671*$t);
$Y1 += 0.00000000049*cos(1.02044068888 + 12416.8323203317*$t);
$Y1 += 0.00000000050*cos(0.93918602686 + 12592.2062022991*$t);
$Y1 += 0.00000000050*cos(4.78759248733 + 26084.2656236997*$t);
$Y1 += 0.00000000051*cos(1.83601012538 + 23006.6698100699*$t);
$Y1 += 0.00000000058*cos(4.03623415117 + 15141.14697682849*$t);
$Y1 += 0.00000000047*cos(5.68903994773 + 24279.3508356971*$t);
$Y1 += 0.00000000049*cos(3.40926939847 + 6816.53375091851*$t);
$Y1 += 0.00000000049*cos(0.09767152059 + 5750.1055840313*$t);
$Y1 += 0.00000000046*cos(1.88054905125 + 19379.1623325523*$t);
$Y1 += 0.00000000052*cos(5.74808775798 + 16737.33341911309*$t);
$Y1 += 0.00000000047*cos(0.52219046486 + 24066.0517402591*$t);
$Y1 += 0.00000000046*cos(4.16717022039 + 104351.85638378029*$t);
$Y1 += 0.00000000063*cos(6.25484174196 + 8662.48414104651*$t);
$Y1 += 0.00000000048*cos(3.28503810088 + 26735.7014447297*$t);
$Y1 += 0.00000000046*cos(3.91775350902 + 12132.6837795895*$t);
$Y1 += 0.00000000050*cos(2.92364175862 + 24602.8562523545*$t);
$Y1 += 0.00000000054*cos(4.75214039499 + 7834.3648901229*$t);
$Y1 += 0.00000000045*cos(3.48807574467 + 161000.92955515759*$t);
$Y1 += 0.00000000049*cos(2.94405201174 + 29303.9727540629*$t);
$Y1 += 0.00000000049*cos(1.43156848803 + 10984.4361691833*$t);
$Y1 += 0.00000000045*cos(0.70883599249 + 45584.9289947039*$t);
$Y1 += 0.00000000046*cos(1.86995211145 + 5244.2930566845*$t);
$Y1 += 0.00000000048*cos(3.53510882628 + 23581.0143598341*$t);
$Y1 += 0.00000000049*cos(2.17177379198 + 19650.8046636145*$t);
$Y1 += 0.00000000049*cos(3.41897587826 + 29289.7456600613*$t);
$Y1 += 0.00000000044*cos(1.44008987426 + 6390.9831914135*$t);
$Y1 += 0.00000000044*cos(2.06685104480 + 6175.6561435363*$t);
$Y1 += 0.00000000051*cos(2.65580143245 + 17789.60180230149*$t);
$Y1 += 0.00000000042*cos(6.18543275273 + 24705.9490265731*$t);
$Y1 += 0.00000000042*cos(5.90805829894 + 15663.79170522509*$t);
$Y1 += 0.00000000043*cos(3.08250524084 + 16460.08971204149*$t);
$Y1 += 0.00000000043*cos(0.28590581328 + 553.8132203259*$t);
$Y1 += 0.00000000041*cos(3.21615501236 + 17370.6047933933*$t);
$Y1 += 0.00000000053*cos(2.59151074700 + 13119.47728534169*$t);
$Y1 += 0.00000000042*cos(5.11995884892 + 4164.5558070965*$t);
$Y1 += 0.00000000041*cos(2.05521298551 + 23020.8969040715*$t);
$Y1 += 0.00000000045*cos(3.70227971577 + 54247.1693182669*$t);
$Y1 += 0.00000000040*cos(4.57473494926 + 32243.2546833971*$t);
$Y1 += 0.00000000040*cos(5.17184328434 + 24336.2492106327*$t);
$Y1 += 0.00000000040*cos(1.71852303243 + 11769.6098756829*$t);
$Y1 += 0.00000000045*cos(6.25985265406 + 16723.10632511149*$t);
$Y1 += 0.00000000045*cos(6.25985265406 + 16723.5939600785*$t);
$Y1 += 0.00000000042*cos(5.89327075469 + 8827.14645239129*$t);
$Y1 += 0.00000000040*cos(4.71493835645 + 8402.0835278533*$t);
$Y1 += 0.00000000039*cos(3.49714273023 + 16062.4283436003*$t);
$Y1 += 0.00000000044*cos(4.44510876745 + 5856.23384163189*$t);
$Y1 += 0.00000000038*cos(1.14212165839 + 6297.5467614765*$t);
$Y1 += 0.00000000038*cos(2.36481926067 + 6269.0925734733*$t);
$Y1 += 0.00000000041*cos(3.38233495451 + 15508.8589407579*$t);
$Y1 += 0.00000000038*cos(4.96796930709 + 6394.50630976251*$t);
$Y1 += 0.00000000038*cos(4.82215691915 + 6172.1330251873*$t);
$Y1 += 0.00000000039*cos(1.74815791619 + 29826.5501721567*$t);
$Y1 += 0.00000000046*cos(0.31322632556 + 17297.9385098427*$t);
$Y1 += 0.00000000041*cos(4.04315782590 + 6309.1303523077*$t);
$Y1 += 0.00000000038*cos(5.82409895120 + 29089.0552334685*$t);
$Y1 += 0.00000000038*cos(4.59409111885 + 11933.6117781531*$t);
$Y1 += 0.00000000037*cos(3.34091252113 + 26482.4146271079*$t);
$Y1 += 0.00000000037*cos(3.64722285417 + 20452.6255947383*$t);
$Y1 += 0.00000000037*cos(0.30900035436 + 18073.46112116669*$t);
$Y1 += 0.00000000036*cos(2.98410187235 + 11499.41240530929*$t);
$Y1 += 0.00000000045*cos(4.75649198460 + 3340.8562441833*$t);
$Y1 += 0.00000000049*cos(4.21088151991 + 18216.6876281445*$t);
$Y1 += 0.00000000038*cos(4.59187061808 + 18202.4605341429*$t);
$Y1 += 0.00000000041*cos(3.91005845267 + 5216.8241902849*$t);
$Y1 += 0.00000000036*cos(6.21139146959 + 4060.97539791089*$t);
$Y1 += 0.00000000048*cos(5.14345155225 + 951.9622237341*$t);
$Y1 += 0.00000000041*cos(3.90932016585 + 18848.98373249069*$t);
$Y1 += 0.00000000038*cos(4.60880580452 + 26709.8907598969*$t);
$Y1 += 0.00000000036*cos(3.12521745961 + 28230.4310401749*$t);
$Y1 += 0.00000000036*cos(1.96840086543 + 24491.18197509989*$t);
$Y1 += 0.00000000036*cos(1.56811412304 + 9924.5666040271*$t);
$Y1 += 0.00000000048*cos(1.89701220521 + 8982.5668518255*$t);
$Y1 += 0.00000000037*cos(3.60669363968 + 22484.0923919761*$t);
$Y1 += 0.00000000047*cos(3.21269518092 + 6040.10342853389*$t);
$Y1 += 0.00000000034*cos(3.68972702028 + 6418.9449924849*$t);
$Y1 += 0.00000000034*cos(6.10039920596 + 6147.69434246491*$t);
$Y1 += 0.00000000034*cos(3.67007112439 + 9380.71585523369*$t);
$Y1 += 0.00000000036*cos(0.30403746373 + 7238.4317741165*$t);
$Y1 += 0.00000000034*cos(0.40887602826 + 17272.1278250099*$t);
$Y1 += 0.00000000037*cos(1.23154839984 + 58953.3892607775*$t);
$Y1 += 0.00000000034*cos(0.33427002863 + 29026.7290469913*$t);
$Y1 += 0.00000000033*cos(3.87501941695 + 12721.32828193349*$t);
$Y1 += 0.00000000035*cos(1.63582276543 + 7322.34627826531*$t);
$Y1 += 0.00000000044*cos(1.21937301495 + 3981.73385156551*$t);
$Y1 += 0.00000000033*cos(3.59821221655 + 19804.5834740993*$t);
$Y1 += 0.00000000033*cos(2.56047890182 + 173567.08125514039*$t);
$Y1 += 0.00000000033*cos(6.16657680956 + 205.9417309537*$t);
$Y1 += 0.00000000033*cos(5.44889821497 + 23013.29572210369*$t);
$Y1 += 0.00000000034*cos(2.13261854972 + 49515.1386909235*$t);
$Y1 += 0.00000000034*cos(3.38050467777 + 38500.5198485557*$t);
$Y1 += 0.00000000032*cos(2.81221233882 + 17686.9966630499*$t);
$Y1 += 0.00000000036*cos(1.67423219491 + 5641.9544251257*$t);
$Y1 += 0.00000000032*cos(2.91090812586 + 21228.63584102931*$t);
$Y1 += 0.00000000033*cos(0.13839577785 + 34520.5531268643*$t);
$Y1 += 0.00000000033*cos(5.65380556855 + 8635.69818627969*$t);
$Y1 += 0.00000000031*cos(1.88042187886 + 5746.0275204125*$t);
$Y1 += 0.00000000041*cos(2.52021697492 + 21202.3375212295*$t);
$Y1 += 0.00000000037*cos(5.92836585991 + 7349.81514466491*$t);
$Y1 += 0.00000000034*cos(2.18099177342 + 16496.11757871889*$t);
$Y1 += 0.00000000032*cos(0.90143427409 + 33019.2649296881*$t);
$Y1 += 0.00000000032*cos(1.54173979189 + 21150.56954840009*$t);
$Y1 += 0.00000000037*cos(1.84830381005 + 29296.8592070621*$t);
$Y1 += 0.00000000036*cos(5.02250294215 + 27511.2240560537*$t);
$Y1 += 0.00000000035*cos(3.77934660139 + 11933.12414318609*$t);
$Y1 += 0.00000000035*cos(4.26341483447 + 11918.89704918449*$t);
$Y1 += 0.00000000035*cos(5.54313072444 + 29062.7569136687*$t);
$Y1 += 0.00000000030*cos(1.38932865248 + 12490.1294461907*$t);
$Y1 += 0.00000000032*cos(5.09927453137 + 6334.60000533731*$t);
$Y1 += 0.00000000032*cos(4.69085169487 + 6232.03932961249*$t);
$Y1 += 0.00000000029*cos(4.05993716780 + 419.2408263917*$t);
$Y1 += 0.00000000029*cos(0.91834451421 + 419.72846135871*$t);
$Y1 += 0.00000000029*cos(1.66178131503 + 16858.23871544969*$t);
$Y1 += 0.00000000030*cos(2.73190240418 + 16208.13008898551*$t);
$Y1 += 0.00000000029*cos(0.69175314473 + 27278.7126339243*$t);
$Y1 += 0.00000000032*cos(4.73525892997 + 5017.2645538815*$t);
$Y1 += 0.00000000028*cos(0.30767945102 + 24080.2788342607*$t);
$Y1 += 0.00000000030*cos(1.00265951424 + 23539.9512038163*$t);
$Y1 += 0.00000000029*cos(1.45883005475 + 18606.25512851669*$t);
$Y1 += 0.00000000030*cos(4.73151177298 + 30665.9111409493*$t);
$Y1 += 0.00000000034*cos(4.29199382621 + 6660.6932753907*$t);
$Y1 += 0.00000000034*cos(5.49813240003 + 5905.94605955911*$t);
$Y1 += 0.00000000038*cos(3.55143054136 + 31571.0434668747*$t);
$Y1 += 0.00000000038*cos(4.53015131722 + 16061.94070863329*$t);
$Y1 += 0.00000000029*cos(1.64885508302 + 23539.46356884929*$t);
$Y1 += 0.00000000033*cos(2.88700963334 + 3738.51761262449*$t);
$Y1 += 0.00000000028*cos(6.02264922068 + 2942.21960580809*$t);
$Y1 += 0.00000000032*cos(2.75250951602 + 15110.7099373497*$t);
$Y1 += 0.00000000030*cos(6.10434010761 + 55023.1795645579*$t);
$Y1 += 0.00000000027*cos(5.24524976767 + 233141.55822184499*$t);
$Y1 += 0.00000000030*cos(0.75326086687 + 12587.1709129587*$t);
$Y1 += 0.00000000028*cos(3.97691648841 + 34911.6558935745*$t);
$Y1 += 0.00000000027*cos(4.60109278395 + 1692.40948698591*$t);
$Y1 += 0.00000000027*cos(6.13743188286 + 2544.07060239989*$t);
$Y1 += 0.00000000027*cos(4.99580076168 + 24382.8352909579*$t);
$Y1 += 0.00000000027*cos(4.42136306455 + 6205.6458970469*$t);
$Y1 += 0.00000000027*cos(5.36876316169 + 6360.99343790291*$t);
$Y1 += 0.00000000027*cos(4.95719787895 + 31172.8944634665*$t);
$Y1 += 0.00000000026*cos(2.19655051246 + 36949.4746259077*$t);
$Y1 += 0.00000000034*cos(4.45594644643 + 18053.1733606413*$t);
$Y1 += 0.00000000027*cos(0.74968073356 + 32367.3414736911*$t);
$Y1 += 0.00000000027*cos(3.34260766105 + 4487.57358878689*$t);
$Y1 += 0.00000000028*cos(5.37411547339 + 10239.3400485273*$t);
$Y1 += 0.00000000026*cos(1.30232025786 + 4796.85191144269*$t);
$Y1 += 0.00000000026*cos(4.70861603764 + 6226.4212925393*$t);
$Y1 += 0.00000000026*cos(5.08151018860 + 6340.2180424105*$t);
$Y1 += 0.00000000029*cos(4.90026899469 + 5974.0413448191*$t);
$Y1 += 0.00000000029*cos(4.88985723155 + 6592.5979901307*$t);
$Y1 += 0.00000000026*cos(4.96950484222 + 19402.55313533309*$t);
$Y1 += 0.00000000028*cos(3.99925126629 + 46386.7499258277*$t);
$Y1 += 0.00000000032*cos(5.04462761864 + 9225.7830907665*$t);
$Y1 += 0.00000000026*cos(4.11745014890 + 9910.33951002549*$t);
$Y1 += 0.00000000025*cos(1.02839985963 + 15265.64270181689*$t);
$Y1 += 0.00000000029*cos(4.33416022359 + 52176.0501006319*$t);
$Y1 += 0.00000000027*cos(2.65258449905 + 62883.5989569971*$t);
$Y1 += 0.00000000024*cos(5.26265995716 + 11617.21990849651*$t);
$Y1 += 0.00000000024*cos(1.04936648816 + 5120.8449630671*$t);
$Y1 += 0.00000000028*cos(4.82143927810 + 6680.98103591609*$t);
$Y1 += 0.00000000024*cos(5.97769334002 + 522.3336006103*$t);
$Y1 += 0.00000000025*cos(2.29282659231 + 6263.64990657511*$t);
$Y1 += 0.00000000025*cos(1.21411432675 + 6302.9894283747*$t);
$Y1 += 0.00000000029*cos(0.87325499796 + 23581.5019948011*$t);
$Y1 += 0.00000000024*cos(5.21948189448 + 29424.8780503995*$t);
$Y1 += 0.00000000028*cos(1.09161353868 + 16737.8210540801*$t);
$Y1 += 0.00000000024*cos(3.55960074091 + 22743.16556203289*$t);
$Y1 += 0.00000000024*cos(3.55960074091 + 22743.6531969999*$t);
$Y1 += 0.00000000024*cos(4.28222488832 + 25158.8455372489*$t);
$Y1 += 0.00000000025*cos(5.52194731109 + 21424.2228268199*$t);
$Y1 += 0.00000000025*cos(5.52194731109 + 21424.7104617869*$t);
$Y1 += 0.00000000024*cos(3.49943174674 + 14712.07329897449*$t);
$Y1 += 0.00000000028*cos(6.07681616993 + 5760.25461441409*$t);
$Y1 += 0.00000000024*cos(2.16376008059 + 31969.1924702829*$t);
$Y1 += 0.00000000023*cos(5.33584675127 + 17893.1822114871*$t);
$Y1 += 0.00000000030*cos(2.28483676839 + 8584.9054833843*$t);
$Y1 += 0.00000000024*cos(1.64666673478 + 23550.5878691661*$t);
$Y1 += 0.00000000023*cos(6.07302432574 + 6717.0314053517*$t);
$Y1 += 0.00000000022*cos(2.42662159283 + 7445.7943718827*$t);
$Y1 += 0.00000000023*cos(3.56571153376 + 5849.6079295981*$t);
$Y1 += 0.00000000025*cos(5.52794317615 + 14155.4684127501*$t);
$Y1 += 0.00000000023*cos(2.01489779401 + 6294.36536773881*$t);
$Y1 += 0.00000000023*cos(1.49204312505 + 6272.273967211*$t);
$Y1 += 0.00000000024*cos(5.81677586075 + 18208.1061251085*$t);
$Y1 += 0.00000000024*cos(5.81677586075 + 18208.5937600755*$t);
$Y1 += 0.00000000021*cos(4.21172313283 + 22779.6810636773*$t);
$Y1 += 0.00000000029*cos(1.74369099855 + 28628.5800435831*$t);
$Y1 += 0.00000000021*cos(3.56347944199 + 40879.6843221273*$t);
$Y1 += 0.00000000021*cos(2.51496251708 + 30221.1760572159*$t);
$Y1 += 0.00000000022*cos(6.09500922463 + 4379.8828549737*$t);
$Y1 += 0.00000000022*cos(3.69512347867 + 8186.7564799761*$t);
$Y1 += 0.00000000022*cos(2.95145769488 + 28760.05469496669*$t);
$Y1 += 0.00000000026*cos(1.83973482412 + 18422.8731765817*$t);
$Y1 += 0.00000000020*cos(2.37799900039 + 12036.21691740469*$t);
$Y1 += 0.00000000020*cos(0.07485283254 + 28313.0449871775*$t);
$Y1 += 0.00000000027*cos(5.38239668902 + 34513.5068901663*$t);
$Y1 += 0.00000000020*cos(0.50551300300 + 34115.3578867581*$t);
$Y1 += 0.00000000020*cos(3.29228335956 + 21548.7185518083*$t);
$Y1 += 0.00000000020*cos(5.25656062979 + 17654.5367222661*$t);
$Y1 += 0.00000000025*cos(1.96130235408 + 55798.7021758819*$t);
$Y1 += 0.00000000020*cos(5.53200449549 + 20597.4877805247*$t);
$Y1 += 0.00000000020*cos(1.03604717996 + 18875.76968725751*$t);
$Y1 += 0.00000000022*cos(2.01853988925 + 1588.82907780029*$t);
$Y1 += 0.00000000024*cos(5.92091322542 + 9411.7084325707*$t);
$Y1 += 0.00000000019*cos(1.14706242910 + 536.5606946119*$t);
$Y1 += 0.00000000020*cos(3.42481272827 + 6187.3404402571*$t);
$Y1 += 0.00000000020*cos(0.08212819079 + 6379.2988946927*$t);
$Y1 += 0.00000000022*cos(2.87392170851 + 18326.8939493639*$t);
$Y1 += 0.00000000022*cos(0.61268580951 + 6233.5626420031*$t);
$Y1 += 0.00000000022*cos(2.89425510955 + 6333.0766929467*$t);
$Y1 += 0.00000000018*cos(0.45956662142 + 5972.4788686065*$t);
$Y1 += 0.00000000018*cos(3.04737429764 + 6594.1604663433*$t);
$Y1 += 0.00000000019*cos(2.71317971903 + 6948.0757126049*$t);
$Y1 += 0.00000000019*cos(0.79376120003 + 5618.5636223449*$t);
$Y1 += 0.00000000019*cos(4.89700264579 + 83974.07917321339*$t);
$Y1 += 0.00000000019*cos(2.72494811319 + 84020.10309797739*$t);
$Y1 += 0.00000000020*cos(5.42036659910 + 50316.9596220473*$t);
$Y1 += 0.00000000020*cos(1.28312164242 + 9070.3626913323*$t);
return $Y1*$t;
}
function Earth_Y2($t) // 248 terms of order 2
{
$Y2 = 0.00052911498*cos(1.75323722235 + 6283.3196674749*$t);
$Y2 += 0.00006074441*cos(0.48406211192 + 0.2438174835*$t);
$Y2 += 0.00002406871*cos(2.66006394470 + 12566.3955174663*$t);
$Y2 += 0.00000096033*cos(2.57406136836 + 18849.4713674577*$t);
$Y2 += 0.00000029888*cos(2.30515825272 + 6282.83203250789*$t);
$Y2 += 0.00000014021*cos(1.64042051619 + 6279.7965491259*$t);
$Y2 += 0.00000013375*cos(1.74320372785 + 6286.84278582391*$t);
$Y2 += 0.00000008148*cos(0.62869530307 + 6309.61798727471*$t);
$Y2 += 0.00000008195*cos(2.81874475342 + 6257.0213476751*$t);
$Y2 += 0.00000008001*cos(4.34877296703 + 6127.8992680407*$t);
$Y2 += 0.00000007754*cos(5.43470598991 + 6438.7400669091*$t);
$Y2 += 0.00000007223*cos(3.81034638754 + 83997.09113559539*$t);
$Y2 += 0.00000004616*cos(4.59623594691 + 710.1768660418*$t);
$Y2 += 0.00000003060*cos(3.26884940633 + 4705.9761250271*$t);
$Y2 += 0.00000003717*cos(0.87961276723 + 5507.7970561509*$t);
$Y2 += 0.00000002991*cos(2.48913608928 + 25132.5472174491*$t);
$Y2 += 0.00000003235*cos(2.53504921673 + 7058.8422787989*$t);
$Y2 += 0.00000002393*cos(1.83696733237 + 775.7664288075*$t);
$Y2 += 0.00000002034*cos(2.77061597204 + 6290.4332144757*$t);
$Y2 += 0.00000002028*cos(0.70943948464 + 6276.2061204741*$t);
$Y2 += 0.00000002064*cos(0.01448293997 + 7860.6632099227*$t);
$Y2 += 0.00000001914*cos(2.85234479868 + 5487.0216606585*$t);
$Y2 += 0.00000001770*cos(3.48783151064 + 1059.6257476727*$t);
$Y2 += 0.00000001761*cos(1.80823220260 + 5753.6287023803*$t);
$Y2 += 0.00000001558*cos(0.56580595512 + 7079.61767429131*$t);
$Y2 += 0.00000001551*cos(0.55852743151 + 6040.5910635009*$t);
$Y2 += 0.00000001436*cos(1.28164050883 + 5885.1706640667*$t);
$Y2 += 0.00000001469*cos(2.94324921966 + 6526.04827144891*$t);
$Y2 += 0.00000001319*cos(1.89155311923 + 6681.46867088311*$t);
$Y2 += 0.00000001180*cos(1.42090963151 + 6813.0106325695*$t);
$Y2 += 0.00000001337*cos(5.75221416852 + 5729.7502646325*$t);
$Y2 += 0.00000001039*cos(4.25243426113 + 6282.3393464067*$t);
$Y2 += 0.00000001313*cos(0.59897551240 + 529.9347825781*$t);
$Y2 += 0.00000001041*cos(5.47801377680 + 6284.2999885431*$t);
$Y2 += 0.00000001202*cos(4.02829547071 + 6836.8890703173*$t);
$Y2 += 0.00000000904*cos(0.85768945907 + 5331.6012612243*$t);
$Y2 += 0.00000000870*cos(2.26660468565 + 4933.4522578161*$t);
$Y2 += 0.00000001149*cos(3.02450680654 + 167284.00540514899*$t);
$Y2 += 0.00000001069*cos(1.09203232944 + 1577.0997249643*$t);
$Y2 += 0.00000000772*cos(2.66290097432 + 7235.0380737255*$t);
$Y2 += 0.00000000846*cos(1.36798976406 + 11790.8729061423*$t);
$Y2 += 0.00000000742*cos(5.02007434299 + 4137.1542509997*$t);
$Y2 += 0.00000000966*cos(2.05227643484 + 11856.462468908*$t);
$Y2 += 0.00000000664*cos(1.21776131888 + 7633.1870771337*$t);
$Y2 += 0.00000000662*cos(3.18968574411 + 1194.6908277081*$t);
$Y2 += 0.00000000659*cos(5.95013449282 + 11507.0135872771*$t);
$Y2 += 0.00000000853*cos(3.65338850674 + 4535.3032544079*$t);
$Y2 += 0.00000000823*cos(1.06126729936 + 155.17658195069*$t);
$Y2 += 0.00000000783*cos(4.30296275012 + 5088.8726572503*$t);
$Y2 += 0.00000000785*cos(3.46658763633 + 2353.1099712553*$t);
$Y2 += 0.00000000694*cos(3.50785804761 + 801.5771136403*$t);
$Y2 += 0.00000000566*cos(4.42922662864 + 796.5418242999*$t);
$Y2 += 0.00000000684*cos(1.11267726523 + 3128.6325825793*$t);
$Y2 += 0.00000000499*cos(1.42594865875 + 12569.91863581531*$t);
$Y2 += 0.00000000596*cos(6.09778115923 + 8031.3360805419*$t);
$Y2 += 0.00000000486*cos(4.54237345712 + 1589.3167127673*$t);
$Y2 += 0.00000000483*cos(4.68204073064 + 8429.4850839501*$t);
$Y2 += 0.00000000441*cos(4.99112466662 + 6496.6187629129*$t);
$Y2 += 0.00000000412*cos(0.87602065813 + 4693.75913722409*$t);
$Y2 += 0.00000000561*cos(5.46330573132 + 7477.7666776995*$t);
$Y2 += 0.00000000390*cos(4.63888431687 + 6070.0205720369*$t);
$Y2 += 0.00000000405*cos(6.26538093406 + 3739.0052475915*$t);
$Y2 += 0.00000000501*cos(1.82149883986 + 1592.8398311163*$t);
$Y2 += 0.00000000392*cos(0.68216396598 + 26.0545023163*$t);
$Y2 += 0.00000000369*cos(5.93410776393 + 553.32558535889*$t);
$Y2 += 0.00000000483*cos(6.07777893059 + 12036.7045523717*$t);
$Y2 += 0.00000000489*cos(3.70668603785 + 5223.4501023187*$t);
$Y2 += 0.00000000481*cos(3.17195852109 + 10213.5293636945*$t);
$Y2 += 0.00000000448*cos(5.56847234629 + 156137.71980228279*$t);
$Y2 += 0.00000000321*cos(4.53991511859 + 951.4745887671*$t);
$Y2 += 0.00000000320*cos(0.43138538654 + 1990.9888345245*$t);
$Y2 += 0.00000000361*cos(2.16599134100 + 12565.9078824993*$t);
$Y2 += 0.00000000361*cos(4.79823251497 + 12721.8159169005*$t);
$Y2 += 0.00000000412*cos(4.34259218946 + 398.3928208917*$t);
$Y2 += 0.00000000304*cos(5.68078111352 + 4690.7236538421*$t);
$Y2 += 0.00000000356*cos(6.00094576166 + 5481.4987363511*$t);
$Y2 += 0.00000000283*cos(0.66912545661 + 242.97242145751*$t);
$Y2 += 0.00000000362*cos(2.31554210740 + 9438.0067523705*$t);
$Y2 += 0.00000000248*cos(3.18243221495 + 8827.6340873583*$t);
$Y2 += 0.00000000252*cos(2.73244620528 + 3154.4432674121*$t);
$Y2 += 0.00000000257*cos(0.22372520009 + 11371.9485072417*$t);
$Y2 += 0.00000000327*cos(1.45001600721 + 14143.7390599141*$t);
$Y2 += 0.00000000230*cos(1.80447328493 + 1747.7725955835*$t);
$Y2 += 0.00000000289*cos(3.67617510107 + 7085.1405985987*$t);
$Y2 += 0.00000000297*cos(3.17045499445 + 1349.62359217529*$t);
$Y2 += 0.00000000209*cos(4.98580572759 + 11770.0975106499*$t);
$Y2 += 0.00000000207*cos(0.21623312501 + 4164.0681721295*$t);
$Y2 += 0.00000000188*cos(4.07593821324 + 7875.91568110771*$t);
$Y2 += 0.00000000189*cos(5.31784128034 + 2389.1378379327*$t);
$Y2 += 0.00000000194*cos(5.12285857348 + 10977.32262218251*$t);
$Y2 += 0.00000000176*cos(2.51491286893 + 7342.7015976641*$t);
$Y2 += 0.00000000164*cos(1.22070775546 + 5223.93773728571*$t);
$Y2 += 0.00000000205*cos(1.64290799201 + 10973.7995038335*$t);
$Y2 += 0.00000000205*cos(0.68022152849 + 13368.2164485901*$t);
$Y2 += 0.00000000139*cos(3.04789845179 + 10575.6505004253*$t);
$Y2 += 0.00000000155*cos(4.24333188820 + 12410.9751180321*$t);
$Y2 += 0.00000000152*cos(4.81739365185 + 3930.4535137031*$t);
$Y2 += 0.00000000129*cos(0.80954637051 + 397.9051859247*$t);
$Y2 += 0.00000000127*cos(5.67893828134 + 12592.6938372661*$t);
$Y2 += 0.00000000132*cos(4.87291664360 + 8636.18582124671*$t);
$Y2 += 0.00000000122*cos(3.21278850975 + 13119.9649203087*$t);
$Y2 += 0.00000000163*cos(2.50359725386 + 5507.3094211839*$t);
$Y2 += 0.00000000114*cos(4.13352060999 + 17260.3984721739*$t);
$Y2 += 0.00000000118*cos(0.80775184774 + 4292.5746504339*$t);
$Y2 += 0.00000000148*cos(4.06616105867 + 17790.08943726851*$t);
$Y2 += 0.00000000123*cos(2.18706277371 + 12562.8723991173*$t);
$Y2 += 0.00000000103*cos(1.79915109205 + 13518.1139237169*$t);
$Y2 += 0.00000000138*cos(2.26785827403 + 12168.2465140581*$t);
$Y2 += 0.00000000107*cos(2.76898193474 + 10989.0519750185*$t);
$Y2 += 0.00000000104*cos(0.56758990747 + 2145.92159899169*$t);
$Y2 += 0.00000000096*cos(0.40713285174 + 6283.25235717211*$t);
$Y2 += 0.00000000099*cos(0.70751931715 + 13096.0864825609*$t);
$Y2 += 0.00000000096*cos(6.24621518908 + 6283.3869777777*$t);
$Y2 += 0.00000000084*cos(3.63516988010 + 16730.70750707931*$t);
$Y2 += 0.00000000111*cos(2.39242858566 + 12540.0971976665*$t);
$Y2 += 0.00000000087*cos(4.45435464785 + 10177.5014970171*$t);
$Y2 += 0.00000000078*cos(2.61342989032 + 12323.6669134923*$t);
$Y2 += 0.00000000076*cos(4.13782411870 + 6709.91785835091*$t);
$Y2 += 0.00000000105*cos(1.96765772501 + 5642.4420600927*$t);
$Y2 += 0.00000000073*cos(5.60932378402 + 5856.7214765989*$t);
$Y2 += 0.00000000102*cos(5.37997051996 + 250570.91967470259*$t);
$Y2 += 0.00000000070*cos(0.51266920771 + 5753.14106741329*$t);
$Y2 += 0.00000000071*cos(5.27404987073 + 14314.4119305333*$t);
$Y2 += 0.00000000092*cos(0.39406209616 + 13916.2629271251*$t);
$Y2 += 0.00000000070*cos(4.10529685600 + 7084.6529636317*$t);
$Y2 += 0.00000000091*cos(1.53880932897 + 6924.1972748571*$t);
$Y2 += 0.00000000083*cos(2.41910116753 + 31415.6230674405*$t);
$Y2 += 0.00000000088*cos(0.30300511757 + 71430.45180064559*$t);
$Y2 += 0.00000000074*cos(3.53618023271 + 529.44714761109*$t);
$Y2 += 0.00000000085*cos(4.40773297118 + 95143.37673846159*$t);
$Y2 += 0.00000000061*cos(2.66034748981 + 8274.0646845159*$t);
$Y2 += 0.00000000060*cos(3.95075537336 + 16496.6052136859*$t);
$Y2 += 0.00000000058*cos(3.04970743906 + 5642.93474619389*$t);
$Y2 += 0.00000000078*cos(0.84061745785 + 213.5429129215*$t);
$Y2 += 0.00000000059*cos(3.10446906052 + 640.1411037975*$t);
$Y2 += 0.00000000057*cos(3.63209087311 + 4690.23601887509*$t);
$Y2 += 0.00000000056*cos(2.23091315346 + 13341.9181287903*$t);
$Y2 += 0.00000000065*cos(4.95952410600 + 4731.7868098599*$t);
$Y2 += 0.00000000051*cos(0.09929724563 + 3893.93801205869*$t);
$Y2 += 0.00000000050*cos(2.60290043400 + 12573.5090644671*$t);
$Y2 += 0.00000000050*cos(5.98749446465 + 3634.37720703489*$t);
$Y2 += 0.00000000049*cos(0.70632876133 + 18319.7804023631*$t);
$Y2 += 0.00000000066*cos(3.92505951821 + 2787.2868413409*$t);
$Y2 += 0.00000000049*cos(0.42825389697 + 13362.6935242827*$t);
$Y2 += 0.00000000048*cos(2.19153498916 + 12964.5445208745*$t);
$Y2 += 0.00000000053*cos(2.55294637714 + 14919.2616712381*$t);
$Y2 += 0.00000000058*cos(5.94322042199 + 1577.5873599313*$t);
$Y2 += 0.00000000052*cos(5.99067773035 + 15721.0826023619*$t);
$Y2 += 0.00000000061*cos(4.99956015956 + 4292.0870154669*$t);
$Y2 += 0.00000000044*cos(5.02285128905 + 24073.1652872599*$t);
$Y2 += 0.00000000044*cos(1.96034093811 + 10447.14402212089*$t);
$Y2 += 0.00000000042*cos(2.52906622396 + 20426.8149099055*$t);
$Y2 += 0.00000000059*cos(2.58678833053 + 84672.23202702119*$t);
$Y2 += 0.00000000051*cos(3.81200106179 + 6370.62787201471*$t);
$Y2 += 0.00000000051*cos(5.97812516445 + 6196.0114629351*$t);
$Y2 += 0.00000000046*cos(5.23410298912 + 2119.00767786191*$t);
$Y2 += 0.00000000041*cos(2.52248241350 + 3185.43584474911*$t);
$Y2 += 0.00000000056*cos(4.84268946755 + 10976.83498721549*$t);
$Y2 += 0.00000000051*cos(3.94604483748 + 9437.5191174035*$t);
$Y2 += 0.00000000049*cos(1.64079935270 + 239424.63407183639*$t);
$Y2 += 0.00000000036*cos(1.49154565635 + 3495.78900865049*$t);
$Y2 += 0.00000000044*cos(2.12316916648 + 18139.5383188994*$t);
$Y2 += 0.00000000035*cos(5.18466509768 + 3929.96587873609*$t);
$Y2 += 0.00000000044*cos(3.23094444076 + 8661.9965060795*$t);
$Y2 += 0.00000000046*cos(2.21535532938 + 3894.4256470257*$t);
$Y2 += 0.00000000034*cos(2.24364878116 + 6262.5442719825*$t);
$Y2 += 0.00000000034*cos(4.40970135798 + 6304.0950629673*$t);
$Y2 += 0.00000000035*cos(5.15488505358 + 18875.2820522905*$t);
$Y2 += 0.00000000035*cos(4.51996316476 + 10420.23010099111*$t);
$Y2 += 0.00000000032*cos(5.33774590597 + 23013.7833570707*$t);
$Y2 += 0.00000000034*cos(2.04067717162 + 7.3573644843*$t);
$Y2 += 0.00000000045*cos(6.20022544523 + 3340.8562441833*$t);
$Y2 += 0.00000000035*cos(1.95669709650 + 10213.0417287275*$t);
$Y2 += 0.00000000031*cos(3.81393239996 + 14712.5609339415*$t);
$Y2 += 0.00000000030*cos(2.82636067861 + 12809.12412144031*$t);
$Y2 += 0.00000000039*cos(5.86021469295 + 9779.3524936089*$t);
$Y2 += 0.00000000041*cos(0.90085517811 + 82576.73740351178*$t);
$Y2 += 0.00000000031*cos(5.47911308336 + 22779.6810636773*$t);
$Y2 += 0.00000000028*cos(2.50895957020 + 2942.7072407751*$t);
$Y2 += 0.00000000028*cos(3.93140481871 + 5429.63565075589*$t);
$Y2 += 0.00000000027*cos(5.61355223000 + 11014.8626598513*$t);
$Y2 += 0.00000000027*cos(0.53944014317 + 9623.9320941747*$t);
$Y2 += 0.00000000025*cos(0.15499921281 + 18209.5740811437*$t);
$Y2 += 0.00000000026*cos(0.97984555070 + 9381.2034902007*$t);
$Y2 += 0.00000000025*cos(1.11733310909 + 3583.5848481573*$t);
$Y2 += 0.00000000030*cos(4.41826131323 + 10447.6316570879*$t);
$Y2 += 0.00000000032*cos(5.65959938774 + 796.0541893329*$t);
$Y2 += 0.00000000023*cos(1.38575591729 + 9917.45305702629*$t);
$Y2 += 0.00000000026*cos(5.61732376806 + 12012.8261146239*$t);
$Y2 += 0.00000000024*cos(3.45407340381 + 14143.2514249471*$t);
$Y2 += 0.00000000023*cos(0.69647593831 + 26709.8907598969*$t);
$Y2 += 0.00000000021*cos(5.43974830479 + 7632.6994421667*$t);
$Y2 += 0.00000000021*cos(0.80058820514 + 17256.8753538249*$t);
$Y2 += 0.00000000028*cos(5.78689433830 + 12353.0964220283*$t);
$Y2 += 0.00000000022*cos(3.26384247748 + 77714.01528560399*$t);
$Y2 += 0.00000000021*cos(4.41664687493 + 6993.2527160332*$t);
$Y2 += 0.00000000020*cos(1.88345295944 + 6836.40143535029*$t);
$Y2 += 0.00000000020*cos(3.87252932348 + 1748.2602305505*$t);
$Y2 += 0.00000000026*cos(0.45595739946 + 9225.7830907665*$t);
$Y2 += 0.00000000023*cos(5.52071600644 + 149854.64395229139*$t);
$Y2 += 0.00000000026*cos(0.60119736394 + 2544.07060239989*$t);
$Y2 += 0.00000000018*cos(0.71176167314 + 11614.6771112157*$t);
$Y2 += 0.00000000020*cos(3.04333652471 + 426.8420083595*$t);
$Y2 += 0.00000000019*cos(2.09021029647 + 30640.1004561165*$t);
$Y2 += 0.00000000018*cos(3.20715016441 + 155.6642169177*$t);
$Y2 += 0.00000000018*cos(0.32502884515 + 11926.4982311523*$t);
$Y2 += 0.00000000022*cos(2.17863705978 + 17298.4261448097*$t);
$Y2 += 0.00000000019*cos(4.82590950931 + 18073.46112116669*$t);
$Y2 += 0.00000000020*cos(1.02950628439 + 19651.2922985815*$t);
$Y2 += 0.00000000024*cos(3.14467908991 + 5856.23384163189*$t);
$Y2 += 0.00000000023*cos(3.21288696705 + 72850.80553272919*$t);
$Y2 += 0.00000000017*cos(2.38623798159 + 8983.0544867925*$t);
$Y2 += 0.00000000016*cos(3.59989563011 + 16460.5773470085*$t);
$Y2 += 0.00000000016*cos(2.77179277240 + 17259.91083720689*$t);
$Y2 += 0.00000000021*cos(2.20286926080 + 16858.7263504167*$t);
$Y2 += 0.00000000020*cos(5.10666464640 + 23543.4743221653*$t);
$Y2 += 0.00000000021*cos(5.36525328799 + 13367.7288136231*$t);
$Y2 += 0.00000000020*cos(2.47582665567 + 2146.4092339587*$t);
$Y2 += 0.00000000014*cos(4.85508264889 + 22484.0923919761*$t);
$Y2 += 0.00000000014*cos(6.23679853613 + 16200.52890701769*$t);
$Y2 += 0.00000000015*cos(2.64768344463 + 20199.3387771165*$t);
$Y2 += 0.00000000019*cos(1.24340851761 + 8672.21368792411*$t);
$Y2 += 0.00000000019*cos(2.89835524904 + 18073.9487561337*$t);
$Y2 += 0.00000000013*cos(3.14350306699 + 16201.0165419847*$t);
$Y2 += 0.00000000017*cos(2.96004801328 + 7860.17557495569*$t);
$Y2 += 0.00000000013*cos(3.12347768998 + 18451.3223640495*$t);
$Y2 += 0.00000000016*cos(4.90276494200 + 5572.8989839496*$t);
$Y2 += 0.00000000012*cos(1.13909733386 + 17996.2749857057*$t);
$Y2 += 0.00000000012*cos(5.43460350187 + 19403.0407703001*$t);
$Y2 += 0.00000000012*cos(0.82655936469 + 14945.0723560709*$t);
$Y2 += 0.00000000015*cos(0.47799392266 + 12559.2819704655*$t);
$Y2 += 0.00000000012*cos(2.80799572996 + 10818.3791043993*$t);
$Y2 += 0.00000000015*cos(5.28864619208 + 12567.37583853451*$t);
$Y2 += 0.00000000011*cos(0.21391675163 + 28767.1682419675*$t);
$Y2 += 0.00000000013*cos(5.80786469706 + 90280.16698558679*$t);
$Y2 += 0.00000000011*cos(0.30991526634 + 22805.4917485101*$t);
$Y2 += 0.00000000011*cos(0.67526353010 + 35372.1310834599*$t);
$Y2 += 0.00000000010*cos(1.54770241799 + 11506.52595231009*$t);
$Y2 += 0.00000000014*cos(0.36722951229 + 21228.63584102931*$t);
$Y2 += 0.00000000010*cos(4.84303300061 + 12779.6946129043*$t);
$Y2 += 0.00000000010*cos(4.48229440272 + 23141.8022004081*$t);
$Y2 += 0.00000000010*cos(5.89241784221 + 1350.1112271423*$t);
$Y2 += 0.00000000010*cos(4.07842068364 + 10575.1628654583*$t);
$Y2 += 0.00000000010*cos(0.98564127078 + 22345.5041935917*$t);
$Y2 += 0.00000000010*cos(0.62034181586 + 9778.8648586419*$t);
$Y2 += 0.00000000009*cos(6.20390809264 + 29826.5501721567*$t);
$Y2 += 0.00000000010*cos(2.66921279687 + 23581.5019948011*$t);
$Y2 += 0.00000000011*cos(5.10849785178 + 25158.8455372489*$t);
return $Y2*$t*$t;
}
function Earth_Y3($t) // 46 terms of order 3
{
$Y3 = 0.00000232790*cos(1.83555296287 + 0.2438174835*$t);
$Y3 += 0.00000076843*cos(0.95359770708 + 12566.3955174663*$t);
$Y3 += 0.00000035331*cos(1.77537067174 + 6283.3196674749*$t);
$Y3 += 0.00000005282*cos(0.83410185910 + 18849.4713674577*$t);
$Y3 += 0.00000001631*cos(0.72620862558 + 6282.83203250789*$t);
$Y3 += 0.00000001483*cos(0.65599216587 + 6438.7400669091*$t);
$Y3 += 0.00000001479*cos(2.83072127404 + 6127.8992680407*$t);
$Y3 += 0.00000000652*cos(3.13796451313 + 6279.7965491259*$t);
$Y3 += 0.00000000656*cos(0.01615422945 + 6286.84278582391*$t);
$Y3 += 0.00000000317*cos(1.43157695840 + 6526.04827144891*$t);
$Y3 += 0.00000000318*cos(2.05944515679 + 6040.5910635009*$t);
$Y3 += 0.00000000227*cos(0.70881980797 + 25132.5472174491*$t);
$Y3 += 0.00000000201*cos(5.52615570373 + 6836.8890703173*$t);
$Y3 += 0.00000000201*cos(4.23563267830 + 5729.7502646325*$t);
$Y3 += 0.00000000036*cos(6.05003898151 + 12569.91863581531*$t);
$Y3 += 0.00000000034*cos(0.36912822345 + 4705.9761250271*$t);
$Y3 += 0.00000000033*cos(2.65665718326 + 12410.9751180321*$t);
$Y3 += 0.00000000032*cos(3.81269087187 + 6257.0213476751*$t);
$Y3 += 0.00000000032*cos(2.84133186500 + 6309.61798727471*$t);
$Y3 += 0.00000000026*cos(5.21573736647 + 775.7664288075*$t);
$Y3 += 0.00000000023*cos(0.44696909593 + 1059.6257476727*$t);
$Y3 += 0.00000000025*cos(0.01326357360 + 7860.6632099227*$t);
$Y3 += 0.00000000027*cos(0.46730161827 + 12565.9078824993*$t);
$Y3 += 0.00000000020*cos(2.19213288615 + 5753.6287023803*$t);
$Y3 += 0.00000000019*cos(1.44435756454 + 5885.1706640667*$t);
$Y3 += 0.00000000019*cos(4.47976718197 + 6813.0106325695*$t);
$Y3 += 0.00000000018*cos(0.72211012099 + 12721.8159169005*$t);
$Y3 += 0.00000000017*cos(5.20474716177 + 6681.46867088311*$t);
$Y3 += 0.00000000013*cos(2.92478174105 + 5487.0216606585*$t);
$Y3 += 0.00000000011*cos(3.72062261949 + 7079.61767429131*$t);
$Y3 += 0.00000000010*cos(2.89167021825 + 5507.7970561509*$t);
$Y3 += 0.00000000010*cos(1.46762801985 + 11790.8729061423*$t);
$Y3 += 0.00000000009*cos(6.21784065295 + 11507.0135872771*$t);
$Y3 += 0.00000000011*cos(4.68801103302 + 12592.6938372661*$t);
$Y3 += 0.00000000009*cos(3.82179163254 + 7058.8422787989*$t);
$Y3 += 0.00000000008*cos(5.97770881958 + 6290.4332144757*$t);
$Y3 += 0.00000000008*cos(0.68313431813 + 6276.2061204741*$t);
$Y3 += 0.00000000008*cos(1.45990791265 + 796.5418242999*$t);
$Y3 += 0.00000000007*cos(4.15465801739 + 4693.75913722409*$t);
$Y3 += 0.00000000007*cos(0.35078036011 + 7.3573644843*$t);
$Y3 += 0.00000000005*cos(3.29483739022 + 3739.0052475915*$t);
$Y3 += 0.00000000005*cos(4.64160679165 + 6070.0205720369*$t);
$Y3 += 0.00000000006*cos(2.38483297622 + 6284.2999885431*$t);
$Y3 += 0.00000000006*cos(4.26851560652 + 6282.3393464067*$t);
$Y3 += 0.00000000005*cos(1.89668032657 + 4137.1542509997*$t);
$Y3 += 0.00000000005*cos(2.01213704309 + 6496.6187629129*$t);
return $Y3*$t*$t*$t;
}
function Earth_Y4($t) // 20 terms of order 4
{
$Y4 = 0.00000114918*cos(4.77291921544 + 6283.3196674749*$t);
$Y4 += 0.00000006817*cos(2.90545031303 + 0.2438174835*$t);
$Y4 += 0.00000003158*cos(5.19149443854 + 12566.3955174663*$t);
$Y4 += 0.00000000211*cos(2.15272014034 + 6438.7400669091*$t);
$Y4 += 0.00000000210*cos(1.31410288968 + 6127.8992680407*$t);
$Y4 += 0.00000000253*cos(5.35904773722 + 18849.4713674577*$t);
$Y4 += 0.00000000073*cos(5.49456429263 + 6282.83203250789*$t);
$Y4 += 0.00000000042*cos(3.03243163257 + 710.1768660418*$t);
$Y4 += 0.00000000023*cos(4.47433896564 + 6279.7965491259*$t);
$Y4 += 0.00000000022*cos(4.47061131203 + 6286.84278582391*$t);
$Y4 += 0.00000000012*cos(5.22878976906 + 25132.5472174491*$t);
$Y4 += 0.00000000009*cos(2.63928422881 + 83997.09113559539*$t);
$Y4 += 0.00000000009*cos(3.62312855703 + 11856.462468908*$t);
$Y4 += 0.00000000008*cos(4.59507616558 + 167284.00540514899*$t);
$Y4 += 0.00000000005*cos(4.40834364231 + 6257.0213476751*$t);
$Y4 += 0.00000000005*cos(2.21798830782 + 6309.61798727471*$t);
$Y4 += 0.00000000005*cos(1.11835906029 + 12410.9751180321*$t);
$Y4 += 0.00000000005*cos(3.99770824807 + 156137.71980228279*$t);
$Y4 += 0.00000000004*cos(4.97197978751 + 12565.9078824993*$t);
$Y4 += 0.00000000003*cos(3.60141861387 + 529.9347825781*$t);
return $Y4*$t*$t*$t*$t;
}
function Earth_Y5($t) // 7 terms of order 5
{
$Y5 = 0.00000000877*cos(4.87375194107 + 6283.3196674749*$t);
$Y5 += 0.00000000305*cos(4.05893642248 + 0.2438174835*$t);
$Y5 += 0.00000000101*cos(3.30997066470 + 12566.3955174663*$t);
$Y5 += 0.00000000025*cos(3.73514325706 + 6438.7400669091*$t);
$Y5 += 0.00000000025*cos(5.99118011879 + 6127.8992680407*$t);
$Y5 += 0.00000000010*cos(3.54319653898 + 18849.4713674577*$t);
$Y5 += 0.00000000003*cos(4.13285368647 + 6282.83203250789*$t);
return $Y5*$t*$t*$t*$t*$t;
}
function Earth_Z0($t) // 178 terms of order 0
{
$Z0 = 0.00000279620*cos(3.19870156017 + 84334.66158130829*$t);
$Z0 += 0.00000101625*cos(5.42248110597 + 5507.5532386674*$t);
$Z0 += 0.00000080461*cos(3.88027157914 + 5223.6939198022*$t);
$Z0 += 0.00000043855*cos(3.70430347723 + 2352.8661537718*$t);
$Z0 += 0.00000031853*cos(3.99997840986 + 1577.3435424478*$t);
$Z0 += 0.00000022724*cos(3.98473831560 + 1047.7473117547*$t);
$Z0 += 0.00000016395*cos(3.56456162523 + 5856.4776591154*$t);
$Z0 += 0.00000018150*cos(4.98479613321 + 6283.0758499914*$t);
$Z0 += 0.00000014477*cos(3.70258423465 + 9437.762934887*$t);
$Z0 += 0.00000014325*cos(3.41020246931 + 10213.285546211*$t);
$Z0 += 0.00000011204*cos(4.83021499098 + 14143.4952424306*$t);
$Z0 += 0.00000010896*cos(2.08023708321 + 6812.766815086*$t);
$Z0 += 0.00000009716*cos(3.47560205064 + 4694.0029547076*$t);
$Z0 += 0.00000010363*cos(4.05663928093 + 71092.88135493269*$t);
$Z0 += 0.00000008792*cos(4.44890729280 + 5753.3848848968*$t);
$Z0 += 0.00000008337*cos(4.99167706048 + 7084.8967811152*$t);
$Z0 += 0.00000006921*cos(4.32559054073 + 6275.9623029906*$t);
$Z0 += 0.00000009145*cos(1.14182646613 + 6620.8901131878*$t);
$Z0 += 0.00000007205*cos(3.62441599378 + 529.6909650946*$t);
$Z0 += 0.00000007698*cos(5.55425745881 + 167621.57585086189*$t);
$Z0 += 0.00000005186*cos(6.25384533126 + 18073.7049386502*$t);
$Z0 += 0.00000005027*cos(2.49727910749 + 4705.7323075436*$t);
$Z0 += 0.00000004529*cos(2.33827747356 + 6309.3741697912*$t);
$Z0 += 0.00000004754*cos(0.71100829534 + 5884.9268465832*$t);
$Z0 += 0.00000004292*cos(1.10034019036 + 6681.2248533996*$t);
$Z0 += 0.00000003855*cos(1.82331477760 + 5486.777843175*$t);
$Z0 += 0.00000005256*cos(4.42445744523 + 7860.4193924392*$t);
$Z0 += 0.00000004025*cos(5.11990285618 + 13367.9726311066*$t);
$Z0 += 0.00000004061*cos(6.02923989849 + 3930.2096962196*$t);
$Z0 += 0.00000003798*cos(0.44370219832 + 3154.6870848956*$t);
$Z0 += 0.00000002933*cos(5.12428135363 + 1059.3819301892*$t);
$Z0 += 0.00000003424*cos(5.42065191700 + 6069.7767545534*$t);
$Z0 += 0.00000003670*cos(4.58210192227 + 12194.0329146209*$t);
$Z0 += 0.00000002912*cos(1.92688087702 + 10977.078804699*$t);
$Z0 += 0.00000002506*cos(0.60484952637 + 6496.3749454294*$t);
$Z0 += 0.00000002680*cos(1.39497359287 + 22003.9146348698*$t);
$Z0 += 0.00000002120*cos(4.30691000285 + 5643.1785636774*$t);
$Z0 += 0.00000002235*cos(0.81363184041 + 8635.9420037632*$t);
$Z0 += 0.00000001819*cos(3.75748003107 + 3340.6124266998*$t);
$Z0 += 0.00000002230*cos(2.76407822446 + 12036.4607348882*$t);
$Z0 += 0.00000001945*cos(5.69949789177 + 11790.6290886588*$t);
$Z0 += 0.00000001529*cos(1.98639348122 + 398.1490034082*$t);
$Z0 += 0.00000001581*cos(3.19976230948 + 5088.6288397668*$t);
$Z0 += 0.00000001424*cos(6.26116472313 + 2544.3144198834*$t);
$Z0 += 0.00000001405*cos(4.69394873481 + 7058.5984613154*$t);
$Z0 += 0.00000001588*cos(0.25704624784 + 17298.1823273262*$t);
$Z0 += 0.00000001478*cos(2.81808207569 + 25934.1243310894*$t);
$Z0 += 0.00000001693*cos(4.95689385293 + 156475.2902479957*$t);
$Z0 += 0.00000001123*cos(2.38605285936 + 3738.761430108*$t);
$Z0 += 0.00000000990*cos(4.29600699156 + 9225.539273283*$t);
$Z0 += 0.00000000923*cos(3.07195736431 + 4164.311989613*$t);
$Z0 += 0.00000000863*cos(0.55119493097 + 8429.2412664666*$t);
$Z0 += 0.00000000984*cos(5.96784225392 + 7079.3738568078*$t);
$Z0 -= 0.00000001086;
$Z0 += 0.00000000824*cos(1.50050055147 + 10447.3878396044*$t);
$Z0 += 0.00000000829*cos(3.51336978167 + 11506.7697697936*$t);
$Z0 += 0.00000000908*cos(0.12102885474 + 11015.1064773348*$t);
$Z0 += 0.00000000742*cos(1.99159139281 + 26087.9031415742*$t);
$Z0 += 0.00000000850*cos(4.24120016095 + 29864.334027309*$t);
$Z0 += 0.00000000762*cos(2.90028034892 + 4732.0306273434*$t);
$Z0 += 0.00000000711*cos(1.38596151724 + 2146.1654164752*$t);
$Z0 += 0.00000000766*cos(0.61397570576 + 796.2980068164*$t);
$Z0 += 0.00000000708*cos(1.91406542362 + 8031.0922630584*$t);
$Z0 += 0.00000000810*cos(5.13961498599 + 2942.4634232916*$t);
$Z0 += 0.00000000751*cos(1.67479850166 + 21228.3920235458*$t);
$Z0 += 0.00000000589*cos(2.02193316047 + 775.522611324*$t);
$Z0 += 0.00000000513*cos(2.60734651128 + 12566.1516999828*$t);
$Z0 += 0.00000000550*cos(1.61119298963 + 801.8209311238*$t);
$Z0 += 0.00000000592*cos(4.59481504319 + 4690.4798363586*$t);
$Z0 += 0.00000000519*cos(5.72925039114 + 8827.3902698748*$t);
$Z0 += 0.00000000515*cos(4.09976487552 + 64809.80550494129*$t);
$Z0 += 0.00000000503*cos(5.66433137112 + 33794.5437235286*$t);
$Z0 += 0.00000000476*cos(3.69640472448 + 213.299095438*$t);
$Z0 += 0.00000000463*cos(1.24987240483 + 15720.8387848784*$t);
$Z0 += 0.00000000411*cos(0.10769444525 + 3128.3887650958*$t);
$Z0 += 0.00000000504*cos(3.26207669160 + 7632.9432596502*$t);
$Z0 += 0.00000000552*cos(1.02926440457 + 239762.20451754928*$t);
$Z0 += 0.00000000394*cos(5.81496021156 + 426.598190876*$t);
$Z0 += 0.00000000476*cos(3.52810472421 + 16496.3613962024*$t);
$Z0 += 0.00000000503*cos(4.85802444134 + 6290.1893969922*$t);
$Z0 += 0.00000000417*cos(0.81920713533 + 5216.5803728014*$t);
$Z0 += 0.00000000363*cos(5.70015720452 + 1589.0728952838*$t);
$Z0 += 0.00000000363*cos(1.28376436579 + 6206.8097787158*$t);
$Z0 += 0.00000000353*cos(4.70059133110 + 7234.794256242*$t);
$Z0 += 0.00000000381*cos(2.61890749829 + 7342.4577801806*$t);
$Z0 += 0.00000000420*cos(0.97821135132 + 4136.9104335162*$t);
$Z0 += 0.00000000335*cos(6.22057967320 + 12168.0026965746*$t);
$Z0 += 0.00000000387*cos(3.09145061418 + 25158.6017197654*$t);
$Z0 += 0.00000000349*cos(2.94840720073 + 9623.6882766912*$t);
$Z0 += 0.00000000418*cos(3.75759994446 + 5230.807466803*$t);
$Z0 += 0.00000000396*cos(1.22507712354 + 6438.4962494256*$t);
$Z0 += 0.00000000322*cos(1.21162178805 + 8662.240323563*$t);
$Z0 += 0.00000000323*cos(5.50254808471 + 1194.4470102246*$t);
$Z0 += 0.00000000372*cos(1.72256107938 + 14945.3161735544*$t);
$Z0 += 0.00000000305*cos(0.80429352049 + 37724.7534197482*$t);
$Z0 += 0.00000000265*cos(6.10358507671 + 6836.6452528338*$t);
$Z0 += 0.00000000250*cos(4.56452895547 + 7477.522860216*$t);
$Z0 += 0.00000000266*cos(2.62926282354 + 7238.67559160*$t);
$Z0 += 0.00000000262*cos(1.34297269105 + 11769.8536931664*$t);
$Z0 += 0.00000000263*cos(6.22089501237 + 6133.5126528568*$t);
$Z0 += 0.00000000302*cos(2.81139045072 + 1748.016413067*$t);
$Z0 += 0.00000000316*cos(1.62662805006 + 250908.49012041549*$t);
$Z0 += 0.00000000226*cos(2.42346415873 + 11371.7046897582*$t);
$Z0 += 0.00000000216*cos(3.68721275185 + 5849.3641121146*$t);
$Z0 += 0.00000000276*cos(2.33399767923 + 19651.048481098*$t);
$Z0 += 0.00000000230*cos(0.36165162947 + 5863.5912061162*$t);
$Z0 += 0.00000000200*cos(5.86073159059 + 4535.0594369244*$t);
$Z0 += 0.00000000277*cos(4.65400292395 + 82239.16695779889*$t);
$Z0 += 0.00000000199*cos(5.05186622555 + 5429.8794682394*$t);
$Z0 += 0.00000000206*cos(3.70556027982 + 10973.55568635*$t);
$Z0 += 0.00000000210*cos(4.50691909144 + 29088.811415985*$t);
$Z0 += 0.00000000181*cos(6.00294783127 + 4292.3308329504*$t);
$Z0 += 0.00000000249*cos(0.12900984422 + 154379.79562448629*$t);
$Z0 += 0.00000000167*cos(6.27348370813 + 10988.808157535*$t);
$Z0 += 0.00000000183*cos(3.19836584401 + 16730.4636895958*$t);
$Z0 += 0.00000000225*cos(3.18339652605 + 18875.525869774*$t);
$Z0 += 0.00000000192*cos(0.87192032514 + 77375.95720492408*$t);
$Z0 += 0.00000000188*cos(2.22746128596 + 41654.9631159678*$t);
$Z0 += 0.00000000160*cos(5.20207795189 + 5481.2549188676*$t);
$Z0 += 0.00000000192*cos(3.89678943865 + 17789.845619785*$t);
$Z0 += 0.00000000159*cos(5.32590846475 + 7.1135470008*$t);
$Z0 += 0.00000000214*cos(4.08171403539 + 337.8142631964*$t);
$Z0 += 0.00000000184*cos(3.75465072369 + 23581.2581773176*$t);
$Z0 += 0.00000000160*cos(4.53897529970 + 18477.1087646123*$t);
$Z0 += 0.00000000144*cos(5.19486374726 + 20426.571092422*$t);
$Z0 += 0.00000000126*cos(1.69446958184 + 15110.4661198662*$t);
$Z0 += 0.00000000149*cos(1.55306832217 + 10021.8372800994*$t);
$Z0 += 0.00000000127*cos(5.31068233515 + 639.897286314*$t);
$Z0 += 0.00000000118*cos(2.73268114062 + 18849.2275499742*$t);
$Z0 += 0.00000000123*cos(2.55361087146 + 12592.4500197826*$t);
$Z0 += 0.00000000113*cos(6.07178776726 + 6709.6740408674*$t);
$Z0 += 0.00000000130*cos(3.94161517411 + 7330.8231617461*$t);
$Z0 += 0.00000000110*cos(3.51203379263 + 18052.9295431578*$t);
$Z0 += 0.00000000147*cos(4.63371971408 + 22805.7355659936*$t);
$Z0 += 0.00000000113*cos(1.20711498905 + 14919.0178537546*$t);
$Z0 += 0.00000000108*cos(3.76359880753 + 14314.1681130498*$t);
$Z0 += 0.00000000148*cos(0.65447253687 + 95480.9471841745*$t);
$Z0 += 0.00000000121*cos(3.13748782783 + 14712.317116458*$t);
$Z0 += 0.00000000119*cos(5.92110458985 + 33019.0211122046*$t);
$Z0 += 0.00000000124*cos(2.93638421840 + 32217.2001810808*$t);
$Z0 += 0.00000000117*cos(3.65065271640 + 45585.1728121874*$t);
$Z0 += 0.00000000127*cos(4.74596574209 + 49515.382508407*$t);
$Z0 += 0.00000000120*cos(1.04211499785 + 6915.8595893046*$t);
$Z0 += 0.00000000120*cos(5.60638811846 + 5650.2921106782*$t);
$Z0 += 0.00000000127*cos(2.70766997307 + 12352.8526045448*$t);
$Z0 += 0.00000000113*cos(5.39691616452 + 5235.3285382367*$t);
$Z0 += 0.00000000097*cos(1.07908724794 + 9917.6968745098*$t);
$Z0 += 0.00000000123*cos(5.15992792934 + 27511.4678735372*$t);
$Z0 += 0.00000000099*cos(4.45774681732 + 4933.2084403326*$t);
$Z0 += 0.00000000087*cos(3.93637812950 + 17654.7805397496*$t);
$Z0 += 0.00000000122*cos(2.23956068680 + 83997.09113559539*$t);
$Z0 += 0.00000000102*cos(3.97386522171 + 10818.1352869158*$t);
$Z0 += 0.00000000084*cos(4.21241958885 + 22779.4372461938*$t);
$Z0 += 0.00000000103*cos(4.63519841733 + 1349.8674096588*$t);
$Z0 += 0.00000000081*cos(4.01655240430 + 1592.5960136328*$t);
$Z0 += 0.00000000092*cos(3.24182657569 + 78051.5857313169*$t);
$Z0 += 0.00000000094*cos(4.33873972800 + 36147.4098773004*$t);
$Z0 += 0.00000000076*cos(2.83897554420 + 17260.1546546904*$t);
$Z0 += 0.00000000100*cos(6.07733097102 + 26735.9452622132*$t);
$Z0 += 0.00000000078*cos(0.72462427283 + 12779.4507954208*$t);
$Z0 += 0.00000000086*cos(5.26029638250 + 28313.288804661*$t);
$Z0 += 0.00000000093*cos(4.31900620254 + 44809.6502008634*$t);
$Z0 += 0.00000000076*cos(6.22743405935 + 13521.7514415914*$t);
$Z0 += 0.00000000081*cos(2.16420552322 + 13095.8426650774*$t);
$Z0 += 0.00000000100*cos(1.38002787119 + 28286.9904848612*$t);
$Z0 += 0.00000000072*cos(1.55820597747 + 6256.7775301916*$t);
$Z0 += 0.00000000082*cos(4.95202664555 + 10575.4066829418*$t);
$Z0 += 0.00000000082*cos(1.69647647075 + 1990.745017041*$t);
$Z0 += 0.00000000096*cos(6.16038106485 + 24356.7807886416*$t);
$Z0 += 0.00000000075*cos(2.29836095644 + 3634.6210245184*$t);
$Z0 += 0.00000000075*cos(2.66367876557 + 16200.7727245012*$t);
$Z0 += 0.00000000087*cos(0.26630214764 + 31441.6775697568*$t);
$Z0 += 0.00000000080*cos(5.00001604436 + 150192.21439800429*$t);
$Z0 += 0.00000000079*cos(0.01398391548 + 90617.7374312997*$t);
$Z0 += 0.00000000054*cos(5.59738773448 + 161338.5000008705*$t);
$Z0 += 0.00000000056*cos(2.60133794851 + 73188.3759784421*$t);
$Z0 += 0.00000000055*cos(5.81483150022 + 143233.51002162008*$t);
$Z0 += 0.00000000054*cos(3.38482031504 + 323049.11878710288*$t);
return $Z0;
}
function Earth_Z1($t) // 97 terms of order 1
{
$Z1 = 0.00000009031*cos(3.89751156799 + 5507.5532386674*$t);
$Z1 += 0.00000006179*cos(1.73051337995 + 5223.6939198022*$t);
$Z1 += 0.00000003793*cos(5.24575814515 + 2352.8661537718*$t);
$Z1 += 0.00000002840*cos(2.47694599818 + 1577.3435424478*$t);
$Z1 += 0.00000001817*cos(0.41874743765 + 6283.0758499914*$t);
$Z1 += 0.00000001499*cos(1.83320979291 + 5856.4776591154*$t);
$Z1 += 0.00000001463*cos(5.68891324948 + 5753.3848848968*$t);
$Z1 += 0.00000001302*cos(2.18800611215 + 9437.762934887*$t);
$Z1 += 0.00000001239*cos(4.95327097854 + 10213.285546211*$t);
$Z1 += 0.00000001029*cos(0.09367831611 + 7860.4193924392*$t);
$Z1 += 0.00000000975*cos(0.08833256880 + 14143.4952424306*$t);
$Z1 += 0.00000000851*cos(1.79547916132 + 3930.2096962196*$t);
$Z1 += 0.00000000581*cos(2.26949174067 + 5884.9268465832*$t);
$Z1 += 0.00000000515*cos(5.64196681593 + 529.6909650946*$t);
$Z1 += 0.00000000473*cos(6.22750969242 + 6309.3741697912*$t);
$Z1 += 0.00000000449*cos(1.52767374606 + 18073.7049386502*$t);
$Z1 += 0.00000000360*cos(3.62344325932 + 13367.9726311066*$t);
$Z1 += 0.00000000372*cos(3.22470721320 + 6275.9623029906*$t);
$Z1 += 0.00000000260*cos(1.87645933242 + 11790.6290886588*$t);
$Z1 += 0.00000000322*cos(0.94084045832 + 6069.7767545534*$t);
$Z1 += 0.00000000232*cos(0.27531852596 + 7058.5984613154*$t);
$Z1 += 0.00000000217*cos(6.03652873142 + 10977.078804699*$t);
$Z1 += 0.00000000232*cos(2.93325646109 + 22003.9146348698*$t);
$Z1 += 0.00000000204*cos(3.86264841382 + 6496.3749454294*$t);
$Z1 += 0.00000000189*cos(2.88937704419 + 15720.8387848784*$t);
$Z1 += 0.00000000179*cos(4.90537280911 + 12036.4607348882*$t);
$Z1 += 0.00000000222*cos(3.98495366315 + 6812.766815086*$t);
$Z1 += 0.00000000213*cos(1.57516933652 + 4694.0029547076*$t);
$Z1 += 0.00000000157*cos(1.08259734788 + 5643.1785636774*$t);
$Z1 += 0.00000000154*cos(5.99434678412 + 5486.777843175*$t);
$Z1 += 0.00000000137*cos(2.67760436027 + 6290.1893969922*$t);
$Z1 += 0.00000000179*cos(2.05905949693 + 7084.8967811152*$t);
$Z1 += 0.00000000121*cos(5.90212574947 + 9225.539273283*$t);
$Z1 += 0.00000000125*cos(2.24111392416 + 1059.3819301892*$t);
$Z1 += 0.00000000150*cos(2.00175038718 + 5230.807466803*$t);
$Z1 += 0.00000000149*cos(5.06157254516 + 17298.1823273262*$t);
$Z1 += 0.00000000118*cos(5.39979058038 + 3340.6124266998*$t);
$Z1 += 0.00000000161*cos(3.32421999691 + 6283.3196674749*$t);
$Z1 += 0.00000000115*cos(5.92406672373 + 4705.7323075436*$t);
$Z1 += 0.00000000118*cos(4.40207874911 + 19651.048481098*$t);
$Z1 += 0.00000000128*cos(4.35489873365 + 25934.1243310894*$t);
$Z1 += 0.00000000109*cos(2.52157834166 + 6438.4962494256*$t);
$Z1 += 0.00000000099*cos(2.70727488041 + 5216.5803728014*$t);
$Z1 += 0.00000000122;
$Z1 += 0.00000000103*cos(0.93782340879 + 8827.3902698748*$t);
$Z1 += 0.00000000083*cos(4.12473540351 + 8635.9420037632*$t);
$Z1 += 0.00000000097*cos(5.50959692365 + 29864.334027309*$t);
$Z1 += 0.00000000073*cos(1.73905345744 + 11506.7697697936*$t);
$Z1 += 0.00000000083*cos(5.69169692653 + 775.522611324*$t);
$Z1 += 0.00000000072*cos(0.21891639822 + 21228.3920235458*$t);
$Z1 += 0.00000000071*cos(2.86755026812 + 6681.2248533996*$t);
$Z1 += 0.00000000074*cos(2.20184828895 + 37724.7534197482*$t);
$Z1 += 0.00000000063*cos(4.45586625948 + 7079.3738568078*$t);
$Z1 += 0.00000000047*cos(2.04946724464 + 3128.3887650958*$t);
$Z1 += 0.00000000061*cos(0.63918772258 + 33794.5437235286*$t);
$Z1 += 0.00000000047*cos(3.32543843300 + 26087.9031415742*$t);
$Z1 += 0.00000000049*cos(1.60680905005 + 6702.5604938666*$t);
$Z1 += 0.00000000057*cos(0.11215813438 + 29088.811415985*$t);
$Z1 += 0.00000000049*cos(3.02832204050 + 20426.571092422*$t);
$Z1 += 0.00000000041*cos(5.55329394890 + 11015.1064773348*$t);
$Z1 += 0.00000000041*cos(5.91861144924 + 23581.2581773176*$t);
$Z1 += 0.00000000045*cos(2.00068583743 + 426.598190876*$t);
$Z1 += 0.00000000045*cos(4.95273290181 + 5863.5912061162*$t);
$Z1 += 0.00000000050*cos(3.62740835096 + 41654.9631159678*$t);
$Z1 += 0.00000000046*cos(1.65798680284 + 25158.6017197654*$t);
$Z1 += 0.00000000036*cos(5.61836577943 + 12566.1516999828*$t);
$Z1 += 0.00000000036*cos(6.24373396652 + 6283.14316029419*$t);
$Z1 += 0.00000000036*cos(0.40465162918 + 6283.0085396886*$t);
$Z1 += 0.00000000032*cos(6.09025731476 + 64809.80550494129*$t);
$Z1 += 0.00000000032*cos(6.03707103538 + 2942.4634232916*$t);
$Z1 += 0.00000000041*cos(4.86809570283 + 1592.5960136328*$t);
$Z1 += 0.00000000037*cos(1.04055368426 + 213.299095438*$t);
$Z1 += 0.00000000031*cos(3.62641145030 + 13095.8426650774*$t);
$Z1 += 0.00000000028*cos(4.38359423735 + 7632.9432596502*$t);
$Z1 += 0.00000000030*cos(2.03616887071 + 12139.5535091068*$t);
$Z1 += 0.00000000028*cos(6.03334294232 + 17789.845619785*$t);
$Z1 += 0.00000000026*cos(3.88971333608 + 5331.3574437408*$t);
$Z1 += 0.00000000031*cos(1.44666331503 + 16730.4636895958*$t);
$Z1 += 0.00000000026*cos(6.26376705837 + 23543.23050468179*$t);
$Z1 += 0.00000000023*cos(4.44388985550 + 18849.2275499742*$t);
$Z1 += 0.00000000025*cos(4.13395006026 + 3154.6870848956*$t);
$Z1 += 0.00000000028*cos(1.53862289477 + 6279.4854213396*$t);
$Z1 += 0.00000000028*cos(1.96831814872 + 6286.6662786432*$t);
$Z1 += 0.00000000028*cos(5.78094918529 + 15110.4661198662*$t);
$Z1 += 0.00000000025*cos(0.62040343662 + 10988.808157535*$t);
$Z1 += 0.00000000022*cos(6.02390113954 + 16496.3613962024*$t);
$Z1 += 0.00000000026*cos(2.48165809843 + 5729.506447149*$t);
$Z1 += 0.00000000020*cos(3.85655029499 + 9623.6882766912*$t);
$Z1 += 0.00000000021*cos(5.83006047147 + 7234.794256242*$t);
$Z1 += 0.00000000021*cos(0.69628570421 + 398.1490034082*$t);
$Z1 += 0.00000000022*cos(5.02222806555 + 6127.6554505572*$t);
$Z1 += 0.00000000020*cos(3.47611265290 + 6148.010769956*$t);
$Z1 += 0.00000000020*cos(0.90769829044 + 5481.2549188676*$t);
$Z1 += 0.00000000020*cos(0.03081589303 + 6418.1409300268*$t);
$Z1 += 0.00000000020*cos(3.74220084927 + 1589.0728952838*$t);
$Z1 += 0.00000000018*cos(1.58348238359 + 2118.7638603784*$t);
$Z1 += 0.00000000019*cos(0.85407021371 + 14712.317116458*$t);
return $Z1*$t;
}
function Earth_Z2($t) // 47 terms of order 2
{
$Z2 = 0.00000001662*cos(1.62703209173 + 84334.66158130829*$t);
$Z2 += 0.00000000492*cos(2.41382223971 + 1047.7473117547*$t);
$Z2 += 0.00000000344*cos(2.24353004539 + 5507.5532386674*$t);
$Z2 += 0.00000000258*cos(6.00906896311 + 5223.6939198022*$t);
$Z2 += 0.00000000131*cos(0.95447345240 + 6283.0758499914*$t);
$Z2 += 0.00000000086*cos(1.69139956945 + 7860.4193924392*$t);
$Z2 += 0.00000000090*cos(0.97606804452 + 1577.3435424478*$t);
$Z2 += 0.00000000090*cos(0.37899871725 + 2352.8661537718*$t);
$Z2 += 0.00000000089*cos(6.25807507963 + 10213.285546211*$t);
$Z2 += 0.00000000075*cos(0.84213523741 + 167621.57585086189*$t);
$Z2 += 0.00000000052*cos(1.70501566089 + 14143.4952424306*$t);
$Z2 += 0.00000000057*cos(6.15295833679 + 12194.0329146209*$t);
$Z2 += 0.00000000051*cos(1.27616016740 + 5753.3848848968*$t);
$Z2 += 0.00000000051*cos(5.37229738682 + 6812.766815086*$t);
$Z2 += 0.00000000034*cos(1.73672994279 + 7058.5984613154*$t);
$Z2 += 0.00000000038*cos(2.77761031485 + 10988.808157535*$t);
$Z2 += 0.00000000046*cos(3.38617099014 + 156475.2902479957*$t);
$Z2 += 0.00000000021*cos(1.95248349228 + 8827.3902698748*$t);
$Z2 += 0.00000000018*cos(3.33419222028 + 8429.2412664666*$t);
$Z2 += 0.00000000019*cos(4.32945160287 + 17789.845619785*$t);
$Z2 += 0.00000000017*cos(0.66191210656 + 6283.0085396886*$t);
$Z2 += 0.00000000018*cos(3.74885333072 + 11769.8536931664*$t);
$Z2 += 0.00000000017*cos(4.23058370776 + 10977.078804699*$t);
$Z2 += 0.00000000017*cos(1.78116162721 + 5486.777843175*$t);
$Z2 += 0.00000000018*cos(6.14348240716 + 11790.6290886588*$t);
$Z2 += 0.00000000022*cos(1.34376831204 + 12036.4607348882*$t);
$Z2 += 0.00000000017*cos(2.79601092529 + 796.2980068164*$t);
$Z2 += 0.00000000015*cos(1.17032155085 + 213.299095438*$t);
$Z2 += 0.00000000018*cos(2.85221514199 + 5088.6288397668*$t);
$Z2 += 0.00000000017*cos(0.21780913672 + 6283.14316029419*$t);
$Z2 += 0.00000000013*cos(1.21201504386 + 25132.3033999656*$t);
$Z2 += 0.00000000012*cos(5.13714452592 + 7079.3738568078*$t);
$Z2 += 0.00000000013*cos(3.79842135217 + 4933.2084403326*$t);
$Z2 += 0.00000000012*cos(4.89407978213 + 3738.761430108*$t);
$Z2 += 0.00000000015*cos(6.05682328852 + 398.1490034082*$t);
$Z2 += 0.00000000014*cos(4.81029291856 + 4694.0029547076*$t);
$Z2 += 0.00000000011*cos(0.61684523405 + 3128.3887650958*$t);
$Z2 += 0.00000000011*cos(5.32876538500 + 6040.3472460174*$t);
$Z2 += 0.00000000014*cos(5.27227350286 + 4535.0594369244*$t);
$Z2 += 0.00000000011*cos(2.39292099451 + 5331.3574437408*$t);
$Z2 += 0.00000000010*cos(4.45296532710 + 6525.8044539654*$t);
$Z2 += 0.00000000014*cos(4.66400985037 + 8031.0922630584*$t);
$Z2 += 0.00000000010*cos(3.22472385926 + 9437.762934887*$t);
$Z2 += 0.00000000011*cos(3.80913404437 + 801.8209311238*$t);
$Z2 += 0.00000000010*cos(5.15032130575 + 11371.7046897582*$t);
$Z2 += 0.00000000013*cos(0.98720797401 + 5729.506447149*$t);
$Z2 += 0.00000000009*cos(5.94191743597 + 7632.9432596502*$t);
return $Z2*$t*$t;
}
function Earth_Z3($t) // 11 terms of order 3
{
$Z3 = 0.00000000011*cos(0.23877262399 + 7860.4193924392*$t);
$Z3 += 0.00000000009*cos(1.16069982609 + 5507.5532386674*$t);
$Z3 += 0.00000000008*cos(1.65357552925 + 5884.9268465832*$t);
$Z3 += 0.00000000008*cos(2.86720038197 + 7058.5984613154*$t);
$Z3 += 0.00000000007*cos(3.04818741666 + 5486.777843175*$t);
$Z3 += 0.00000000007*cos(2.59437103785 + 529.6909650946*$t);
$Z3 += 0.00000000008*cos(4.02863090524 + 6256.7775301916*$t);
$Z3 += 0.00000000008*cos(2.42003508927 + 5753.3848848968*$t);
$Z3 += 0.00000000006*cos(0.84181087594 + 6275.9623029906*$t);
$Z3 += 0.00000000006*cos(5.40160929468 + 1577.3435424478*$t);
$Z3 += 0.00000000007*cos(2.73399865247 + 6309.3741697912*$t);
return $Z3*$t*$t*$t;
}
function Earth_Z4($t) // 5 terms of order 4
{
$Z4 = 0.00000000004*cos(0.79662198849 + 6438.4962494256*$t);
$Z4 += 0.00000000005*cos(0.84308705203 + 1047.7473117547*$t);
$Z4 += 0.00000000005*cos(0.05711572303 + 84334.66158130829*$t);
$Z4 += 0.00000000003*cos(3.46779895686 + 6279.5527316424*$t);
$Z4 += 0.00000000003*cos(2.89822201212 + 6127.6554505572*$t);
return $Z4*$t*$t*$t*$t;
}
// There are no terms of order 5 (they equate to zero).
// ****************************************************************************
/*
This function computes the calendrical JD number, which is always a positive
integer (or zero). This is the JD number used for simple, basic calendrical
computations where the time of day can be ignored, such as when computing
the exact number of whole calendar days between two dates. For example,
when we want to compute how many days it is until Christmas, we do not
need to consider the time of day on either of the dates to perform the
computation - we simply count whole days.
This Julian Day Number corresponds to the astronomical Julian Date at
12:00:00 (Noon), the midpoint of the given date.
To obtain the astronomical JD number for 00h, the beginning of the date,
simply subtract 0.5 from this integer value. This is the value to which
may later be added the fraction of a day corresponding to a given time so
that we may obtain the general Julian Date for any given time of day.
(yNum, mNum, dNum) = Numerical (Year, Month, Day) date elements.
*/
function JD_Num_For_Ymd ($yNum,$mNum,$dNum)
{
// --------------------------------------
// Read numerical date arguments (y,m,d).
$y = 0 + trim($yNum);
$m = IntVal(trim($mNum));
$d = IntVal(trim($dNum));
// Compute JD Number for Julian Calendar.
// Dates up to 1582-Oct-04
$JDNum = JulianToJD($m, $d, $y);
// Adjust for Gregorian calendar, if necessary.
// Dates from Oct-15-1582 to date and after.
if ($JDNum > 2299160)
{$JDNum = GregorianToJD($m, $d, $y);}
return $JDNum - 0.0;
}
// ****************************************************************************
?>