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Cách xác định 24 tiết khí

Hồ Ngọc Đức

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#1 maphuong

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Gửi vào 30/11/2016 - 11:12

Cách xác định 24 tiết khí

Tiết khí là các thời điểm mà kinh độ mặt trời (KĐMT) có các giá trị 0°, 15°, 30°, 45°, 60°, ..., 345°. (0° là Xuân Phân, 15° là Thanh Minh v.v.). Như vậy để xác định tiết khí ta cần tìm xem vào khoảng thời gian nào thì kinh độ mặt trời có các giá trị này.

Tìm ngày chứa tiết khí

Thường thì ta chỉ quan tâm tới tiết khí rơi vào ngày nào chứ không cần chính xác tới giờ/phút. Ngày chứa một tiết khí nhất định có thể được xác định như sau:
  • Chọn một ngày có khả năng chứa tiết khí cần xác định. Ngày có tiết khí chỉ xê dịch trong khoảng 1-2 ngày nên ta có thể chọn khá sát.
  • Tính kinh độ mặt trời lúc 0h sáng ngày hôm đó và 0h sáng ngày hôm sau
  • Nếu kinh độ mặt trời tương ứng với tiết khí cần xác định nằm giữa hai giá trị này thì ngày đã chọn chính là ngày chứa tiết khí, nếu không ta lặp lại việc tìm kiếm này với ngày trước hoặc sau đó.
Tìm thời điểm tiết khí

Để tìm thời điểm chính xác của một tiết khí, sau khi xác định được ngày chứa tiết khí đó ta có thể thực hiện một phép tìm kiếm nhị phân đơn giản để tìm ra ngày giờ của tiết khí này.
  • Chọn mốc trên và dưới là 0h và 24h (tức 0h sáng ngày hôm sau). Tính điểm giữa 2 mốc (12h trưa) và tính KĐMT tại điểm đó.
  • Nếu KĐMT này nhỏ hơn KĐMT của tiết khí, tìm tiếp trong khoảng từ 0h đến 12h, nếu không sẽ tìm trong khoảng từ 12h đến 24h.
  • Lặp lại việc tìm kiếm đến khi KĐMT của hai điểm mốc cách nhau không quá 0.001 độ.
Bước tính toán quan trọng nhất trong việc xác định tiết khí là tìm kinh độ mặt trời tại một thời điểm bất kỳ. Việc tính toán này được thực hiện với 2 bước:
  • Tính niên kỷ Julius của thời điểm đã cho
  • Tính kinh độ mặt trời cho thời điểm đó
Ngày và niên kỷ Julius

Số ngày Julius (Julian Day Number) của một ngày trong lịch Gregory có thể tính bởi các công thức sau, sử dụng năm thiên văn (1 TCN là 0, 2 TCN là −1, 4713 TCN là −4712):
a = [(14 - tháng)/ 12]
y = năm + 4800 - a
m= tháng + 12a - 3
JDN = ngày + [(153m + 2)/5] + 365y + [y/4] - [y/100] + [y/400] - 32045

Trong các công thức trên [x/y] là phần nguyên của phép chia x/y.
Để tính niên kỷ Julius (Julian date), thêm giờ, phút, giây theo UT (Universal Time):
JD = JDN + (giờ - 12)/24 + phút/1440 + giây/86400

Nếu giờ, phút, giây được tính theo giờ Hà Nội (UTC+7:00) thì kết quả phải trừ đi 7/24 ngày.

Tính kinh độ mặt trời tại một thời điểm

Để tính kinh độ mặt trời tại thời điểm, trước hết tìm niên kỷ Julius JD của thời điểm đó theo phương pháp trên. Sau đó thực hiện các bước sau:
T = (JD - 2451545.0) / 36525
L0 = 280°.46645 + 36000°.76983*T + 0°.0003032*T2
M = 357°.52910 + 35999°.05030*T - 0°.0001559*T2 - 0°.00000048*T3
C = (1°.914600 - 0°.004817*T - 0°.000014*T2) * sin M + (0°.01993 - 0°.000101*T) * sin 2M + 0°.000290 * sin 3M
theta = L0 + C
lambda = theta - 0.00569 - 0.00478 * sin(125°.04 - 1934°.136*T)
lambda = lambda - 360 * [lambda/360]

Kết quả lambda là kinh độ mặt trời cần tìm. Đó là một góc (tính bằng độ) trong khoảng (0,360).

Ví dụ (xem ví dụ tính toán tại site

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Chọn ngày giờ (giờ Hà Nội, UTC+7:00) và nhấn OK để tính kinh độ mặt trời tại thời điểm đó: 0 h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 h 10 h 11 h 12 h 13 h 14 h 15 h 16 h 17 h 18 h 19 h 20 h 21 h 22 h 23 h Ngày: tháng 1 2 3 4 5 6 7 8 9 10 11 12 năm
Kết quả: 247.9131449315555

Tìm ngày Đông Chí năm 2008. Kinh độ mặt trời ứng với Đông Chí là 270°. Ngày Đông Chí thường rơi vào khoảng 20/12-22/12 hàng năm. Như vậy trước hết ta thử ngày 20/12/2008. KĐMT lúc 0h sáng ngày 20/12/2008 là 268°.17811 và lúc 0h sáng 21/12/2008 là 269°.19634. Góc 270° nằm sau cả hai giá trị này, như vậy ta phải thử ngày hôm sau. KĐMT lúc 0h sáng ngày 22/12/2008 là 270°.21471, như thế điểm Đông Chí nằm trong ngày 21/12/2008.

Để xác định thời điểm Đông Chí, ta tính KĐMT lúc 12h ngày 21/12/2008, được kết quả 269°.70551, nhỏ hơn 270°, như vậy điểm Đông Chí nằm trong khoảng từ 12h đến 24h. Chọn 18h00 ngày 21/12/2008 sẽ tìm thấy KĐMT 269°.96010, như vậy ta phải tìm tiếp trong khoảng 18h đến 24h. Vào lúc 21h, KĐMT là 270°.08741, như thế khoảng tìm kiếm bây giờ là 18h đến 21h. Lặp lại việc tìm kiếm này thêm khoảng 7 bước nữa sẽ tìm được thời điểm Đông Chí là 18h56. (Kết quả 'chính xác' tính theo lý thuyết VSOP87 là 19h04).


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#2 MikeDo

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Gửi vào 01/12/2016 - 17:34

Chúng ta cần chú ý, sai số do sử dụng code ở đây rất lớn. Tôi có sử dụng code ở đây, và gặp sai sót trung bình 5 phút một năm, mà không hiệu chỉnh được.

Một trong những điều mà Hồ Ngọc Đức dấu mọi người không nhắc tới, đó là anh sử dụng lý thuyết VSOP để tính toán trong các code khác của anh, mà lại dấu mã nguồn và đưa thành các bảng tra sẵn.

Đây mới là bảng mã

<?PHP

/*

EARTH - VSOP87 Series Version D
HELIOCENTRIC DYNAMICAL ECLIPTIC AND EQUINOX OF THE DATE
Spherical (L,B,R) Coordinates

Series Validity Span: 2000 BC < Date < 6000 AD
Theoretical accuracy over span: ±1 arc sec

L = Longitude in radians
B = Latitude in radians
R = Radius vector in AU (Astronomical Units)

t = (JD - 2451545) / 365250


PHP Programming Language

VSOP87 Functions Source Code
Generated By The VSOP87 Source Code Generator Tool
© Jay Tanner 2016

Ref:
Planetary Theories in Rectangular and Spherical Variables
VSOP87 Solutions
Pierre Bretagnon, Gerard Francou
Journal of Astronomy & Astrophysics
vol. 202, p309-p315
1988

Source code provided under the provisions of the
GNU Affero General Public License, version 3.

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*/


function Earth_L0($t) // 559 terms of order 0
{
$L0 = 1.75347045673;
$L0 += 0.03341656456*cos(4.66925680417 + 6283.0758499914*$t);
$L0 += 0.00034894275*cos(4.62610241759 + 12566.1516999828*$t);
$L0 += 0.00003417571*cos(2.82886579606 + 3.523118349*$t);
$L0 += 0.00003497056*cos(2.74411800971 + 5753.3848848968*$t);
$L0 += 0.00003135896*cos(3.62767041758 + 77713.7714681205*$t);
$L0 += 0.00002676218*cos(4.41808351397 + 7860.4193924392*$t);
$L0 += 0.00002342687*cos(6.13516237631 + 3930.2096962196*$t);
$L0 += 0.00001273166*cos(2.03709655772 + 529.6909650946*$t);
$L0 += 0.00001324292*cos(0.74246356352 + 11506.7697697936*$t);
$L0 += 0.00000901855*cos(2.04505443513 + 26.2983197998*$t);
$L0 += 0.00001199167*cos(1.10962944315 + 1577.3435424478*$t);
$L0 += 0.00000857223*cos(3.50849156957 + 398.1490034082*$t);
$L0 += 0.00000779786*cos(1.17882652114 + 5223.6939198022*$t);
$L0 += 0.00000990250*cos(5.23268129594 + 5884.9268465832*$t);
$L0 += 0.00000753141*cos(2.53339053818 + 5507.5532386674*$t);
$L0 += 0.00000505264*cos(4.58292563052 + 18849.2275499742*$t);
$L0 += 0.00000492379*cos(4.20506639861 + 775.522611324*$t);
$L0 += 0.00000356655*cos(2.91954116867 + 0.0673103028*$t);
$L0 += 0.00000284125*cos(1.89869034186 + 796.2980068164*$t);
$L0 += 0.00000242810*cos(0.34481140906 + 5486.777843175*$t);
$L0 += 0.00000317087*cos(5.84901952218 + 11790.6290886588*$t);
$L0 += 0.00000271039*cos(0.31488607649 + 10977.078804699*$t);
$L0 += 0.00000206160*cos(4.80646606059 + 2544.3144198834*$t);
$L0 += 0.00000205385*cos(1.86947813692 + 5573.1428014331*$t);
$L0 += 0.00000202261*cos(2.45767795458 + 6069.7767545534*$t);
$L0 += 0.00000126184*cos(1.08302630210 + 20.7753954924*$t);
$L0 += 0.00000155516*cos(0.83306073807 + 213.299095438*$t);
$L0 += 0.00000115132*cos(0.64544911683 + 0.9803210682*$t);
$L0 += 0.00000102851*cos(0.63599846727 + 4694.0029547076*$t);
$L0 += 0.00000101724*cos(4.26679821365 + 7.1135470008*$t);
$L0 += 0.00000099206*cos(6.20992940258 + 2146.1654164752*$t);
$L0 += 0.00000132212*cos(3.41118275555 + 2942.4634232916*$t);
$L0 += 0.00000097607*cos(0.68101272270 + 155.4203994342*$t);
$L0 += 0.00000085128*cos(1.29870743025 + 6275.9623029906*$t);
$L0 += 0.00000074651*cos(1.75508916159 + 5088.6288397668*$t);
$L0 += 0.00000101895*cos(0.97569221824 + 15720.8387848784*$t);
$L0 += 0.00000084711*cos(3.67080093025 + 71430.69561812909*$t);
$L0 += 0.00000073547*cos(4.67926565481 + 801.8209311238*$t);
$L0 += 0.00000073874*cos(3.50319443167 + 3154.6870848956*$t);
$L0 += 0.00000078756*cos(3.03698313141 + 12036.4607348882*$t);
$L0 += 0.00000079637*cos(1.80791330700 + 17260.1546546904*$t);
$L0 += 0.00000085803*cos(5.98322631256 + 161000.6857376741*$t);
$L0 += 0.00000056963*cos(2.78430398043 + 6286.5989683404*$t);
$L0 += 0.00000061148*cos(1.81839811024 + 7084.8967811152*$t);
$L0 += 0.00000069627*cos(0.83297596966 + 9437.762934887*$t);
$L0 += 0.00000056116*cos(4.38694880779 + 14143.4952424306*$t);
$L0 += 0.00000062449*cos(3.97763880587 + 8827.3902698748*$t);
$L0 += 0.00000051145*cos(0.28306864501 + 5856.4776591154*$t);
$L0 += 0.00000055577*cos(3.47006009062 + 6279.5527316424*$t);
$L0 += 0.00000041036*cos(5.36817351402 + 8429.2412664666*$t);
$L0 += 0.00000051605*cos(1.33282746983 + 1748.016413067*$t);
$L0 += 0.00000051992*cos(0.18914945834 + 12139.5535091068*$t);
$L0 += 0.00000049000*cos(0.48735065033 + 1194.4470102246*$t);
$L0 += 0.00000039200*cos(6.16832995016 + 10447.3878396044*$t);
$L0 += 0.00000035566*cos(1.77597314691 + 6812.766815086*$t);
$L0 += 0.00000036770*cos(6.04133859347 + 10213.285546211*$t);
$L0 += 0.00000036596*cos(2.56955238628 + 1059.3819301892*$t);
$L0 += 0.00000033291*cos(0.59309499459 + 17789.845619785*$t);
$L0 += 0.00000035954*cos(1.70876111898 + 2352.8661537718*$t);
$L0 += 0.00000040938*cos(2.39850881707 + 19651.048481098*$t);
$L0 += 0.00000030047*cos(2.73975123935 + 1349.8674096588*$t);
$L0 += 0.00000030412*cos(0.44294464135 + 83996.84731811189*$t);
$L0 += 0.00000023663*cos(0.48473567763 + 8031.0922630584*$t);
$L0 += 0.00000023574*cos(2.06527720049 + 3340.6124266998*$t);
$L0 += 0.00000021089*cos(4.14825464101 + 951.7184062506*$t);
$L0 += 0.00000024738*cos(0.21484762138 + 3.5904286518*$t);
$L0 += 0.00000025352*cos(3.16470953405 + 4690.4798363586*$t);
$L0 += 0.00000022820*cos(5.22197888032 + 4705.7323075436*$t);
$L0 += 0.00000021419*cos(1.42563735525 + 16730.4636895958*$t);
$L0 += 0.00000021891*cos(5.55594302562 + 553.5694028424*$t);
$L0 += 0.00000017481*cos(4.56052900359 + 135.0650800354*$t);
$L0 += 0.00000019925*cos(5.22208471269 + 12168.0026965746*$t);
$L0 += 0.00000019860*cos(5.77470167653 + 6309.3741697912*$t);
$L0 += 0.00000020300*cos(0.37133792946 + 283.8593188652*$t);
$L0 += 0.00000014421*cos(4.19315332546 + 242.728603974*$t);
$L0 += 0.00000016225*cos(5.98837722564 + 11769.8536931664*$t);
$L0 += 0.00000015077*cos(4.19567181073 + 6256.7775301916*$t);
$L0 += 0.00000019124*cos(3.82219996949 + 23581.2581773176*$t);
$L0 += 0.00000018888*cos(5.38626880969 + 149854.40013480789*$t);
$L0 += 0.00000014346*cos(3.72355084422 + 38.0276726358*$t);
$L0 += 0.00000017898*cos(2.21490735647 + 13367.9726311066*$t);
$L0 += 0.00000012054*cos(2.62229588349 + 955.5997416086*$t);
$L0 += 0.00000011287*cos(0.17739328092 + 4164.311989613*$t);
$L0 += 0.00000013971*cos(4.40138139996 + 6681.2248533996*$t);
$L0 += 0.00000013621*cos(1.88934471407 + 7632.9432596502*$t);
$L0 += 0.00000012503*cos(1.13052412208 + 5.5229243074*$t);
$L0 += 0.00000010498*cos(5.35909518669 + 1592.5960136328*$t);
$L0 += 0.00000009803*cos(0.99947478995 + 11371.7046897582*$t);
$L0 += 0.00000009220*cos(4.57138609781 + 4292.3308329504*$t);
$L0 += 0.00000010327*cos(6.19982566125 + 6438.4962494256*$t);
$L0 += 0.00000012003*cos(1.00351456700 + 632.7837393132*$t);
$L0 += 0.00000010827*cos(0.32734520222 + 103.0927742186*$t);
$L0 += 0.00000008356*cos(4.53902685948 + 25132.3033999656*$t);
$L0 += 0.00000010005*cos(6.02914963280 + 5746.271337896*$t);
$L0 += 0.00000008409*cos(3.29946744189 + 7234.794256242*$t);
$L0 += 0.00000008006*cos(5.82145271907 + 28.4491874678*$t);
$L0 += 0.00000010523*cos(0.93871805506 + 11926.2544136688*$t);
$L0 += 0.00000007686*cos(3.12142363172 + 7238.67559160*$t);
$L0 += 0.00000009378*cos(2.62414241032 + 5760.4984318976*$t);
$L0 += 0.00000008127*cos(6.11228001785 + 4732.0306273434*$t);
$L0 += 0.00000009232*cos(0.48343968736 + 522.5774180938*$t);
$L0 += 0.00000009802*cos(5.24413991147 + 27511.4678735372*$t);
$L0 += 0.00000007871*cos(0.99590177926 + 5643.1785636774*$t);
$L0 += 0.00000008123*cos(6.27053013650 + 426.598190876*$t);
$L0 += 0.00000009048*cos(5.33686335897 + 6386.16862421*$t);
$L0 += 0.00000008620*cos(4.16538210888 + 7058.5984613154*$t);
$L0 += 0.00000006297*cos(4.71724819317 + 6836.6452528338*$t);
$L0 += 0.00000007575*cos(3.97382858911 + 11499.6562227928*$t);
$L0 += 0.00000007756*cos(2.95729056763 + 23013.5395395872*$t);
$L0 += 0.00000007314*cos(0.60652505806 + 11513.8833167944*$t);
$L0 += 0.00000005955*cos(2.87641047971 + 6283.14316029419*$t);
$L0 += 0.00000006534*cos(5.79072926033 + 18073.7049386502*$t);
$L0 += 0.00000007188*cos(3.99831508699 + 74.7815985673*$t);
$L0 += 0.00000007346*cos(4.38582365437 + 316.3918696566*$t);
$L0 += 0.00000005413*cos(5.39199024641 + 419.4846438752*$t);
$L0 += 0.00000005127*cos(2.36062848786 + 10973.55568635*$t);
$L0 += 0.00000007056*cos(0.32258441903 + 263.0839233728*$t);
$L0 += 0.00000006625*cos(3.66475158672 + 17298.1823273262*$t);
$L0 += 0.00000006762*cos(5.91132535899 + 90955.5516944961*$t);
$L0 += 0.00000004938*cos(5.73672165674 + 9917.6968745098*$t);
$L0 += 0.00000005547*cos(2.45152597661 + 12352.8526045448*$t);
$L0 += 0.00000005958*cos(3.32051344676 + 6283.0085396886*$t);
$L0 += 0.00000004471*cos(2.06385999536 + 7079.3738568078*$t);
$L0 += 0.00000006153*cos(1.45823331144 + 233141.31440436149*$t);
$L0 += 0.00000004348*cos(4.42342175480 + 5216.5803728014*$t);
$L0 += 0.00000006123*cos(1.07494905258 + 19804.8272915828*$t);
$L0 += 0.00000004488*cos(3.65285037150 + 206.1855484372*$t);
$L0 += 0.00000004020*cos(0.83995823171 + 20.3553193988*$t);
$L0 += 0.00000005188*cos(4.06503864016 + 6208.2942514241*$t);
$L0 += 0.00000005307*cos(0.38217636096 + 31441.6775697568*$t);
$L0 += 0.00000003785*cos(2.34369213733 + 3.881335358*$t);
$L0 += 0.00000004497*cos(3.27230796845 + 11015.1064773348*$t);
$L0 += 0.00000004132*cos(0.92128915753 + 3738.761430108*$t);
$L0 += 0.00000003521*cos(5.97844807108 + 3894.1818295422*$t);
$L0 += 0.00000004215*cos(1.90601120623 + 245.8316462294*$t);
$L0 += 0.00000003701*cos(5.03069397926 + 536.8045120954*$t);
$L0 += 0.00000003865*cos(1.82634360607 + 11856.2186514245*$t);
$L0 += 0.00000003652*cos(1.01838584934 + 16200.7727245012*$t);
$L0 += 0.00000003390*cos(0.97785123922 + 8635.9420037632*$t);
$L0 += 0.00000003737*cos(2.95380107829 + 3128.3887650958*$t);
$L0 += 0.00000003507*cos(3.71291946325 + 6290.1893969922*$t);
$L0 += 0.00000003086*cos(3.64646921512 + 10.6366653498*$t);
$L0 += 0.00000003397*cos(1.10590684017 + 14712.317116458*$t);
$L0 += 0.00000003334*cos(0.83684924911 + 6496.3749454294*$t);
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$L0 += 0.00000000179*cos(4.49471798090 + 31415.379249957*$t);
$L0 += 0.00000000216*cos(0.42177594328 + 23539.7073863328*$t);
$L0 += 0.00000000189*cos(0.37542530191 + 9814.6041002912*$t);
$L0 += 0.00000000218*cos(2.36835880025 + 16627.3709153772*$t);
$L0 += 0.00000000166*cos(4.23182968446 + 16840.67001081519*$t);
$L0 += 0.00000000200*cos(2.02153258098 + 16097.6799502826*$t);
$L0 += 0.00000000169*cos(0.91318727000 + 95.9792272178*$t);
$L0 += 0.00000000211*cos(5.73370637657 + 151.8972810852*$t);
$L0 += 0.00000000204*cos(0.42643085174 + 515.463871093*$t);
$L0 += 0.00000000212*cos(3.00233538977 + 12043.574281889*$t);
$L0 += 0.00000000192*cos(5.46153589821 + 6379.0550772092*$t);
$L0 += 0.00000000165*cos(1.38698167064 + 4171.4255366138*$t);
$L0 += 0.00000000160*cos(6.23798383332 + 202.2533951741*$t);
$L0 += 0.00000000215*cos(0.20889073407 + 5621.8429232104*$t);
$L0 += 0.00000000181*cos(4.12439203622 + 13341.6743113068*$t);
$L0 += 0.00000000153*cos(1.24460848836 + 29826.3063546732*$t);
$L0 += 0.00000000150*cos(3.12999753018 + 799.8211251654*$t);
$L0 += 0.00000000175*cos(4.55671604437 + 239424.39025435288*$t);
$L0 += 0.00000000192*cos(1.33928820063 + 394.6258850592*$t);
$L0 += 0.00000000149*cos(2.65697593276 + 21.335640467*$t);
$L0 += 0.00000000146*cos(5.58021191726 + 412.3710968744*$t);
$L0 += 0.00000000156*cos(3.75650175503 + 12323.4230960088*$t);
$L0 += 0.00000000143*cos(3.75708566606 + 58864.5439181463*$t);
$L0 += 0.00000000143*cos(3.28248547724 + 29.8214381488*$t);
$L0 += 0.00000000144*cos(1.07862546598 + 1265.5674786264*$t);
$L0 += 0.00000000148*cos(0.23389236655 + 10021.8372800994*$t);
$L0 += 0.00000000193*cos(5.92751083086 + 40879.4405046438*$t);
$L0 += 0.00000000140*cos(4.97612440269 + 158.9435177832*$t);
$L0 += 0.00000000148*cos(2.61640453469 + 17157.0618804718*$t);
$L0 += 0.00000000141*cos(3.66871308723 + 26084.0218062162*$t);
$L0 += 0.00000000147*cos(5.09968173403 + 661.232926781*$t);
$L0 += 0.00000000146*cos(4.96885605695 + 57375.8019008462*$t);
$L0 += 0.00000000142*cos(0.78678347839 + 12779.4507954208*$t);
$L0 += 0.00000000134*cos(4.79432636012 + 111.1866422876*$t);
$L0 += 0.00000000140*cos(1.27748013377 + 107.6635239386*$t);
$L0 += 0.00000000169*cos(2.74893543762 + 26735.9452622132*$t);
$L0 += 0.00000000165*cos(3.95288000638 + 6357.8574485587*$t);
$L0 += 0.00000000183*cos(5.43418358741 + 369.6998159404*$t);
$L0 += 0.00000000134*cos(3.09132862833 + 17.812522118*$t);
$L0 += 0.00000000132*cos(3.05633896779 + 22490.9621214934*$t);
$L0 += 0.00000000134*cos(4.09472795832 + 6599.467719648*$t);
$L0 += 0.00000000181*cos(4.22950689891 + 966.9708774356*$t);
$L0 += 0.00000000152*cos(5.28885894415 + 12669.2444742014*$t);
$L0 += 0.00000000150*cos(5.86819430908 + 97238.62754448749*$t);
$L0 += 0.00000000142*cos(5.87266532526 + 22476.73502749179*$t);
$L0 += 0.00000000145*cos(5.07330784304 + 87.30820453981*$t);
$L0 += 0.00000000133*cos(5.65471067133 + 31.9723058168*$t);
$L0 += 0.00000000124*cos(2.83326217072 + 12566.2190102856*$t);
$L0 += 0.00000000135*cos(3.12861731644 + 32217.2001810808*$t);
$L0 += 0.00000000137*cos(0.86487461904 + 9924.8104215106*$t);
$L0 += 0.00000000172*cos(1.98369595114 + 174242.4659640497*$t);
$L0 += 0.00000000170*cos(4.41115280254 + 327574.51427678125*$t);
$L0 += 0.00000000151*cos(0.46542099527 + 39609.6545831656*$t);
$L0 += 0.00000000148*cos(2.13439571118 + 491.6632924588*$t);
$L0 += 0.00000000153*cos(3.78801830344 + 17363.24742890899*$t);
$L0 += 0.00000000165*cos(5.31654110459 + 16943.7627850338*$t);
$L0 += 0.00000000165*cos(4.06747587817 + 58953.145443294*$t);
$L0 += 0.00000000118*cos(0.63846333239 + 6.0659156298*$t);
$L0 += 0.00000000159*cos(0.86086959274 + 221995.02880149524*$t);
$L0 += 0.00000000119*cos(5.96432932413 + 1385.8952763362*$t);
$L0 += 0.00000000114*cos(5.16516114595 + 25685.872802808*$t);
$L0 += 0.00000000112*cos(3.39403722178 + 21393.5419698576*$t);
$L0 += 0.00000000112*cos(4.92889233335 + 56.8032621698*$t);
$L0 += 0.00000000119*cos(2.40637635942 + 18635.9284545362*$t);
$L0 += 0.00000000115*cos(0.23374479051 + 418.9243989006*$t);
$L0 += 0.00000000122*cos(0.93575234049 + 24492.40611365159*$t);
$L0 += 0.00000000115*cos(4.58880032176 + 26709.6469424134*$t);
$L0 += 0.00000000130*cos(4.85539251000 + 22345.2603761082*$t);
$L0 += 0.00000000140*cos(1.09413073202 + 44809.6502008634*$t);
$L0 += 0.00000000112*cos(6.05401806281 + 433.7117378768*$t);
$L0 += 0.00000000104*cos(1.54931540602 + 127.9515330346*$t);
$L0 += 0.00000000105*cos(4.82620858888 + 33794.5437235286*$t);
$L0 += 0.00000000102*cos(4.12448497391 + 15664.03552270859*$t);
$L0 += 0.00000000107*cos(4.67919356465 + 77690.75950573849*$t);
$L0 += 0.00000000118*cos(4.52320170120 + 19004.6479494084*$t);
$L0 += 0.00000000107*cos(5.71774478555 + 77736.78343050249*$t);
$L0 += 0.00000000143*cos(1.81201813018 + 4214.0690150848*$t);
$L0 += 0.00000000125*cos(1.14419195615 + 625.6701923124*$t);
$L0 += 0.00000000124*cos(3.27736514057 + 12566.08438968*$t);
$L0 += 0.00000000110*cos(1.08682570828 + 2787.0430238574*$t);
$L0 += 0.00000000105*cos(1.78318141871 + 18139.2945014159*$t);
$L0 += 0.00000000102*cos(4.75119578149 + 12242.6462833254*$t);
$L0 += 0.00000000137*cos(1.43510636754 + 86464.61331683119*$t);
$L0 += 0.00000000101*cos(4.91289409429 + 401.6721217572*$t);
$L0 += 0.00000000129*cos(1.23567904485 + 12029.3471878874*$t);
$L0 += 0.00000000138*cos(2.45654707999 + 7576.560073574*$t);
$L0 += 0.00000000103*cos(0.40004073416 + 90279.92316810328*$t);
$L0 += 0.00000000108*cos(0.98989774940 + 5636.0650166766*$t);
$L0 += 0.00000000117*cos(5.17362872063 + 34520.3093093808*$t);
$L0 += 0.00000000100*cos(3.95534628189 + 5547.1993364596*$t);
$L0 += 0.00000000098*cos(1.28118280598 + 21548.9623692918*$t);
$L0 += 0.00000000097*cos(3.34717130592 + 16310.9790457206*$t);
$L0 += 0.00000000098*cos(4.37041908717 + 34513.2630726828*$t);
$L0 += 0.00000000125*cos(2.72164432960 + 24065.80792277559*$t);
$L0 += 0.00000000102*cos(0.66938025772 + 10239.5838660108*$t);
$L0 += 0.00000000119*cos(1.21689479331 + 1478.8665740644*$t);
$L0 += 0.00000000094*cos(1.99595224256 + 13362.4497067992*$t);
$L0 += 0.00000000094*cos(4.30965982872 + 26880.3198130326*$t);
$L0 += 0.00000000095*cos(2.89807657534 + 34911.412076091*$t);
$L0 += 0.00000000106*cos(1.00156653590 + 16522.6597160022*$t);
$L0 += 0.00000000097*cos(0.89642320201 + 71980.63357473118*$t);
$L0 += 0.00000000116*cos(4.19967201116 + 206.7007372966*$t);
$L0 += 0.00000000099*cos(1.37437847718 + 1039.0266107904*$t);
$L0 += 0.00000000126*cos(3.21642544972 + 305281.94307104882*$t);
$L0 += 0.00000000094*cos(0.68997876060 + 7834.1210726394*$t);
$L0 += 0.00000000094*cos(5.58132218606 + 3104.9300594238*$t);
$L0 += 0.00000000095*cos(3.03823741110 + 8982.810669309*$t);
$L0 += 0.00000000108*cos(0.52696637156 + 276.7457718644*$t);
$L0 += 0.00000000124*cos(3.43899862683 + 172146.97134054029*$t);
$L0 += 0.00000000102*cos(1.04031728553 + 95143.1329209781*$t);
$L0 += 0.00000000104*cos(3.39218586218 + 290.972865866*$t);
$L0 += 0.00000000110*cos(3.68205877433 + 22380.755800274*$t);
$L0 += 0.00000000117*cos(0.78475956902 + 83286.91426955358*$t);
$L0 += 0.00000000083*cos(0.18241793425 + 15141.390794312*$t);
$L0 += 0.00000000089*cos(4.45371820659 + 792.7748884674*$t);
$L0 += 0.00000000082*cos(4.80703651241 + 6819.8803620868*$t);
$L0 += 0.00000000087*cos(3.43122851097 + 27707.5424942948*$t);
$L0 += 0.00000000101*cos(5.32081603011 + 2301.58581590939*$t);
$L0 += 0.00000000082*cos(0.87060089842 + 10241.2022911672*$t);
$L0 += 0.00000000086*cos(4.61919461931 + 36147.4098773004*$t);
$L0 += 0.00000000095*cos(2.87032884659 + 23020.65308658799*$t);
$L0 += 0.00000000088*cos(3.21133165690 + 33326.5787331742*$t);
$L0 += 0.00000000080*cos(1.84900424847 + 21424.4666443034*$t);
$L0 += 0.00000000101*cos(4.18796434479 + 30666.1549584328*$t);
$L0 += 0.00000000107*cos(5.77864921649 + 34115.1140692746*$t);
$L0 += 0.00000000104*cos(1.08739495962 + 6288.5987742988*$t);
$L0 += 0.00000000110*cos(3.32898859416 + 72140.62866668739*$t);
$L0 += 0.00000000087*cos(4.40657711727 + 142.1786270362*$t);
$L0 += 0.00000000109*cos(1.94546030825 + 24279.10701821359*$t);
$L0 += 0.00000000087*cos(4.32472045435 + 742.9900605326*$t);
$L0 += 0.00000000107*cos(4.91580912547 + 277.0349937414*$t);
$L0 += 0.00000000088*cos(2.10180220766 + 26482.1708096244*$t);
$L0 += 0.00000000086*cos(4.01887374432 + 12491.3701014155*$t);
$L0 += 0.00000000106*cos(5.49092372854 + 62883.3551395136*$t);
$L0 += 0.00000000080*cos(6.19781316983 + 6709.6740408674*$t);
$L0 += 0.00000000088*cos(2.09872810657 + 238004.52415723629*$t);
$L0 += 0.00000000083*cos(4.90662164029 + 51.28033786241*$t);
$L0 += 0.00000000095*cos(4.13387406591 + 18216.443810661*$t);
$L0 += 0.00000000078*cos(6.06949391680 + 148434.53403769129*$t);
$L0 += 0.00000000079*cos(3.03048221644 + 838.9692877504*$t);
$L0 += 0.00000000074*cos(5.49813051211 + 29026.48522950779*$t);
$L0 += 0.00000000073*cos(3.05008665738 + 567.7186377304*$t);
$L0 += 0.00000000084*cos(0.46604373274 + 45.1412196366*$t);
$L0 += 0.00000000093*cos(2.52267536308 + 48739.859897083*$t);
$L0 += 0.00000000076*cos(1.76418124905 + 41654.9631159678*$t);
$L0 += 0.00000000067*cos(5.77851227793 + 6311.5250374592*$t);
$L0 += 0.00000000062*cos(3.32967880172 + 15508.6151232744*$t);
$L0 += 0.00000000079*cos(5.59773841328 + 71960.38658322369*$t);
$L0 += 0.00000000057*cos(3.90629505268 + 5999.2165311262*$t);
$L0 += 0.00000000061*cos(0.05695043232 + 7856.89627409019*$t);
$L0 += 0.00000000061*cos(5.63297958433 + 7863.9425107882*$t);
$L0 += 0.00000000065*cos(3.72178394016 + 12573.2652469836*$t);
$L0 += 0.00000000057*cos(4.18217219541 + 26087.9031415742*$t);
$L0 += 0.00000000066*cos(3.92262333487 + 69853.35207568129*$t);
$L0 += 0.00000000053*cos(5.51119362045 + 77710.24834977149*$t);
$L0 += 0.00000000053*cos(4.88573986961 + 77717.29458646949*$t);
$L0 += 0.00000000062*cos(2.88876342225 + 9411.4646150872*$t);
$L0 += 0.00000000051*cos(1.12657183874 + 82576.98122099529*$t);
$L0 += 0.00000000045*cos(2.95671076719 + 24602.61243487099*$t);
$L0 += 0.00000000040*cos(5.55145719241 + 12565.1713789146*$t);
$L0 += 0.00000000039*cos(1.20838190039 + 18842.11400297339*$t);
$L0 += 0.00000000045*cos(3.18590558749 + 45585.1728121874*$t);
$L0 += 0.00000000049*cos(2.44790934886 + 13613.804277336*$t);
return $L0;
}



function Earth_L1($t) // 341 terms of order 1
{
$L1 = 6283.31966747491;
$L1 += 0.00206058863*cos(2.67823455584 + 6283.0758499914*$t);
$L1 += 0.00004303430*cos(2.63512650414 + 12566.1516999828*$t);
$L1 += 0.00000425264*cos(1.59046980729 + 3.523118349*$t);
$L1 += 0.00000108977*cos(2.96618001993 + 1577.3435424478*$t);
$L1 += 0.00000093478*cos(2.59212835365 + 18849.2275499742*$t);
$L1 += 0.00000119261*cos(5.79557487799 + 26.2983197998*$t);
$L1 += 0.00000072122*cos(1.13846158196 + 529.6909650946*$t);
$L1 += 0.00000067768*cos(1.87472304791 + 398.1490034082*$t);
$L1 += 0.00000067327*cos(4.40918235168 + 5507.5532386674*$t);
$L1 += 0.00000059027*cos(2.88797038460 + 5223.6939198022*$t);
$L1 += 0.00000055976*cos(2.17471680261 + 155.4203994342*$t);
$L1 += 0.00000045407*cos(0.39803079805 + 796.2980068164*$t);
$L1 += 0.00000036369*cos(0.46624739835 + 775.522611324*$t);
$L1 += 0.00000028958*cos(2.64707383882 + 7.1135470008*$t);
$L1 += 0.00000019097*cos(1.84628332577 + 5486.777843175*$t);
$L1 += 0.00000020844*cos(5.34138275149 + 0.9803210682*$t);
$L1 += 0.00000018508*cos(4.96855124577 + 213.299095438*$t);
$L1 += 0.00000016233*cos(0.03216483047 + 2544.3144198834*$t);
$L1 += 0.00000017293*cos(2.99116864949 + 6275.9623029906*$t);
$L1 += 0.00000015832*cos(1.43049285325 + 2146.1654164752*$t);
$L1 += 0.00000014615*cos(1.20532366323 + 10977.078804699*$t);
$L1 += 0.00000011877*cos(3.25804815607 + 5088.6288397668*$t);
$L1 += 0.00000011514*cos(2.07502418155 + 4694.0029547076*$t);
$L1 += 0.00000009721*cos(4.23925472239 + 1349.8674096588*$t);
$L1 += 0.00000009969*cos(1.30262991097 + 6286.5989683404*$t);
$L1 += 0.00000009452*cos(2.69957062864 + 242.728603974*$t);
$L1 += 0.00000012461*cos(2.83432285512 + 1748.016413067*$t);
$L1 += 0.00000011808*cos(5.27379790480 + 1194.4470102246*$t);
$L1 += 0.00000008577*cos(5.64475868067 + 951.7184062506*$t);
$L1 += 0.00000010641*cos(0.76614199202 + 553.5694028424*$t);
$L1 += 0.00000007576*cos(5.30062664886 + 2352.8661537718*$t);
$L1 += 0.00000005834*cos(1.76649917904 + 1059.3819301892*$t);
$L1 += 0.00000006385*cos(2.65033984967 + 9437.762934887*$t);
$L1 += 0.00000005223*cos(5.66135767624 + 71430.69561812909*$t);
$L1 += 0.00000005305*cos(0.90857521574 + 3154.6870848956*$t);
$L1 += 0.00000006101*cos(4.66632584188 + 4690.4798363586*$t);
$L1 += 0.00000004330*cos(0.24102555403 + 6812.766815086*$t);
$L1 += 0.00000005041*cos(1.42490103709 + 6438.4962494256*$t);
$L1 += 0.00000004259*cos(0.77355900599 + 10447.3878396044*$t);
$L1 += 0.00000005198*cos(1.85353197345 + 801.8209311238*$t);
$L1 += 0.00000003744*cos(2.00119516488 + 8031.0922630584*$t);
$L1 += 0.00000003558*cos(2.42901552681 + 14143.4952424306*$t);
$L1 += 0.00000003372*cos(3.86210700128 + 1592.5960136328*$t);
$L1 += 0.00000003374*cos(0.88776219727 + 12036.4607348882*$t);
$L1 += 0.00000003175*cos(3.18785710594 + 4705.7323075436*$t);
$L1 += 0.00000003221*cos(0.61599835472 + 8429.2412664666*$t);
$L1 += 0.00000004132*cos(5.23992859705 + 7084.8967811152*$t);
$L1 += 0.00000002970*cos(6.07026318493 + 4292.3308329504*$t);
$L1 += 0.00000002900*cos(2.32464208411 + 20.3553193988*$t);
$L1 += 0.00000003504*cos(4.79975694359 + 6279.5527316424*$t);
$L1 += 0.00000002950*cos(1.43108874817 + 5746.271337896*$t);
$L1 += 0.00000002697*cos(4.80368225199 + 7234.794256242*$t);
$L1 += 0.00000002531*cos(6.22290682655 + 6836.6452528338*$t);
$L1 += 0.00000002745*cos(0.93466065396 + 5760.4984318976*$t);
$L1 += 0.00000003250*cos(3.39954640038 + 7632.9432596502*$t);
$L1 += 0.00000002277*cos(5.00277837672 + 17789.845619785*$t);
$L1 += 0.00000002075*cos(3.95534978634 + 10213.285546211*$t);
$L1 += 0.00000002061*cos(2.22411683077 + 5856.4776591154*$t);
$L1 += 0.00000002252*cos(5.67166499885 + 11499.6562227928*$t);
$L1 += 0.00000002148*cos(5.20184578235 + 11513.8833167944*$t);
$L1 += 0.00000001886*cos(0.53198320577 + 3340.6124266998*$t);
$L1 += 0.00000001875*cos(4.73511970207 + 83996.84731811189*$t);
$L1 += 0.00000002060*cos(2.54987293999 + 25132.3033999656*$t);
$L1 += 0.00000001794*cos(1.47435409831 + 4164.311989613*$t);
$L1 += 0.00000001778*cos(3.02473091781 + 5.5229243074*$t);
$L1 += 0.00000002029*cos(0.90960209983 + 6256.7775301916*$t);
$L1 += 0.00000002075*cos(2.26767270157 + 522.5774180938*$t);
$L1 += 0.00000001772*cos(3.02622802353 + 5753.3848848968*$t);
$L1 += 0.00000001569*cos(6.12410242782 + 5216.5803728014*$t);
$L1 += 0.00000001590*cos(4.63713748247 + 3.2863574178*$t);
$L1 += 0.00000001542*cos(4.20004448567 + 13367.9726311066*$t);
$L1 += 0.00000001427*cos(1.19088061711 + 3894.1818295422*$t);
$L1 += 0.00000001375*cos(3.09301252193 + 135.0650800354*$t);
$L1 += 0.00000001359*cos(4.24532506641 + 426.598190876*$t);
$L1 += 0.00000001340*cos(5.76511818622 + 6040.3472460174*$t);
$L1 += 0.00000001284*cos(3.08524663344 + 5643.1785636774*$t);
$L1 += 0.00000001250*cos(3.07748157144 + 11926.2544136688*$t);
$L1 += 0.00000001551*cos(3.07665451458 + 6681.2248533996*$t);
$L1 += 0.00000001268*cos(2.09196018331 + 6290.1893969922*$t);
$L1 += 0.00000001144*cos(3.24444699514 + 12168.0026965746*$t);
$L1 += 0.00000001248*cos(3.44504937285 + 536.8045120954*$t);
$L1 += 0.00000001118*cos(2.31829670425 + 16730.4636895958*$t);
$L1 += 0.00000001105*cos(5.31966001019 + 23.8784377478*$t);
$L1 += 0.00000001051*cos(3.75015946014 + 7860.4193924392*$t);
$L1 += 0.00000001025*cos(2.44688534235 + 1990.745017041*$t);
$L1 += 0.00000000962*cos(0.81771017882 + 3.881335358*$t);
$L1 += 0.00000000910*cos(0.41727865299 + 7079.3738568078*$t);
$L1 += 0.00000000883*cos(5.16833917651 + 11790.6290886588*$t);
$L1 += 0.00000000957*cos(4.07673573735 + 6127.6554505572*$t);
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$L1 += 0.00000000025*cos(5.71466092822 + 25934.1243310894*$t);
return $L1*$t;
}



function Earth_L2($t) // 142 terms of order 2
{
$L2 = 0.00052918870;
$L2 += 0.00008719837*cos(1.07209665242 + 6283.0758499914*$t);
$L2 += 0.00000309125*cos(0.86728818832 + 12566.1516999828*$t);
$L2 += 0.00000027339*cos(0.05297871691 + 3.523118349*$t);
$L2 += 0.00000016334*cos(5.18826691036 + 26.2983197998*$t);
$L2 += 0.00000015752*cos(3.68457889430 + 155.4203994342*$t);
$L2 += 0.00000009541*cos(0.75742297675 + 18849.2275499742*$t);
$L2 += 0.00000008937*cos(2.05705419118 + 77713.7714681205*$t);
$L2 += 0.00000006952*cos(0.82673305410 + 775.522611324*$t);
$L2 += 0.00000005064*cos(4.66284525271 + 1577.3435424478*$t);
$L2 += 0.00000004061*cos(1.03057162962 + 7.1135470008*$t);
$L2 += 0.00000003463*cos(5.14074632811 + 796.2980068164*$t);
$L2 += 0.00000003169*cos(6.05291851171 + 5507.5532386674*$t);
$L2 += 0.00000003020*cos(1.19246506441 + 242.728603974*$t);
$L2 += 0.00000002886*cos(6.11652627155 + 529.6909650946*$t);
$L2 += 0.00000003810*cos(3.44050803490 + 5573.1428014331*$t);
$L2 += 0.00000002714*cos(0.30637881025 + 398.1490034082*$t);
$L2 += 0.00000002371*cos(4.38118838167 + 5223.6939198022*$t);
$L2 += 0.00000002538*cos(2.27992810679 + 553.5694028424*$t);
$L2 += 0.00000002079*cos(3.75435330484 + 0.9803210682*$t);
$L2 += 0.00000001675*cos(0.90216407959 + 951.7184062506*$t);
$L2 += 0.00000001534*cos(5.75900462759 + 1349.8674096588*$t);
$L2 += 0.00000001224*cos(2.97328088405 + 2146.1654164752*$t);
$L2 += 0.00000001449*cos(4.36415913970 + 1748.016413067*$t);
$L2 += 0.00000001341*cos(3.72061130861 + 1194.4470102246*$t);
$L2 += 0.00000001254*cos(2.94846826628 + 6438.4962494256*$t);
$L2 += 0.00000000999*cos(5.98640014468 + 6286.5989683404*$t);
$L2 += 0.00000000917*cos(4.79788687522 + 5088.6288397668*$t);
$L2 += 0.00000000828*cos(3.31321076572 + 213.299095438*$t);
$L2 += 0.00000001103*cos(1.27104454479 + 161000.6857376741*$t);
$L2 += 0.00000000762*cos(3.41582762988 + 5486.777843175*$t);
$L2 += 0.00000001044*cos(0.60409577691 + 3154.6870848956*$t);
$L2 += 0.00000000887*cos(5.23465144638 + 7084.8967811152*$t);
$L2 += 0.00000000645*cos(1.60096192515 + 2544.3144198834*$t);
$L2 += 0.00000000681*cos(3.43155669169 + 4694.0029547076*$t);
$L2 += 0.00000000605*cos(2.47806340546 + 10977.078804699*$t);
$L2 += 0.00000000706*cos(6.19393222575 + 4690.4798363586*$t);
$L2 += 0.00000000643*cos(1.98042503148 + 801.8209311238*$t);
$L2 += 0.00000000502*cos(1.44394375363 + 6836.6452528338*$t);
$L2 += 0.00000000490*cos(2.34129524194 + 1592.5960136328*$t);
$L2 += 0.00000000458*cos(1.30876448575 + 4292.3308329504*$t);
$L2 += 0.00000000431*cos(0.03526421494 + 7234.794256242*$t);
$L2 += 0.00000000379*cos(3.17030522615 + 6309.3741697912*$t);
$L2 += 0.00000000348*cos(0.99049550009 + 6040.3472460174*$t);
$L2 += 0.00000000386*cos(1.57019797263 + 71430.69561812909*$t);
$L2 += 0.00000000347*cos(0.67013291338 + 1059.3819301892*$t);
$L2 += 0.00000000458*cos(3.81499443681 + 149854.40013480789*$t);
$L2 += 0.00000000302*cos(1.91760044838 + 10447.3878396044*$t);
$L2 += 0.00000000307*cos(3.55343347416 + 8031.0922630584*$t);
$L2 += 0.00000000395*cos(4.93701776616 + 7632.9432596502*$t);
$L2 += 0.00000000314*cos(3.18093696547 + 2352.8661537718*$t);
$L2 += 0.00000000282*cos(4.41936437052 + 9437.762934887*$t);
$L2 += 0.00000000276*cos(2.71314254553 + 3894.1818295422*$t);
$L2 += 0.00000000298*cos(2.52037474210 + 6127.6554505572*$t);
$L2 += 0.00000000230*cos(1.37790215549 + 4705.7323075436*$t);
$L2 += 0.00000000252*cos(0.55330133471 + 6279.5527316424*$t);
$L2 += 0.00000000255*cos(5.26570187369 + 6812.766815086*$t);
$L2 += 0.00000000275*cos(0.67264264272 + 25132.3033999656*$t);
$L2 += 0.00000000178*cos(0.92820785174 + 1990.745017041*$t);
$L2 += 0.00000000221*cos(0.63897368842 + 6256.7775301916*$t);
$L2 += 0.00000000155*cos(0.77319790838 + 14143.4952424306*$t);
$L2 += 0.00000000150*cos(2.40470465561 + 426.598190876*$t);
$L2 += 0.00000000196*cos(6.06877865012 + 640.8776073822*$t);
$L2 += 0.00000000137*cos(2.21679460145 + 8429.2412664666*$t);
$L2 += 0.00000000127*cos(3.26094223174 + 17789.845619785*$t);
$L2 += 0.00000000128*cos(5.47237279946 + 12036.4607348882*$t);
$L2 += 0.00000000122*cos(2.16291082757 + 10213.285546211*$t);
$L2 += 0.00000000118*cos(0.45789822268 + 7058.5984613154*$t);
$L2 += 0.00000000141*cos(2.34932647403 + 11506.7697697936*$t);
$L2 += 0.00000000100*cos(0.85621569847 + 6290.1893969922*$t);
$L2 += 0.00000000092*cos(5.10587476002 + 7079.3738568078*$t);
$L2 += 0.00000000126*cos(2.65428307012 + 88860.05707098669*$t);
$L2 += 0.00000000106*cos(5.85646710022 + 7860.4193924392*$t);
$L2 += 0.00000000084*cos(3.57457554262 + 16730.4636895958*$t);
$L2 += 0.00000000089*cos(4.21433259618 + 83996.84731811189*$t);
$L2 += 0.00000000097*cos(5.57938280855 + 13367.9726311066*$t);
$L2 += 0.00000000102*cos(2.05853060226 + 87.30820453981*$t);
$L2 += 0.00000000080*cos(4.73792651816 + 11926.2544136688*$t);
$L2 += 0.00000000080*cos(5.41418965044 + 10973.55568635*$t);
$L2 += 0.00000000106*cos(4.10978997399 + 3496.032826134*$t);
$L2 += 0.00000000102*cos(3.62650006043 + 244287.60000722769*$t);
$L2 += 0.00000000075*cos(4.89483161769 + 5643.1785636774*$t);
$L2 += 0.00000000087*cos(0.42863750683 + 11015.1064773348*$t);
$L2 += 0.00000000069*cos(1.88908760720 + 10177.2576795336*$t);
$L2 += 0.00000000089*cos(1.35567273119 + 6681.2248533996*$t);
$L2 += 0.00000000066*cos(0.99455837265 + 6525.8044539654*$t);
$L2 += 0.00000000067*cos(5.51240997070 + 3097.88382272579*$t);
$L2 += 0.00000000076*cos(2.72016814799 + 4164.311989613*$t);
$L2 += 0.00000000063*cos(1.44349902540 + 9917.6968745098*$t);
$L2 += 0.00000000078*cos(3.51469733747 + 11856.2186514245*$t);
$L2 += 0.00000000085*cos(0.50956043858 + 10575.4066829418*$t);
$L2 += 0.00000000067*cos(3.62043033405 + 16496.3613962024*$t);
$L2 += 0.00000000055*cos(5.24637517308 + 3340.6124266998*$t);
$L2 += 0.00000000048*cos(5.43966777314 + 20426.571092422*$t);
$L2 += 0.00000000064*cos(5.79535817813 + 2388.8940204492*$t);
$L2 += 0.00000000046*cos(5.43499966519 + 6275.9623029906*$t);
$L2 += 0.00000000050*cos(3.86263598617 + 5729.506447149*$t);
$L2 += 0.00000000044*cos(1.52269529228 + 12168.0026965746*$t);
$L2 += 0.00000000057*cos(4.96352373486 + 14945.3161735544*$t);
$L2 += 0.00000000045*cos(1.00861230160 + 8635.9420037632*$t);
$L2 += 0.00000000043*cos(3.30685683359 + 9779.1086761254*$t);
$L2 += 0.00000000042*cos(0.63481258930 + 2699.7348193176*$t);
$L2 += 0.00000000041*cos(5.67996766641 + 11712.9553182308*$t);
$L2 += 0.00000000056*cos(4.34024451468 + 90955.5516944961*$t);
$L2 += 0.00000000041*cos(5.81722212845 + 709.9330485583*$t);
$L2 += 0.00000000053*cos(6.17052087143 + 233141.31440436149*$t);
$L2 += 0.00000000037*cos(3.12495025087 + 16200.7727245012*$t);
$L2 += 0.00000000035*cos(5.76973458495 + 12569.6748183318*$t);
$L2 += 0.00000000037*cos(0.31656444326 + 24356.7807886416*$t);
$L2 += 0.00000000035*cos(0.96229051027 + 17298.1823273262*$t);
$L2 += 0.00000000033*cos(5.23130355867 + 5331.3574437408*$t);
$L2 += 0.00000000035*cos(0.62517020593 + 25158.6017197654*$t);
$L2 += 0.00000000035*cos(0.80004512129 + 13916.0191096416*$t);
$L2 += 0.00000000037*cos(2.89336088688 + 12721.572099417*$t);
$L2 += 0.00000000030*cos(4.50198402401 + 23543.23050468179*$t);
$L2 += 0.00000000030*cos(5.31355708693 + 18319.5365848796*$t);
$L2 += 0.00000000029*cos(3.47275229977 + 13119.72110282519*$t);
$L2 += 0.00000000029*cos(3.11002782516 + 4136.9104335162*$t);
$L2 += 0.00000000032*cos(5.52273255667 + 5753.3848848968*$t);
$L2 += 0.00000000035*cos(3.79699996680 + 143571.32428481648*$t);
$L2 += 0.00000000026*cos(1.50634201907 + 154717.60988768269*$t);
$L2 += 0.00000000030*cos(3.53519084118 + 6284.0561710596*$t);
$L2 += 0.00000000023*cos(4.41808025967 + 5884.9268465832*$t);
$L2 += 0.00000000025*cos(1.38477355808 + 65147.6197681377*$t);
$L2 += 0.00000000023*cos(3.49782549797 + 7477.522860216*$t);
$L2 += 0.00000000019*cos(3.14329413716 + 6496.3749454294*$t);
$L2 += 0.00000000019*cos(2.20135125199 + 18073.7049386502*$t);
$L2 += 0.00000000019*cos(4.95020255309 + 3930.2096962196*$t);
$L2 += 0.00000000019*cos(0.57998702747 + 31415.379249957*$t);
$L2 += 0.00000000021*cos(1.75474323399 + 12139.5535091068*$t);
$L2 += 0.00000000019*cos(3.92233070499 + 19651.048481098*$t);
$L2 += 0.00000000014*cos(0.98131213224 + 12559.038152982*$t);
$L2 += 0.00000000019*cos(4.93309333729 + 2942.4634232916*$t);
$L2 += 0.00000000016*cos(5.55997534558 + 8827.3902698748*$t);
$L2 += 0.00000000013*cos(1.68808165516 + 4535.0594369244*$t);
$L2 += 0.00000000013*cos(0.33982116161 + 4933.2084403326*$t);
$L2 += 0.00000000012*cos(1.85426309994 + 5856.4776591154*$t);
$L2 += 0.00000000010*cos(4.82763996845 + 13095.8426650774*$t);
$L2 += 0.00000000011*cos(5.38005490571 + 11790.6290886588*$t);
$L2 += 0.00000000010*cos(1.40815507226 + 10988.808157535*$t);
$L2 += 0.00000000011*cos(3.05005267431 + 17260.1546546904*$t);
$L2 += 0.00000000010*cos(4.93364992366 + 12352.8526045448*$t);
return $L2*$t*$t;
}

function Earth_L3($t) // 22 terms of order 3
{
$L3 = 0.00000289226*cos(5.84384198723 + 6283.0758499914*$t);
$L3 += 0.00000034955;
$L3 += 0.00000016819*cos(5.48766912348 + 12566.1516999828*$t);
$L3 += 0.00000002962*cos(5.19577265202 + 155.4203994342*$t);
$L3 += 0.00000001288*cos(4.72200252235 + 3.523118349*$t);
$L3 += 0.00000000635*cos(5.96925937141 + 242.728603974*$t);
$L3 += 0.00000000714*cos(5.30045809128 + 18849.2275499742*$t);
$L3 += 0.00000000402*cos(3.78682982419 + 553.5694028424*$t);
$L3 += 0.00000000072*cos(4.29768126180 + 6286.5989683404*$t);
$L3 += 0.00000000067*cos(0.90721687647 + 6127.6554505572*$t);
$L3 += 0.00000000036*cos(5.24029648014 + 6438.4962494256*$t);
$L3 += 0.00000000024*cos(5.16003960716 + 25132.3033999656*$t);
$L3 += 0.00000000023*cos(3.01921570335 + 6309.3741697912*$t);
$L3 += 0.00000000017*cos(5.82863573502 + 6525.8044539654*$t);
$L3 += 0.00000000017*cos(3.67772863930 + 71430.69561812909*$t);
$L3 += 0.00000000009*cos(4.58467294499 + 1577.3435424478*$t);
$L3 += 0.00000000008*cos(1.40626662824 + 11856.2186514245*$t);
$L3 += 0.00000000008*cos(5.07561257196 + 6256.7775301916*$t);
$L3 += 0.00000000007*cos(2.82473374405 + 83996.84731811189*$t);
$L3 += 0.00000000005*cos(2.71488713339 + 10977.078804699*$t);
$L3 += 0.00000000005*cos(3.76879847273 + 12036.4607348882*$t);
$L3 += 0.00000000005*cos(4.28412873331 + 6275.9623029906*$t);
return $L3*$t*$t*$t;
}



function Earth_L4($t) // 11 terms of order 4
{
$L4 = 0.00000114084;
$L4 += 0.00000007717*cos(4.13446589358 + 6283.0758499914*$t);
$L4 += 0.00000000765*cos(3.83803776214 + 12566.1516999828*$t);
$L4 += 0.00000000420*cos(0.41925861858 + 155.4203994342*$t);
$L4 += 0.00000000040*cos(3.59847585840 + 18849.2275499742*$t);
$L4 += 0.00000000041*cos(3.14398414077 + 3.523118349*$t);
$L4 += 0.00000000035*cos(5.00298940826 + 5573.1428014331*$t);
$L4 += 0.00000000013*cos(0.48794833701 + 77713.7714681205*$t);
$L4 += 0.00000000010*cos(5.64801766350 + 6127.6554505572*$t);
$L4 += 0.00000000008*cos(2.84160570605 + 161000.6857376741*$t);
$L4 += 0.00000000002*cos(0.54912904658 + 6438.4962494256*$t);
return $L4*$t*$t*$t*$t;
}



function Earth_L5($t) // 5 terms of order 5
{
$L5 = 0.00000000878;
$L5 += 0.00000000172*cos(2.76579069510 + 6283.0758499914*$t);
$L5 += 0.00000000050*cos(2.01353298182 + 155.4203994342*$t);
$L5 += 0.00000000028*cos(2.21496423926 + 12566.1516999828*$t);
$L5 += 0.00000000005*cos(1.75600058765 + 18849.2275499742*$t);
return $L5*$t*$t*$t*$t*$t;
}



function Earth_B0($t) // 184 terms of order 0
{
$B0 = 0.00000279620*cos(3.19870156017 + 84334.66158130829*$t);
$B0 += 0.00000101643*cos(5.42248619256 + 5507.5532386674*$t);
$B0 += 0.00000080445*cos(3.88013204458 + 5223.6939198022*$t);
$B0 += 0.00000043806*cos(3.70444689758 + 2352.8661537718*$t);
$B0 += 0.00000031933*cos(4.00026369781 + 1577.3435424478*$t);
$B0 += 0.00000022724*cos(3.98473831560 + 1047.7473117547*$t);
$B0 += 0.00000016392*cos(3.56456119782 + 5856.4776591154*$t);
$B0 += 0.00000018141*cos(4.98367470263 + 6283.0758499914*$t);
$B0 += 0.00000014443*cos(3.70275614914 + 9437.762934887*$t);
$B0 += 0.00000014304*cos(3.41117857525 + 10213.285546211*$t);
$B0 += 0.00000011246*cos(4.82820690530 + 14143.4952424306*$t);
$B0 += 0.00000010900*cos(2.08574562327 + 6812.766815086*$t);
$B0 += 0.00000009714*cos(3.47303947752 + 4694.0029547076*$t);
$B0 += 0.00000010367*cos(4.05663927946 + 71092.88135493269*$t);
$B0 += 0.00000008775*cos(4.44016515669 + 5753.3848848968*$t);
$B0 += 0.00000008366*cos(4.99251512180 + 7084.8967811152*$t);
$B0 += 0.00000006921*cos(4.32559054073 + 6275.9623029906*$t);
$B0 += 0.00000009145*cos(1.14182646613 + 6620.8901131878*$t);
$B0 += 0.00000007194*cos(3.60193205752 + 529.6909650946*$t);
$B0 += 0.00000007698*cos(5.55425745881 + 167621.57585086189*$t);
$B0 += 0.00000005285*cos(2.48446991566 + 4705.7323075436*$t);
$B0 += 0.00000005208*cos(6.24992674537 + 18073.7049386502*$t);
$B0 += 0.00000004529*cos(2.33827747356 + 6309.3741697912*$t);
$B0 += 0.00000005579*cos(4.41023653738 + 7860.4193924392*$t);
$B0 += 0.00000004743*cos(0.70995680136 + 5884.9268465832*$t);
$B0 += 0.00000004301*cos(1.10255777773 + 6681.2248533996*$t);
$B0 += 0.00000003849*cos(1.82229412531 + 5486.777843175*$t);
$B0 += 0.00000004093*cos(5.11700141207 + 13367.9726311066*$t);
$B0 += 0.00000003681*cos(0.43793170356 + 3154.6870848956*$t);
$B0 += 0.00000003420*cos(5.42034800952 + 6069.7767545534*$t);
$B0 += 0.00000003617*cos(6.04641937526 + 3930.2096962196*$t);
$B0 += 0.00000003670*cos(4.58210192227 + 12194.0329146209*$t);
$B0 += 0.00000002918*cos(1.95463881126 + 10977.078804699*$t);
$B0 += 0.00000002797*cos(5.61259275048 + 11790.6290886588*$t);
$B0 += 0.00000002502*cos(0.60499729367 + 6496.3749454294*$t);
$B0 += 0.00000002319*cos(5.01648216014 + 1059.3819301892*$t);
$B0 += 0.00000002684*cos(1.39470396488 + 22003.9146348698*$t);
$B0 += 0.00000002428*cos(3.24183056052 + 78051.5857313169*$t);
$B0 += 0.00000002120*cos(4.30691000285 + 5643.1785636774*$t);
$B0 += 0.00000002257*cos(3.15557225618 + 90617.7374312997*$t);
$B0 += 0.00000001813*cos(3.75574218285 + 3340.6124266998*$t);
$B0 += 0.00000002226*cos(2.79699346659 + 12036.4607348882*$t);
$B0 += 0.00000001888*cos(0.86991545823 + 8635.9420037632*$t);
$B0 += 0.00000001517*cos(1.95852055701 + 398.1490034082*$t);
$B0 += 0.00000001581*cos(3.19976230948 + 5088.6288397668*$t);
$B0 += 0.00000001421*cos(6.25530883827 + 2544.3144198834*$t);
$B0 += 0.00000001595*cos(0.25619915135 + 17298.1823273262*$t);
$B0 += 0.00000001391*cos(4.69964175561 + 7058.5984613154*$t);
$B0 += 0.00000001478*cos(2.81808207569 + 25934.1243310894*$t);
$B0 += 0.00000001481*cos(3.65823554806 + 11506.7697697936*$t);
$B0 += 0.00000001693*cos(4.95689385293 + 156475.2902479957*$t);
$B0 += 0.00000001183*cos(1.29343061246 + 775.522611324*$t);
$B0 += 0.00000001114*cos(2.37889311846 + 3738.761430108*$t);
$B0 += 0.00000000994*cos(4.30088900425 + 9225.539273283*$t);
$B0 += 0.00000000924*cos(3.06451026812 + 4164.311989613*$t);
$B0 += 0.00000000867*cos(0.55606931068 + 8429.2412664666*$t);
$B0 += 0.00000000988*cos(5.97286104208 + 7079.3738568078*$t);
$B0 += 0.00000000824*cos(1.50984806173 + 10447.3878396044*$t);
$B0 += 0.00000000915*cos(0.12635654592 + 11015.1064773348*$t);
$B0 += 0.00000000742*cos(1.99159139281 + 26087.9031415742*$t);
$B0 -= 0.00000001039;
$B0 += 0.00000000850*cos(4.24120016095 + 29864.334027309*$t);
$B0 += 0.00000000755*cos(2.89631873320 + 4732.0306273434*$t);
$B0 += 0.00000000714*cos(1.37548118603 + 2146.1654164752*$t);
$B0 += 0.00000000708*cos(1.91406542362 + 8031.0922630584*$t);
$B0 += 0.00000000746*cos(0.57893808616 + 796.2980068164*$t);
$B0 += 0.00000000802*cos(5.12339137230 + 2942.4634232916*$t);
$B0 += 0.00000000751*cos(1.67479850166 + 21228.3920235458*$t);
$B0 += 0.00000000602*cos(4.09976538826 + 64809.80550494129*$t);
$B0 += 0.00000000594*cos(3.49580704962 + 16496.3613962024*$t);
$B0 += 0.00000000592*cos(4.59481504319 + 4690.4798363586*$t);
$B0 += 0.00000000530*cos(5.73979295200 + 8827.3902698748*$t);
$B0 += 0.00000000503*cos(5.66433137112 + 33794.5437235286*$t);
$B0 += 0.00000000483*cos(1.57106522411 + 801.8209311238*$t);
$B0 += 0.00000000438*cos(0.06707733767 + 3128.3887650958*$t);
$B0 += 0.00000000423*cos(2.86944595927 + 12566.1516999828*$t);
$B0 += 0.00000000504*cos(3.26207669160 + 7632.9432596502*$t);
$B0 += 0.00000000552*cos(1.02926440457 + 239762.20451754928*$t);
$B0 += 0.00000000427*cos(3.67434378210 + 213.299095438*$t);
$B0 += 0.00000000404*cos(1.46193297142 + 15720.8387848784*$t);
$B0 += 0.00000000503*cos(4.85802444134 + 6290.1893969922*$t);
$B0 += 0.00000000417*cos(0.81920713533 + 5216.5803728014*$t);
$B0 += 0.00000000365*cos(0.01002966162 + 12168.0026965746*$t);
$B0 += 0.00000000363*cos(1.28376436579 + 6206.8097787158*$t);
$B0 += 0.00000000353*cos(4.70059133110 + 7234.794256242*$t);
$B0 += 0.00000000415*cos(0.96862624175 + 4136.9104335162*$t);
$B0 += 0.00000000387*cos(3.09145061418 + 25158.6017197654*$t);
$B0 += 0.00000000373*cos(2.65119262792 + 7342.4577801806*$t);
$B0 += 0.00000000361*cos(2.97762937739 + 9623.6882766912*$t);
$B0 += 0.00000000418*cos(3.75759994446 + 5230.807466803*$t);
$B0 += 0.00000000396*cos(1.22507712354 + 6438.4962494256*$t);
$B0 += 0.00000000322*cos(1.21162178805 + 8662.240323563*$t);
$B0 += 0.00000000284*cos(5.64170320068 + 1589.0728952838*$t);
$B0 += 0.00000000379*cos(1.72248432748 + 14945.3161735544*$t);
$B0 += 0.00000000320*cos(3.94161159962 + 7330.8231617461*$t);
$B0 += 0.00000000313*cos(5.47602376446 + 1194.4470102246*$t);
$B0 += 0.00000000292*cos(1.38971327603 + 11769.8536931664*$t);
$B0 += 0.00000000305*cos(0.80429352049 + 37724.7534197482*$t);
$B0 += 0.00000000257*cos(5.81382809757 + 426.598190876*$t);
$B0 += 0.00000000265*cos(6.10358507671 + 6836.6452528338*$t);
$B0 += 0.00000000250*cos(4.56452895547 + 7477.522860216*$t);
$B0 += 0.00000000266*cos(2.62926282354 + 7238.67559160*$t);
$B0 += 0.00000000263*cos(6.22089501237 + 6133.5126528568*$t);
$B0 += 0.00000000306*cos(2.79682380531 + 1748.016413067*$t);
$B0 += 0.00000000236*cos(2.46093023714 + 11371.7046897582*$t);
$B0 += 0.00000000316*cos(1.62662805006 + 250908.49012041549*$t);
$B0 += 0.00000000216*cos(3.68721275185 + 5849.3641121146*$t);
$B0 += 0.00000000230*cos(0.36165162947 + 5863.5912061162*$t);
$B0 += 0.00000000233*cos(5.03509933858 + 20426.571092422*$t);
$B0 += 0.00000000200*cos(5.86073159059 + 4535.0594369244*$t);
$B0 += 0.00000000277*cos(4.65400292395 + 82239.16695779889*$t);
$B0 += 0.00000000209*cos(3.72323200804 + 10973.55568635*$t);
$B0 += 0.00000000199*cos(5.05186622555 + 5429.8794682394*$t);
$B0 += 0.00000000256*cos(2.40923279770 + 19651.048481098*$t);
$B0 += 0.00000000210*cos(4.50691909144 + 29088.811415985*$t);
$B0 += 0.00000000181*cos(6.00294783127 + 4292.3308329504*$t);
$B0 += 0.00000000249*cos(0.12900984422 + 154379.79562448629*$t);
$B0 += 0.00000000209*cos(3.87759458598 + 17789.845619785*$t);
$B0 += 0.00000000225*cos(3.18339652605 + 18875.525869774*$t);
$B0 += 0.00000000191*cos(4.53897489299 + 18477.1087646123*$t);
$B0 += 0.00000000172*cos(2.09694183014 + 13095.8426650774*$t);
$B0 += 0.00000000182*cos(3.16107943500 + 16730.4636895958*$t);
$B0 += 0.00000000188*cos(2.22746128596 + 41654.9631159678*$t);
$B0 += 0.00000000164*cos(5.18686275017 + 5481.2549188676*$t);
$B0 += 0.00000000160*cos(2.49298855159 + 12592.4500197826*$t);
$B0 += 0.00000000155*cos(1.59595438230 + 10021.8372800994*$t);
$B0 += 0.00000000135*cos(0.21349051064 + 10988.808157535*$t);
$B0 += 0.00000000178*cos(3.80375177970 + 23581.2581773176*$t);
$B0 += 0.00000000123*cos(1.66800739151 + 15110.4661198662*$t);
$B0 += 0.00000000122*cos(2.72678272244 + 18849.2275499742*$t);
$B0 += 0.00000000126*cos(1.17675512910 + 14919.0178537546*$t);
$B0 += 0.00000000142*cos(3.95053441332 + 337.8142631964*$t);
$B0 += 0.00000000116*cos(6.06340906229 + 6709.6740408674*$t);
$B0 += 0.00000000137*cos(3.52143246757 + 12139.5535091068*$t);
$B0 += 0.00000000136*cos(2.92179113542 + 32217.2001810808*$t);
$B0 += 0.00000000110*cos(3.51203379263 + 18052.9295431578*$t);
$B0 += 0.00000000147*cos(4.63371971408 + 22805.7355659936*$t);
$B0 += 0.00000000108*cos(5.45280814878 + 7.1135470008*$t);
$B0 += 0.00000000148*cos(0.65447253687 + 95480.9471841745*$t);
$B0 += 0.00000000119*cos(5.92110458985 + 33019.0211122046*$t);
$B0 += 0.00000000110*cos(5.34824206306 + 639.897286314*$t);
$B0 += 0.00000000106*cos(3.71081682629 + 14314.1681130498*$t);
$B0 += 0.00000000139*cos(6.17607198418 + 24356.7807886416*$t);
$B0 += 0.00000000118*cos(5.59738712670 + 161338.5000008705*$t);
$B0 += 0.00000000117*cos(3.65065271640 + 45585.1728121874*$t);
$B0 += 0.00000000127*cos(4.74596574209 + 49515.382508407*$t);
$B0 += 0.00000000120*cos(1.04211499785 + 6915.8595893046*$t);
$B0 += 0.00000000120*cos(5.60638811846 + 5650.2921106782*$t);
$B0 += 0.00000000115*cos(3.10668213289 + 14712.317116458*$t);
$B0 += 0.00000000099*cos(0.69018940049 + 12779.4507954208*$t);
$B0 += 0.00000000097*cos(1.07908724794 + 9917.6968745098*$t);
$B0 += 0.00000000093*cos(2.62295197319 + 17260.1546546904*$t);
$B0 += 0.00000000099*cos(4.45774681732 + 4933.2084403326*$t);
$B0 += 0.00000000123*cos(1.37488922089 + 28286.9904848612*$t);
$B0 += 0.00000000121*cos(5.19767249813 + 27511.4678735372*$t);
$B0 += 0.00000000105*cos(0.87192267806 + 77375.95720492408*$t);
$B0 += 0.00000000087*cos(3.93637812950 + 17654.7805397496*$t);
$B0 += 0.00000000122*cos(2.23956068680 + 83997.09113559539*$t);
$B0 += 0.00000000087*cos(4.18201600952 + 22779.4372461938*$t);
$B0 += 0.00000000104*cos(4.59580877295 + 1349.8674096588*$t);
$B0 += 0.00000000102*cos(2.83545248411 + 12352.8526045448*$t);
$B0 += 0.00000000102*cos(3.97386522171 + 10818.1352869158*$t);
$B0 += 0.00000000101*cos(4.32892825857 + 36147.4098773004*$t);
$B0 += 0.00000000094*cos(5.00001709261 + 150192.21439800429*$t);
$B0 += 0.00000000077*cos(3.97199369296 + 1592.5960136328*$t);
$B0 += 0.00000000100*cos(6.07733097102 + 26735.9452622132*$t);
$B0 += 0.00000000086*cos(5.26029638250 + 28313.288804661*$t);
$B0 += 0.00000000093*cos(4.31900620254 + 44809.6502008634*$t);
$B0 += 0.00000000076*cos(6.22743405935 + 13521.7514415914*$t);
$B0 += 0.00000000072*cos(1.55820597747 + 6256.7775301916*$t);
$B0 += 0.00000000082*cos(4.95202664555 + 10575.4066829418*$t);
$B0 += 0.00000000082*cos(1.69647647075 + 1990.745017041*$t);
$B0 += 0.00000000075*cos(2.29836095644 + 3634.6210245184*$t);
$B0 += 0.00000000075*cos(2.66367876557 + 16200.7727245012*$t);
$B0 += 0.00000000087*cos(0.26630214764 + 31441.6775697568*$t);
$B0 += 0.00000000077*cos(2.25530954137 + 5235.3285382367*$t);
$B0 += 0.00000000076*cos(1.09869730846 + 12903.9659631792*$t);
$B0 += 0.00000000058*cos(4.28246138307 + 12559.038152982*$t);
$B0 += 0.00000000064*cos(5.51112830114 + 173904.65170085328*$t);
$B0 += 0.00000000056*cos(2.60133794851 + 73188.3759784421*$t);
$B0 += 0.00000000055*cos(5.81483150022 + 143233.51002162008*$t);
$B0 += 0.00000000054*cos(3.38482031504 + 323049.11878710288*$t);
$B0 += 0.00000000039*cos(3.28500401343 + 71768.50988132549*$t);
$B0 += 0.00000000039*cos(3.11239910690 + 96900.81328129109*$t);
return $B0;
}



function Earth_B1($t) // 99 terms of order 1
{
$B1 = 0.00000009030*cos(3.89729061890 + 5507.5532386674*$t);
$B1 += 0.00000006177*cos(1.73038850355 + 5223.6939198022*$t);
$B1 += 0.00000003800*cos(5.24404145734 + 2352.8661537718*$t);
$B1 += 0.00000002834*cos(2.47345037450 + 1577.3435424478*$t);
$B1 += 0.00000001817*cos(0.41874743765 + 6283.0758499914*$t);
$B1 += 0.00000001499*cos(1.83320979291 + 5856.4776591154*$t);
$B1 += 0.00000001466*cos(5.69401926017 + 5753.3848848968*$t);
$B1 += 0.00000001301*cos(2.18890066314 + 9437.762934887*$t);
$B1 += 0.00000001233*cos(4.95222451476 + 10213.285546211*$t);
$B1 += 0.00000001021*cos(0.12866660208 + 7860.4193924392*$t);
$B1 += 0.00000000982*cos(0.09005453285 + 14143.4952424306*$t);
$B1 += 0.00000000865*cos(1.73949953555 + 3930.2096962196*$t);
$B1 += 0.00000000581*cos(2.26949174067 + 5884.9268465832*$t);
$B1 += 0.00000000524*cos(5.65662503159 + 529.6909650946*$t);
$B1 += 0.00000000473*cos(6.22750969242 + 6309.3741697912*$t);
$B1 += 0.00000000451*cos(1.53288619213 + 18073.7049386502*$t);
$B1 += 0.00000000364*cos(3.61614477374 + 13367.9726311066*$t);
$B1 += 0.00000000372*cos(3.22470721320 + 6275.9623029906*$t);
$B1 += 0.00000000268*cos(2.34341267879 + 11790.6290886588*$t);
$B1 += 0.00000000322*cos(0.94084045832 + 6069.7767545534*$t);
$B1 += 0.00000000232*cos(0.26781182579 + 7058.5984613154*$t);
$B1 += 0.00000000216*cos(6.05952221329 + 10977.078804699*$t);
$B1 += 0.00000000232*cos(2.93325646109 + 22003.9146348698*$t);
$B1 += 0.00000000204*cos(3.86264841382 + 6496.3749454294*$t);
$B1 += 0.00000000202*cos(2.81892511133 + 15720.8387848784*$t);
$B1 += 0.00000000185*cos(4.93512381859 + 12036.4607348882*$t);
$B1 += 0.00000000220*cos(3.99305643742 + 6812.766815086*$t);
$B1 += 0.00000000166*cos(1.74970002999 + 11506.7697697936*$t);
$B1 += 0.00000000212*cos(1.57166285369 + 4694.0029547076*$t);
$B1 += 0.00000000157*cos(1.08259734788 + 5643.1785636774*$t);
$B1 += 0.00000000154*cos(5.99434678412 + 5486.777843175*$t);
$B1 += 0.00000000144*cos(5.23285656085 + 78051.5857313169*$t);
$B1 += 0.00000000144*cos(1.16454655948 + 90617.7374312997*$t);
$B1 += 0.00000000137*cos(2.67760436027 + 6290.1893969922*$t);
$B1 += 0.00000000180*cos(2.06509026215 + 7084.8967811152*$t);
$B1 += 0.00000000121*cos(5.90212574947 + 9225.539273283*$t);
$B1 += 0.00000000150*cos(2.00175038718 + 5230.807466803*$t);
$B1 += 0.00000000149*cos(5.06157254516 + 17298.1823273262*$t);
$B1 += 0.00000000118*cos(5.39979058038 + 3340.6124266998*$t);
$B1 += 0.00000000161*cos(3.32421999691 + 6283.3196674749*$t);
$B1 += 0.00000000121*cos(4.36722193162 + 19651.048481098*$t);
$B1 += 0.00000000116*cos(5.83462858507 + 4705.7323075436*$t);
$B1 += 0.00000000128*cos(4.35489873365 + 25934.1243310894*$t);
$B1 += 0.00000000143;
$B1 += 0.00000000109*cos(2.52157834166 + 6438.4962494256*$t);
$B1 += 0.00000000099*cos(2.70727488041 + 5216.5803728014*$t);
$B1 += 0.00000000103*cos(0.93782340879 + 8827.3902698748*$t);
$B1 += 0.00000000082*cos(4.29214680390 + 8635.9420037632*$t);
$B1 += 0.00000000079*cos(2.24085737326 + 1059.3819301892*$t);
$B1 += 0.00000000097*cos(5.50959692365 + 29864.334027309*$t);
$B1 += 0.00000000072*cos(0.21891639822 + 21228.3920235458*$t);
$B1 += 0.00000000071*cos(2.86755026812 + 6681.2248533996*$t);
$B1 += 0.00000000074*cos(2.20184828895 + 37724.7534197482*$t);
$B1 += 0.00000000063*cos(4.45586625948 + 7079.3738568078*$t);
$B1 += 0.00000000061*cos(0.63918772258 + 33794.5437235286*$t);
$B1 += 0.00000000047*cos(2.09070235724 + 3128.3887650958*$t);
$B1 += 0.00000000047*cos(3.32543843300 + 26087.9031415742*$t);
$B1 += 0.00000000049*cos(1.60680905005 + 6702.5604938666*$t);
$B1 += 0.00000000057*cos(0.11215813438 + 29088.811415985*$t);
$B1 += 0.00000000056*cos(5.47982934911 + 775.522611324*$t);
$B1 += 0.00000000050*cos(1.89396788463 + 12139.5535091068*$t);
$B1 += 0.00000000047*cos(2.97214907240 + 20426.571092422*$t);
$B1 += 0.00000000041*cos(5.55329394890 + 11015.1064773348*$t);
$B1 += 0.00000000041*cos(5.91861144924 + 23581.2581773176*$t);
$B1 += 0.00000000045*cos(4.95273290181 + 5863.5912061162*$t);
$B1 += 0.00000000050*cos(3.62740835096 + 41654.9631159678*$t);
$B1 += 0.00000000037*cos(6.09033460601 + 64809.80550494129*$t);
$B1 += 0.00000000037*cos(5.86153655431 + 12566.1516999828*$t);
$B1 += 0.00000000046*cos(1.65798680284 + 25158.6017197654*$t);
$B1 += 0.00000000038*cos(2.00673650251 + 426.598190876*$t);
$B1 += 0.00000000036*cos(6.24373396652 + 6283.14316029419*$t);
$B1 += 0.00000000036*cos(0.40465162918 + 6283.0085396886*$t);
$B1 += 0.00000000032*cos(6.03707103538 + 2942.4634232916*$t);
$B1 += 0.00000000041*cos(4.86809570283 + 1592.5960136328*$t);
$B1 += 0.00000000028*cos(4.38359423735 + 7632.9432596502*$t);
$B1 += 0.00000000028*cos(6.03334294232 + 17789.845619785*$t);
$B1 += 0.00000000026*cos(3.88971333608 + 5331.3574437408*$t);
$B1 += 0.00000000026*cos(5.94932724051 + 16496.3613962024*$t);
$B1 += 0.00000000031*cos(1.44666331503 + 16730.4636895958*$t);
$B1 += 0.00000000026*cos(6.26376705837 + 23543.23050468179*$t);
$B1 += 0.00000000033*cos(0.93797239147 + 213.299095438*$t);
$B1 += 0.00000000026*cos(3.71858432944 + 13095.8426650774*$t);
$B1 += 0.00000000027*cos(0.60565274405 + 10988.808157535*$t);
$B1 += 0.00000000023*cos(4.44388985550 + 18849.2275499742*$t);
$B1 += 0.00000000028*cos(1.53862289477 + 6279.4854213396*$t);
$B1 += 0.00000000028*cos(1.96831814872 + 6286.6662786432*$t);
$B1 += 0.00000000028*cos(5.78094918529 + 15110.4661198662*$t);
$B1 += 0.00000000026*cos(2.48165809843 + 5729.506447149*$t);
$B1 += 0.00000000020*cos(3.85655029499 + 9623.6882766912*$t);
$B1 += 0.00000000021*cos(5.83006047147 + 7234.794256242*$t);
$B1 += 0.00000000021*cos(0.69628570421 + 398.1490034082*$t);
$B1 += 0.00000000022*cos(5.02222806555 + 6127.6554505572*$t);
$B1 += 0.00000000020*cos(3.47611265290 + 6148.010769956*$t);
$B1 += 0.00000000020*cos(0.90769829044 + 5481.2549188676*$t);
$B1 += 0.00000000020*cos(0.03081589303 + 6418.1409300268*$t);
$B1 += 0.00000000020*cos(3.74220084927 + 1589.0728952838*$t);
$B1 += 0.00000000021*cos(4.00149269576 + 3154.6870848956*$t);
$B1 += 0.00000000018*cos(1.58348238359 + 2118.7638603784*$t);
$B1 += 0.00000000019*cos(0.85407021371 + 14712.317116458*$t);
return $B1*$t;
}



function Earth_B2($t) // 49 terms of order 2
{
$B2 = 0.00000001662*cos(1.62703209173 + 84334.66158130829*$t);
$B2 += 0.00000000492*cos(2.41382223971 + 1047.7473117547*$t);
$B2 += 0.00000000344*cos(2.24353004539 + 5507.5532386674*$t);
$B2 += 0.00000000258*cos(6.00906896311 + 5223.6939198022*$t);
$B2 += 0.00000000131*cos(0.95447345240 + 6283.0758499914*$t);
$B2 += 0.00000000086*cos(1.67530247303 + 7860.4193924392*$t);
$B2 += 0.00000000090*cos(0.97606804452 + 1577.3435424478*$t);
$B2 += 0.00000000090*cos(0.37899871725 + 2352.8661537718*$t);
$B2 += 0.00000000089*cos(6.25807507963 + 10213.285546211*$t);
$B2 += 0.00000000075*cos(0.84213523741 + 167621.57585086189*$t);
$B2 += 0.00000000052*cos(1.70501566089 + 14143.4952424306*$t);
$B2 += 0.00000000057*cos(6.15295833679 + 12194.0329146209*$t);
$B2 += 0.00000000051*cos(1.27616016740 + 5753.3848848968*$t);
$B2 += 0.00000000051*cos(5.37229738682 + 6812.766815086*$t);
$B2 += 0.00000000034*cos(1.73672994279 + 7058.5984613154*$t);
$B2 += 0.00000000038*cos(2.77761031485 + 10988.808157535*$t);
$B2 += 0.00000000046*cos(3.38617099014 + 156475.2902479957*$t);
$B2 += 0.00000000021*cos(1.95248349228 + 8827.3902698748*$t);
$B2 += 0.00000000018*cos(3.33419222028 + 8429.2412664666*$t);
$B2 += 0.00000000019*cos(4.32945160287 + 17789.845619785*$t);
$B2 += 0.00000000017*cos(0.66191210656 + 6283.0085396886*$t);
$B2 += 0.00000000018*cos(3.74885333072 + 11769.8536931664*$t);
$B2 += 0.00000000017*cos(4.23058370776 + 10977.078804699*$t);
$B2 += 0.00000000017*cos(1.78116162721 + 5486.777843175*$t);
$B2 += 0.00000000021*cos(1.36972913918 + 12036.4607348882*$t);
$B2 += 0.00000000017*cos(2.79601092529 + 796.2980068164*$t);
$B2 += 0.00000000015*cos(0.43087848850 + 11790.6290886588*$t);
$B2 += 0.00000000017*cos(1.35132152761 + 78051.5857313169*$t);
$B2 += 0.00000000015*cos(1.17032155085 + 213.299095438*$t);
$B2 += 0.00000000018*cos(2.85221514199 + 5088.6288397668*$t);
$B2 += 0.00000000017*cos(0.21780913672 + 6283.14316029419*$t);
$B2 += 0.00000000013*cos(1.21201504386 + 25132.3033999656*$t);
$B2 += 0.00000000012*cos(1.12953712197 + 90617.7374312997*$t);
$B2 += 0.00000000012*cos(5.13714452592 + 7079.3738568078*$t);
$B2 += 0.00000000013*cos(3.79842135217 + 4933.2084403326*$t);
$B2 += 0.00000000012*cos(4.89407978213 + 3738.761430108*$t);
$B2 += 0.00000000015*cos(6.05682328852 + 398.1490034082*$t);
$B2 += 0.00000000014*cos(4.81029291856 + 4694.0029547076*$t);
$B2 += 0.00000000011*cos(0.61684523405 + 3128.3887650958*$t);
$B2 += 0.00000000011*cos(5.32876538500 + 6040.3472460174*$t);
$B2 += 0.00000000014*cos(5.27227350286 + 4535.0594369244*$t);
$B2 += 0.00000000011*cos(2.39292099451 + 5331.3574437408*$t);
$B2 += 0.00000000010*cos(4.45296532710 + 6525.8044539654*$t);
$B2 += 0.00000000014*cos(4.66400985037 + 8031.0922630584*$t);
$B2 += 0.00000000010*cos(3.22472385926 + 9437.762934887*$t);
$B2 += 0.00000000011*cos(3.80913404437 + 801.8209311238*$t);
$B2 += 0.00000000010*cos(5.15032130575 + 11371.7046897582*$t);
$B2 += 0.00000000013*cos(0.98720797401 + 5729.506447149*$t);
$B2 += 0.00000000009*cos(5.94191743597 + 7632.9432596502*$t);
return $B2*$t*$t;
}



function Earth_B3($t) // 11 terms of order 3
{
$B3 = 0.00000000011*cos(0.23877262399 + 7860.4193924392*$t);
$B3 += 0.00000000009*cos(1.16069982609 + 5507.5532386674*$t);
$B3 += 0.00000000008*cos(1.65357552925 + 5884.9268465832*$t);
$B3 += 0.00000000008*cos(2.86720038197 + 7058.5984613154*$t);
$B3 += 0.00000000007*cos(3.04818741666 + 5486.777843175*$t);
$B3 += 0.00000000007*cos(2.59437103785 + 529.6909650946*$t);
$B3 += 0.00000000008*cos(4.02863090524 + 6256.7775301916*$t);
$B3 += 0.00000000008*cos(2.42003508927 + 5753.3848848968*$t);
$B3 += 0.00000000006*cos(0.84181087594 + 6275.9623029906*$t);
$B3 += 0.00000000006*cos(5.40160929468 + 1577.3435424478*$t);
$B3 += 0.00000000007*cos(2.73399865247 + 6309.3741697912*$t);
return $B3*$t*$t*$t;
}



function Earth_B4($t) // 5 terms of order 4
{
$B4 = 0.00000000004*cos(0.79662198849 + 6438.4962494256*$t);
$B4 += 0.00000000005*cos(0.84308705203 + 1047.7473117547*$t);
$B4 += 0.00000000005*cos(0.05711572303 + 84334.66158130829*$t);
$B4 += 0.00000000003*cos(3.46779895686 + 6279.5527316424*$t);
$B4 += 0.00000000003*cos(2.89822201212 + 6127.6554505572*$t);
return $B4*$t*$t*$t*$t;
}



function Earth_B5($t) // 1 term of order 5
{
$B5 = 0.00000000000;
return $B5*$t*$t*$t*$t*$t;
}



function Earth_R0($t) // 526 terms of order 0
{
$R0 = 1.00013988799;
$R0 += 0.01670699626*cos(3.09846350771 + 6283.0758499914*$t);
$R0 += 0.00013956023*cos(3.05524609620 + 12566.1516999828*$t);
$R0 += 0.00003083720*cos(5.19846674381 + 77713.7714681205*$t);
$R0 += 0.00001628461*cos(1.17387749012 + 5753.3848848968*$t);
$R0 += 0.00001575568*cos(2.84685245825 + 7860.4193924392*$t);
$R0 += 0.00000924799*cos(5.45292234084 + 11506.7697697936*$t);
$R0 += 0.00000542444*cos(4.56409149777 + 3930.2096962196*$t);
$R0 += 0.00000472110*cos(3.66100022149 + 5884.9268465832*$t);
$R0 += 0.00000328780*cos(5.89983646482 + 5223.6939198022*$t);
$R0 += 0.00000345983*cos(0.96368617687 + 5507.5532386674*$t);
$R0 += 0.00000306784*cos(0.29867139512 + 5573.1428014331*$t);
$R0 += 0.00000174844*cos(3.01193636534 + 18849.2275499742*$t);
$R0 += 0.00000243189*cos(4.27349536153 + 11790.6290886588*$t);
$R0 += 0.00000211829*cos(5.84714540314 + 1577.3435424478*$t);
$R0 += 0.00000185752*cos(5.02194447178 + 10977.078804699*$t);
$R0 += 0.00000109835*cos(5.05510636285 + 5486.777843175*$t);
$R0 += 0.00000098316*cos(0.88681311277 + 6069.7767545534*$t);
$R0 += 0.00000086499*cos(5.68959778254 + 15720.8387848784*$t);
$R0 += 0.00000085825*cos(1.27083733351 + 161000.6857376741*$t);
$R0 += 0.00000062916*cos(0.92177108832 + 529.6909650946*$t);
$R0 += 0.00000057056*cos(2.01374292014 + 83996.84731811189*$t);
$R0 += 0.00000064903*cos(0.27250613787 + 17260.1546546904*$t);
$R0 += 0.00000049384*cos(3.24501240359 + 2544.3144198834*$t);
$R0 += 0.00000055736*cos(5.24159798933 + 71430.69561812909*$t);
$R0 += 0.00000042515*cos(6.01110242003 + 6275.9623029906*$t);
$R0 += 0.00000046963*cos(2.57805070386 + 775.522611324*$t);
$R0 += 0.00000038968*cos(5.36071738169 + 4694.0029547076*$t);
$R0 += 0.00000044661*cos(5.53715807302 + 9437.762934887*$t);
$R0 += 0.00000035660*cos(1.67468058995 + 12036.4607348882*$t);
$R0 += 0.00000031921*cos(0.18368229781 + 5088.6288397668*$t);
$R0 += 0.00000031846*cos(1.77775642085 + 398.1490034082*$t);
$R0 += 0.00000033193*cos(0.24370300098 + 7084.8967811152*$t);
$R0 += 0.00000038245*cos(2.39255343974 + 8827.3902698748*$t);
$R0 += 0.00000028464*cos(1.21344868176 + 6286.5989683404*$t);
$R0 += 0.00000037490*cos(0.82952922332 + 19651.048481098*$t);
$R0 += 0.00000036957*cos(4.90107591914 + 12139.5535091068*$t);
$R0 += 0.00000034537*cos(1.84270693282 + 2942.4634232916*$t);
$R0 += 0.00000026275*cos(4.58896850401 + 10447.3878396044*$t);
$R0 += 0.00000024596*cos(3.78660875483 + 8429.2412664666*$t);
$R0 += 0.00000023587*cos(0.26866117066 + 796.2980068164*$t);
$R0 += 0.00000027793*cos(1.89934330904 + 6279.5527316424*$t);
$R0 += 0.00000023927*cos(4.99598548138 + 5856.4776591154*$t);
$R0 += 0.00000020349*cos(4.65267995431 + 2146.1654164752*$t);
$R0 += 0.00000023287*cos(2.80783650928 + 14143.4952424306*$t);
$R0 += 0.00000022103*cos(1.95004702988 + 3154.6870848956*$t);
$R0 += 0.00000019506*cos(5.38227371393 + 2352.8661537718*$t);
$R0 += 0.00000017958*cos(0.19871379385 + 6812.766815086*$t);
$R0 += 0.00000017174*cos(4.43315560735 + 10213.285546211*$t);
$R0 += 0.00000016190*cos(5.23160507859 + 17789.845619785*$t);
$R0 += 0.00000017314*cos(6.15200787916 + 16730.4636895958*$t);
$R0 += 0.00000013814*cos(5.18962074032 + 8031.0922630584*$t);
$R0 += 0.00000018833*cos(0.67306674027 + 149854.40013480789*$t);
$R0 += 0.00000018331*cos(2.25348733734 + 23581.2581773176*$t);
$R0 += 0.00000013641*cos(3.68516118804 + 4705.7323075436*$t);
$R0 += 0.00000013139*cos(0.65289581324 + 13367.9726311066*$t);
$R0 += 0.00000010414*cos(4.33285688538 + 11769.8536931664*$t);
$R0 += 0.00000009978*cos(4.20126336355 + 6309.3741697912*$t);
$R0 += 0.00000010169*cos(1.59390681369 + 4690.4798363586*$t);
$R0 += 0.00000007564*cos(2.62560597390 + 6256.7775301916*$t);
$R0 += 0.00000009661*cos(3.67586791220 + 27511.4678735372*$t);
$R0 += 0.00000006743*cos(0.56270332741 + 3340.6124266998*$t);
$R0 += 0.00000008743*cos(6.06359123461 + 1748.016413067*$t);
$R0 += 0.00000007786*cos(3.67371235637 + 12168.0026965746*$t);
$R0 += 0.00000006633*cos(5.66149277792 + 11371.7046897582*$t);
$R0 += 0.00000007712*cos(0.31242577789 + 7632.9432596502*$t);
$R0 += 0.00000006592*cos(3.13576266188 + 801.8209311238*$t);
$R0 += 0.00000007460*cos(5.64757188143 + 11926.2544136688*$t);
$R0 += 0.00000006933*cos(2.92384586400 + 6681.2248533996*$t);
$R0 += 0.00000006802*cos(1.42329806420 + 23013.5395395872*$t);
$R0 += 0.00000006115*cos(5.13393615454 + 1194.4470102246*$t);
$R0 += 0.00000006477*cos(2.64986648492 + 19804.8272915828*$t);
$R0 += 0.00000005233*cos(4.62434053374 + 6438.4962494256*$t);
$R0 += 0.00000006147*cos(3.02863936662 + 233141.31440436149*$t);
$R0 += 0.00000004608*cos(1.72194702724 + 7234.794256242*$t);
$R0 += 0.00000004221*cos(1.55697533729 + 7238.67559160*$t);
$R0 += 0.00000005314*cos(2.40716580847 + 11499.6562227928*$t);
$R0 += 0.00000005128*cos(5.32398965690 + 11513.8833167944*$t);
$R0 += 0.00000004770*cos(0.25554312006 + 11856.2186514245*$t);
$R0 += 0.00000005519*cos(2.09089154502 + 17298.1823273262*$t);
$R0 += 0.00000005625*cos(4.34052903053 + 90955.5516944961*$t);
$R0 += 0.00000004578*cos(4.46569641570 + 5746.271337896*$t);
$R0 += 0.00000003788*cos(4.90729383510 + 4164.311989613*$t);
$R0 += 0.00000005337*cos(5.09957905104 + 31441.6775697568*$t);
$R0 += 0.00000003967*cos(1.20054555174 + 1349.8674096588*$t);
$R0 += 0.00000004008*cos(3.03007204392 + 1059.3819301892*$t);
$R0 += 0.00000003476*cos(0.76080277030 + 10973.55568635*$t);
$R0 += 0.00000004232*cos(1.05485713117 + 5760.4984318976*$t);
$R0 += 0.00000004582*cos(3.76570026763 + 6386.16862421*$t);
$R0 += 0.00000003335*cos(3.13829943354 + 6836.6452528338*$t);
$R0 += 0.00000003418*cos(3.00072390334 + 4292.3308329504*$t);
$R0 += 0.00000003598*cos(5.70718084323 + 5643.1785636774*$t);
$R0 += 0.00000003237*cos(4.16448773994 + 9917.6968745098*$t);
$R0 += 0.00000004154*cos(2.59941292162 + 7058.5984613154*$t);
$R0 += 0.00000003362*cos(4.54577697964 + 4732.0306273434*$t);
$R0 += 0.00000002978*cos(1.30561268820 + 6283.14316029419*$t);
$R0 += 0.00000002765*cos(0.51311975679 + 26.2983197998*$t);
$R0 += 0.00000002802*cos(5.66263240521 + 8635.9420037632*$t);
$R0 += 0.00000002927*cos(5.73787481548 + 16200.7727245012*$t);
$R0 += 0.00000003164*cos(1.69140262657 + 11015.1064773348*$t);
$R0 += 0.00000002598*cos(2.96244118586 + 25132.3033999656*$t);
$R0 += 0.00000003519*cos(3.62639325753 + 244287.60000722769*$t);
$R0 += 0.00000002676*cos(4.20725700850 + 18073.7049386502*$t);
$R0 += 0.00000002978*cos(1.74971565805 + 6283.0085396886*$t);
$R0 += 0.00000002287*cos(1.06975704977 + 14314.1681130498*$t);
$R0 += 0.00000002863*cos(5.92838131397 + 14712.317116458*$t);
$R0 += 0.00000003071*cos(0.23793217002 + 35371.8872659764*$t);
$R0 += 0.00000002656*cos(0.89959301780 + 12352.8526045448*$t);
$R0 += 0.00000002415*cos(2.79975176257 + 709.9330485583*$t);
$R0 += 0.00000002814*cos(3.51488206882 + 21228.3920235458*$t);
$R0 += 0.00000001977*cos(2.61358297550 + 951.7184062506*$t);
$R0 += 0.00000002548*cos(2.47684686575 + 6208.2942514241*$t);
$R0 += 0.00000001999*cos(0.56090388160 + 7079.3738568078*$t);
$R0 += 0.00000002305*cos(1.05376461628 + 22483.84857449259*$t);
$R0 += 0.00000001855*cos(2.86090681163 + 5216.5803728014*$t);
$R0 += 0.00000002157*cos(1.31396741861 + 154717.60988768269*$t);
$R0 += 0.00000001970*cos(4.36929875289 + 167283.76158766549*$t);
$R0 += 0.00000001635*cos(5.85571606764 + 10984.1923516998*$t);
$R0 += 0.00000001754*cos(2.14452408833 + 6290.1893969922*$t);
$R0 += 0.00000002154*cos(6.03828341543 + 10873.9860304804*$t);
$R0 += 0.00000001714*cos(3.70157691113 + 1592.5960136328*$t);
$R0 += 0.00000001541*cos(6.21598380732 + 23543.23050468179*$t);
$R0 += 0.00000001611*cos(1.99824499377 + 10969.9652576982*$t);
$R0 += 0.00000001712*cos(1.34295663542 + 3128.3887650958*$t);
$R0 += 0.00000001642*cos(5.55026665339 + 6496.3749454294*$t);
$R0 += 0.00000001502*cos(5.43948825854 + 155.4203994342*$t);
$R0 += 0.00000001827*cos(5.91227480261 + 3738.761430108*$t);
$R0 += 0.00000001726*cos(2.16764983583 + 10575.4066829418*$t);
$R0 += 0.00000001532*cos(5.35683107070 + 13521.7514415914*$t);
$R0 += 0.00000001829*cos(1.66006148731 + 39302.096962196*$t);
$R0 += 0.00000001605*cos(1.90928637633 + 6133.5126528568*$t);
$R0 += 0.00000001282*cos(2.46014880418 + 13916.0191096416*$t);
$R0 += 0.00000001211*cos(4.41360631550 + 3894.1818295422*$t);
$R0 += 0.00000001394*cos(1.77801929354 + 9225.539273283*$t);
$R0 += 0.00000001571*cos(4.95512957592 + 25158.6017197654*$t);
$R0 += 0.00000001205*cos(1.19212540615 + 3.523118349*$t);
$R0 += 0.00000001132*cos(2.69830084955 + 6040.3472460174*$t);
$R0 += 0.00000001504*cos(5.77002730341 + 18209.33026366019*$t);
$R0 += 0.00000001393*cos(1.62621805428 + 5120.6011455836*$t);
$R0 += 0.00000001077*cos(2.93931554233 + 17256.6315363414*$t);
$R0 += 0.00000001232*cos(0.71655165307 + 143571.32428481648*$t);
$R0 += 0.00000001087*cos(0.99769687939 + 955.5997416086*$t);
$R0 += 0.00000001068*cos(5.28472576231 + 65147.6197681377*$t);
$R0 += 0.00000000980*cos(5.10949204607 + 6172.869528772*$t);
$R0 += 0.00000001169*cos(3.11664290862 + 14945.3161735544*$t);
$R0 += 0.00000001202*cos(4.02992510402 + 553.5694028424*$t);
$R0 += 0.00000000979*cos(2.00000879212 + 15110.4661198662*$t);
$R0 += 0.00000000962*cos(4.02380771400 + 6282.0955289232*$t);
$R0 += 0.00000000999*cos(3.62643002790 + 6262.300454499*$t);
$R0 += 0.00000001030*cos(5.84989900289 + 213.299095438*$t);
$R0 += 0.00000001014*cos(2.84221578218 + 8662.240323563*$t);
$R0 += 0.00000001185*cos(1.51330541132 + 17654.7805397496*$t);
$R0 += 0.00000000967*cos(2.67081017562 + 5650.2921106782*$t);
$R0 += 0.00000001222*cos(2.65423784904 + 88860.05707098669*$t);
$R0 += 0.00000000981*cos(2.36370360283 + 6206.8097787158*$t);
$R0 += 0.00000001033*cos(0.13874927606 + 11712.9553182308*$t);
$R0 += 0.00000001103*cos(3.08477302937 + 43232.3066584156*$t);
$R0 += 0.00000000781*cos(2.53372735932 + 16496.3613962024*$t);
$R0 += 0.00000001019*cos(3.04569392376 + 6037.244203762*$t);
$R0 += 0.00000000795*cos(5.80662989111 + 5230.807466803*$t);
$R0 += 0.00000000813*cos(3.57710279439 + 10177.2576795336*$t);
$R0 += 0.00000000962*cos(5.31470594766 + 6284.0561710596*$t);
$R0 += 0.00000000721*cos(5.96264301567 + 12559.038152982*$t);
$R0 += 0.00000000966*cos(2.74714939953 + 6244.9428143536*$t);
$R0 += 0.00000000921*cos(0.10155275926 + 29088.811415985*$t);
$R0 += 0.00000000692*cos(3.89764447548 + 1589.0728952838*$t);
$R0 += 0.00000000719*cos(5.91791450402 + 4136.9104335162*$t);
$R0 += 0.00000000772*cos(4.05505682353 + 6127.6554505572*$t);
$R0 += 0.00000000712*cos(5.49291532439 + 22003.9146348698*$t);
$R0 += 0.00000000672*cos(1.60700490811 + 11087.2851259184*$t);
$R0 += 0.00000000690*cos(4.50539825563 + 426.598190876*$t);
$R0 += 0.00000000854*cos(3.26104981596 + 20426.571092422*$t);
$R0 += 0.00000000656*cos(4.32410182940 + 16858.4825329332*$t);
$R0 += 0.00000000840*cos(2.59572585222 + 28766.924424484*$t);
$R0 += 0.00000000692*cos(0.61650089011 + 11403.676995575*$t);
$R0 += 0.00000000700*cos(3.40901167143 + 7.1135470008*$t);
$R0 += 0.00000000726*cos(0.04243053594 + 5481.2549188676*$t);
$R0 += 0.00000000557*cos(4.78317696534 + 20199.094959633*$t);
$R0 += 0.00000000649*cos(1.04027912958 + 6062.6632075526*$t);
$R0 += 0.00000000633*cos(5.70229959167 + 45892.73043315699*$t);
$R0 += 0.00000000592*cos(6.11836729658 + 9623.6882766912*$t);
$R0 += 0.00000000523*cos(3.62840021266 + 5333.9002410216*$t);
$R0 += 0.00000000604*cos(5.57734696185 + 10344.2950653858*$t);
$R0 += 0.00000000496*cos(2.21023499449 + 1990.745017041*$t);
$R0 += 0.00000000691*cos(1.96071732602 + 12416.5885028482*$t);
$R0 += 0.00000000640*cos(1.59074172032 + 18319.5365848796*$t);
$R0 += 0.00000000625*cos(3.82362791378 + 13517.8701062334*$t);
$R0 += 0.00000000663*cos(5.08444996779 + 283.8593188652*$t);
$R0 += 0.00000000475*cos(1.17025894287 + 12569.6748183318*$t);
$R0 += 0.00000000664*cos(4.50029469969 + 47162.5163546352*$t);
$R0 += 0.00000000569*cos(0.16310365162 + 17267.26820169119*$t);
$R0 += 0.00000000568*cos(3.86100969474 + 6076.8903015542*$t);
$R0 += 0.00000000539*cos(4.83282276086 + 18422.62935909819*$t);
$R0 += 0.00000000466*cos(0.75872342878 + 7342.4577801806*$t);
$R0 += 0.00000000541*cos(3.07212190507 + 226858.23855437008*$t);
$R0 += 0.00000000458*cos(0.26774483096 + 4590.910180489*$t);
$R0 += 0.00000000610*cos(1.53597051291 + 33019.0211122046*$t);
$R0 += 0.00000000617*cos(2.62356328726 + 11190.377900137*$t);
$R0 += 0.00000000548*cos(4.55798855791 + 18875.525869774*$t);
$R0 += 0.00000000633*cos(4.60110281228 + 66567.48586525429*$t);
$R0 += 0.00000000596*cos(5.78202396722 + 632.7837393132*$t);
$R0 += 0.00000000533*cos(5.01786882904 + 12132.439962106*$t);
$R0 += 0.00000000603*cos(5.38458554802 + 316428.22867391503*$t);
$R0 += 0.00000000469*cos(0.59168241917 + 21954.15760939799*$t);
$R0 += 0.00000000548*cos(3.50613163558 + 17253.04110768959*$t);
$R0 += 0.00000000502*cos(0.98804327589 + 11609.8625440122*$t);
$R0 += 0.00000000568*cos(1.98497313089 + 7668.6374249425*$t);
$R0 += 0.00000000482*cos(1.62141803864 + 12146.6670561076*$t);
$R0 += 0.00000000391*cos(3.68718382989 + 18052.9295431578*$t);
$R0 += 0.00000000457*cos(3.77205737340 + 156137.47598479928*$t);
$R0 += 0.00000000401*cos(5.28260651958 + 15671.0817594066*$t);
$R0 += 0.00000000469*cos(1.80963184268 + 12562.6285816338*$t);
$R0 += 0.00000000508*cos(3.36399024699 + 20597.2439630412*$t);
$R0 += 0.00000000450*cos(5.66054299250 + 10454.5013866052*$t);
$R0 += 0.00000000375*cos(4.98534633105 + 9779.1086761254*$t);
$R0 += 0.00000000523*cos(0.97215560834 + 155427.54293624099*$t);
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$R0 += 0.00000000055*cos(0.83886167974 + 20452.8694122218*$t);
$R0 += 0.00000000050*cos(1.46327331958 + 37455.7264959744*$t);
$R0 += 0.00000000048*cos(4.53854727167 + 29822.7832363242*$t);
$R0 += 0.00000000058*cos(3.34847975377 + 33990.6183442862*$t);
$R0 += 0.00000000065*cos(1.45522693982 + 76251.32777062019*$t);
$R0 += 0.00000000056*cos(2.35650663692 + 37724.7534197482*$t);
$R0 += 0.00000000052*cos(2.61551081496 + 5999.2165311262*$t);
$R0 += 0.00000000053*cos(0.17334326094 + 77717.29458646949*$t);
$R0 += 0.00000000053*cos(0.79879700631 + 77710.24834977149*$t);
$R0 += 0.00000000047*cos(0.43240779709 + 735.8765135318*$t);
$R0 += 0.00000000053*cos(4.58763261686 + 11616.976091013*$t);
$R0 += 0.00000000048*cos(6.20230111054 + 4171.4255366138*$t);
$R0 += 0.00000000052*cos(1.09723616404 + 640.8776073822*$t);
$R0 += 0.00000000057*cos(3.42008310383 + 50317.2034395308*$t);
$R0 += 0.00000000053*cos(1.01528448581 + 149144.46708624958*$t);
$R0 += 0.00000000047*cos(3.00924906195 + 52175.8062831484*$t);
$R0 += 0.00000000052*cos(2.03254070404 + 6293.7125153412*$t);
$R0 += 0.00000000048*cos(0.12356889734 + 13362.4497067992*$t);
$R0 += 0.00000000045*cos(3.37963782356 + 10763.779709261*$t);
$R0 += 0.00000000047*cos(5.50981287869 + 12779.4507954208*$t);
$R0 += 0.00000000062*cos(5.45209070099 + 949.1756089698*$t);
$R0 += 0.00000000061*cos(2.93237974631 + 5791.4125575326*$t);
$R0 += 0.00000000044*cos(2.87440620802 + 8584.6616659008*$t);
$R0 += 0.00000000046*cos(4.03141796560 + 10667.8004820432*$t);
$R0 += 0.00000000047*cos(3.89902931422 + 3903.9113764198*$t);
$R0 += 0.00000000046*cos(2.75700467329 + 6993.0088985497*$t);
$R0 += 0.00000000045*cos(1.93386293300 + 206.1855484372*$t);
$R0 += 0.00000000047*cos(2.57670800912 + 11492.542675792*$t);
$R0 += 0.00000000044*cos(3.62570223167 + 63658.8777508376*$t);
$R0 += 0.00000000051*cos(0.84536826273 + 12345.739057544*$t);
$R0 += 0.00000000043*cos(0.01524970172 + 37853.8754993826*$t);
$R0 += 0.00000000041*cos(3.27146326065 + 8858.3149443206*$t);
$R0 += 0.00000000045*cos(3.03765521215 + 65236.2212932854*$t);
$R0 += 0.00000000047*cos(1.44447548944 + 21393.5419698576*$t);
$R0 += 0.00000000058*cos(5.45843180927 + 1975.492545856*$t);
$R0 += 0.00000000050*cos(2.13285524146 + 12573.2652469836*$t);
$R0 += 0.00000000041*cos(1.32190847146 + 2547.8375382324*$t);
$R0 += 0.00000000047*cos(3.67579608544 + 28313.288804661*$t);
$R0 += 0.00000000041*cos(2.24013475126 + 8273.8208670324*$t);
$R0 += 0.00000000047*cos(6.21438985953 + 10991.3058987006*$t);
$R0 += 0.00000000042*cos(3.01631817350 + 853.196381752*$t);
$R0 += 0.00000000056*cos(1.09773690181 + 77376.20102240759*$t);
$R0 += 0.00000000040*cos(2.35698541041 + 2699.7348193176*$t);
$R0 += 0.00000000043*cos(5.28030898459 + 17796.9591667858*$t);
$R0 += 0.00000000054*cos(2.59175932091 + 22910.44676536859*$t);
$R0 += 0.00000000054*cos(0.88027764102 + 71960.38658322369*$t);
$R0 += 0.00000000055*cos(0.07988899477 + 83467.15635301729*$t);
$R0 += 0.00000000039*cos(1.12867321442 + 9910.583327509*$t);
$R0 += 0.00000000040*cos(1.35670430524 + 27177.8515292002*$t);
$R0 += 0.00000000039*cos(4.39624220245 + 5618.3198048614*$t);
$R0 += 0.00000000042*cos(4.78798367468 + 7856.89627409019*$t);
$R0 += 0.00000000047*cos(2.75482175292 + 18202.21671665939*$t);
$R0 += 0.00000000039*cos(1.97008298629 + 24491.4257925834*$t);
$R0 += 0.00000000042*cos(4.04346599946 + 7863.9425107882*$t);
$R0 += 0.00000000038*cos(0.49178679251 + 38650.173506199*$t);
$R0 += 0.00000000036*cos(4.86047906533 + 4157.1984426122*$t);
$R0 += 0.00000000043*cos(5.64354880978 + 1062.9050485382*$t);
$R0 += 0.00000000036*cos(3.98066313627 + 12565.1713789146*$t);
$R0 += 0.00000000042*cos(2.30753932657 + 6549.6828917132*$t);
$R0 += 0.00000000040*cos(5.39694918320 + 9498.2122306346*$t);
$R0 += 0.00000000040*cos(3.30603243754 + 23536.11695768099*$t);
$R0 += 0.00000000050*cos(6.15760345261 + 78051.34191383338*$t);
return $R0;
}

function Earth_R1($t) // 292 terms of order 1
{
$R1 = 0.00103018608*cos(1.10748969588 + 6283.0758499914*$t);
$R1 += 0.00001721238*cos(1.06442301418 + 12566.1516999828*$t);
$R1 -= 0.00000702215;
$R1 += 0.00000032346*cos(1.02169059149 + 18849.2275499742*$t);
$R1 += 0.00000030799*cos(2.84353804832 + 5507.5532386674*$t);
$R1 += 0.00000024971*cos(1.31906709482 + 5223.6939198022*$t);
$R1 += 0.00000018485*cos(1.42429748614 + 1577.3435424478*$t);
$R1 += 0.00000010078*cos(5.91378194648 + 10977.078804699*$t);
$R1 += 0.00000008634*cos(0.27146150602 + 5486.777843175*$t);
$R1 += 0.00000008654*cos(1.42046854427 + 6275.9623029906*$t);
$R1 += 0.00000005069*cos(1.68613426734 + 5088.6288397668*$t);
$R1 += 0.00000004985*cos(6.01401770704 + 6286.5989683404*$t);
$R1 += 0.00000004669*cos(5.98724494073 + 529.6909650946*$t);
$R1 += 0.00000004395*cos(0.51800238019 + 4694.0029547076*$t);
$R1 += 0.00000003872*cos(4.74969833437 + 2544.3144198834*$t);
$R1 += 0.00000003750*cos(5.07097685568 + 796.2980068164*$t);
$R1 += 0.00000004100*cos(1.08424786092 + 9437.762934887*$t);
$R1 += 0.00000003518*cos(0.02290216272 + 83996.84731811189*$t);
$R1 += 0.00000003436*cos(0.94937019624 + 71430.69561812909*$t);
$R1 += 0.00000003221*cos(6.15628775313 + 2146.1654164752*$t);
$R1 += 0.00000003414*cos(5.41218322538 + 775.522611324*$t);
$R1 += 0.00000002863*cos(5.48432847146 + 10447.3878396044*$t);
$R1 += 0.00000002520*cos(0.24276941146 + 398.1490034082*$t);
$R1 += 0.00000002201*cos(4.95216196651 + 6812.766815086*$t);
$R1 += 0.00000002186*cos(0.41991743105 + 8031.0922630584*$t);
$R1 += 0.00000002838*cos(3.42034351366 + 2352.8661537718*$t);
$R1 += 0.00000002554*cos(6.13241878525 + 6438.4962494256*$t);
$R1 += 0.00000001932*cos(5.31374608366 + 8429.2412664666*$t);
$R1 += 0.00000002429*cos(3.09164528262 + 4690.4798363586*$t);
$R1 += 0.00000001730*cos(1.53686208550 + 4705.7323075436*$t);
$R1 += 0.00000002250*cos(3.68863633842 + 7084.8967811152*$t);
$R1 += 0.00000002093*cos(1.28191783032 + 1748.016413067*$t);
$R1 += 0.00000001441*cos(0.81656250862 + 14143.4952424306*$t);
$R1 += 0.00000001483*cos(3.22225357771 + 7234.794256242*$t);
$R1 += 0.00000001754*cos(3.22883705112 + 6279.5527316424*$t);
$R1 += 0.00000001583*cos(4.09702349428 + 11499.6562227928*$t);
$R1 += 0.00000001575*cos(5.53890170575 + 3154.6870848956*$t);
$R1 += 0.00000001847*cos(1.82040335363 + 7632.9432596502*$t);
$R1 += 0.00000001504*cos(3.63293385726 + 11513.8833167944*$t);
$R1 += 0.00000001337*cos(4.64440864339 + 6836.6452528338*$t);
$R1 += 0.00000001275*cos(2.69341415363 + 1349.8674096588*$t);
$R1 += 0.00000001352*cos(6.15101580257 + 5746.271337896*$t);
$R1 += 0.00000001125*cos(3.35673439497 + 17789.845619785*$t);
$R1 += 0.00000001470*cos(3.65282991755 + 1194.4470102246*$t);
$R1 += 0.00000001177*cos(2.57676109092 + 13367.9726311066*$t);
$R1 += 0.00000001101*cos(4.49748696552 + 4292.3308329504*$t);
$R1 += 0.00000001234*cos(5.65036509521 + 5760.4984318976*$t);
$R1 += 0.00000000984*cos(0.65517395136 + 5856.4776591154*$t);
$R1 += 0.00000000928*cos(2.32420318751 + 10213.285546211*$t);
$R1 += 0.00000001077*cos(5.82812169132 + 12036.4607348882*$t);
$R1 += 0.00000000916*cos(0.76613009583 + 16730.4636895958*$t);
$R1 += 0.00000000877*cos(1.50137505051 + 11926.2544136688*$t);
$R1 += 0.00000001023*cos(5.62076589825 + 6256.7775301916*$t);
$R1 += 0.00000000851*cos(0.65709335533 + 155.4203994342*$t);
$R1 += 0.00000000802*cos(4.10519132088 + 951.7184062506*$t);
$R1 += 0.00000000857*cos(1.41661697538 + 5753.3848848968*$t);
$R1 += 0.00000000994*cos(1.14418521187 + 1059.3819301892*$t);
$R1 += 0.00000000813*cos(1.63948433322 + 6681.2248533996*$t);
$R1 += 0.00000000662*cos(4.55200452260 + 5216.5803728014*$t);
$R1 += 0.00000000644*cos(4.19478168733 + 6040.3472460174*$t);
$R1 += 0.00000000626*cos(1.50767713598 + 5643.1785636774*$t);
$R1 += 0.00000000590*cos(6.18277145205 + 4164.311989613*$t);
$R1 += 0.00000000635*cos(0.52413263542 + 6290.1893969922*$t);
$R1 += 0.00000000650*cos(0.97935690350 + 25132.3033999656*$t);
$R1 += 0.00000000568*cos(2.30125315873 + 10973.55568635*$t);
$R1 += 0.00000000547*cos(5.27256412213 + 3340.6124266998*$t);
$R1 += 0.00000000547*cos(2.20144422886 + 1592.5960136328*$t);
$R1 += 0.00000000526*cos(0.92464258226 + 11371.7046897582*$t);
$R1 += 0.00000000490*cos(5.90951388655 + 3894.1818295422*$t);
$R1 += 0.00000000478*cos(1.66857963179 + 12168.0026965746*$t);
$R1 += 0.00000000516*cos(3.59803483887 + 10969.9652576982*$t);
$R1 += 0.00000000518*cos(3.97914412373 + 17298.1823273262*$t);
$R1 += 0.00000000534*cos(5.03740926442 + 9917.6968745098*$t);
$R1 += 0.00000000487*cos(2.50545369269 + 6127.6554505572*$t);
$R1 += 0.00000000416*cos(4.04828175503 + 10984.1923516998*$t);
$R1 += 0.00000000538*cos(5.54081539805 + 553.5694028424*$t);
$R1 += 0.00000000402*cos(2.16544019233 + 7860.4193924392*$t);
$R1 += 0.00000000553*cos(2.32177369366 + 11506.7697697936*$t);
$R1 += 0.00000000367*cos(3.39152532250 + 6496.3749454294*$t);
$R1 += 0.00000000360*cos(5.34379853282 + 7079.3738568078*$t);
$R1 += 0.00000000337*cos(3.61563704045 + 11790.6290886588*$t);
$R1 += 0.00000000456*cos(0.30754294809 + 801.8209311238*$t);
$R1 += 0.00000000417*cos(3.70009308674 + 10575.4066829418*$t);
$R1 += 0.00000000381*cos(5.82033971802 + 7058.5984613154*$t);
$R1 += 0.00000000321*cos(0.31988767355 + 16200.7727245012*$t);
$R1 += 0.00000000364*cos(1.08414306177 + 6309.3741697912*$t);
$R1 += 0.00000000294*cos(4.54798604957 + 11856.2186514245*$t);
$R1 += 0.00000000290*cos(1.26473978562 + 8635.9420037632*$t);
$R1 += 0.00000000399*cos(4.16998866302 + 26.2983197998*$t);
$R1 += 0.00000000262*cos(5.08316906342 + 10177.2576795336*$t);
$R1 += 0.00000000243*cos(2.25746091190 + 11712.9553182308*$t);
$R1 += 0.00000000237*cos(1.05070575346 + 242.728603974*$t);
$R1 += 0.00000000275*cos(3.45319481756 + 5884.9268465832*$t);
$R1 += 0.00000000255*cos(5.38496831087 + 21228.3920235458*$t);
$R1 += 0.00000000307*cos(4.24313526604 + 3738.761430108*$t);
$R1 += 0.00000000216*cos(3.46037894728 + 213.299095438*$t);
$R1 += 0.00000000196*cos(0.69029243914 + 1990.745017041*$t);
$R1 += 0.00000000198*cos(5.16301829964 + 12352.8526045448*$t);
$R1 += 0.00000000214*cos(3.91876200279 + 13916.0191096416*$t);
$R1 += 0.00000000212*cos(4.00861198517 + 5230.807466803*$t);
$R1 += 0.00000000184*cos(5.59805976614 + 6283.14316029419*$t);
$R1 += 0.00000000184*cos(2.85275392124 + 7238.67559160*$t);
$R1 += 0.00000000179*cos(2.54259058334 + 14314.1681130498*$t);
$R1 += 0.00000000225*cos(1.64458698399 + 4732.0306273434*$t);
$R1 += 0.00000000236*cos(5.58826125715 + 6069.7767545534*$t);
$R1 += 0.00000000187*cos(2.72805985443 + 6062.6632075526*$t);
$R1 += 0.00000000184*cos(6.04216273598 + 6283.0085396886*$t);
$R1 += 0.00000000230*cos(3.62591335086 + 6284.0561710596*$t);
$R1 += 0.00000000163*cos(2.19117396803 + 18073.7049386502*$t);
$R1 += 0.00000000172*cos(0.97612950740 + 3930.2096962196*$t);
$R1 += 0.00000000215*cos(1.04672844028 + 3496.032826134*$t);
$R1 += 0.00000000169*cos(4.75084479006 + 17267.26820169119*$t);
$R1 += 0.00000000152*cos(0.19390712179 + 9779.1086761254*$t);
$R1 += 0.00000000182*cos(5.16288118255 + 17253.04110768959*$t);
$R1 += 0.00000000149*cos(0.80944184260 + 709.9330485583*$t);
$R1 += 0.00000000163*cos(2.19209570390 + 6076.8903015542*$t);
$R1 += 0.00000000186*cos(5.01159497089 + 11015.1064773348*$t);
$R1 += 0.00000000134*cos(0.97765485759 + 65147.6197681377*$t);
$R1 += 0.00000000141*cos(4.38421981312 + 4136.9104335162*$t);
$R1 += 0.00000000158*cos(4.60974280627 + 9623.6882766912*$t);
$R1 += 0.00000000133*cos(3.30508592837 + 154717.60988768269*$t);
$R1 += 0.00000000163*cos(6.11782626245 + 3.523118349*$t);
$R1 += 0.00000000174*cos(1.58078542187 + 7.1135470008*$t);
$R1 += 0.00000000141*cos(0.49976927274 + 25158.6017197654*$t);
$R1 += 0.00000000124*cos(6.03440460031 + 9225.539273283*$t);
$R1 += 0.00000000150*cos(5.30166336812 + 13517.8701062334*$t);
$R1 += 0.00000000127*cos(1.92389511438 + 22483.84857449259*$t);
$R1 += 0.00000000121*cos(2.37813129011 + 167283.76158766549*$t);
$R1 += 0.00000000120*cos(3.98423684853 + 4686.8894077068*$t);
$R1 += 0.00000000117*cos(5.81072642211 + 12569.6748183318*$t);
$R1 += 0.00000000122*cos(5.60973054224 + 5642.1982426092*$t);
$R1 += 0.00000000157*cos(3.40236426002 + 16496.3613962024*$t);
$R1 += 0.00000000129*cos(2.10705116371 + 1589.0728952838*$t);
$R1 += 0.00000000116*cos(0.55839966736 + 5849.3641121146*$t);
$R1 += 0.00000000123*cos(1.52961392771 + 12559.038152982*$t);
$R1 += 0.00000000111*cos(0.44848279675 + 6172.869528772*$t);
$R1 += 0.00000000123*cos(5.81645568991 + 6282.0955289232*$t);
$R1 += 0.00000000150*cos(4.26278409223 + 3128.3887650958*$t);
$R1 += 0.00000000106*cos(2.27437761356 + 5429.8794682394*$t);
$R1 += 0.00000000104*cos(4.42743707728 + 23543.23050468179*$t);
$R1 += 0.00000000121*cos(0.39459045915 + 12132.439962106*$t);
$R1 += 0.00000000104*cos(2.41842602527 + 426.598190876*$t);
$R1 += 0.00000000110*cos(5.80381480447 + 16858.4825329332*$t);
$R1 += 0.00000000100*cos(2.93805577485 + 4535.0594369244*$t);
$R1 += 0.00000000097*cos(3.97935904984 + 6133.5126528568*$t);
$R1 += 0.00000000110*cos(6.22339014386 + 12146.6670561076*$t);
$R1 += 0.00000000098*cos(0.87576563709 + 6525.8044539654*$t);
$R1 += 0.00000000098*cos(3.15248421301 + 10440.2742926036*$t);
$R1 += 0.00000000095*cos(2.46168411100 + 3097.88382272579*$t);
$R1 += 0.00000000088*cos(0.23371480284 + 13119.72110282519*$t);
$R1 += 0.00000000098*cos(5.77016493489 + 7342.4577801806*$t);
$R1 += 0.00000000092*cos(6.03915555063 + 20426.571092422*$t);
$R1 += 0.00000000096*cos(5.56909292561 + 2388.8940204492*$t);
$R1 += 0.00000000081*cos(1.32131147691 + 5650.2921106782*$t);
$R1 += 0.00000000086*cos(3.94529200528 + 10454.5013866052*$t);
$R1 += 0.00000000076*cos(2.70729716925 + 143571.32428481648*$t);
$R1 += 0.00000000091*cos(5.64100034152 + 8827.3902698748*$t);
$R1 += 0.00000000076*cos(1.80783856698 + 28286.9904848612*$t);
$R1 += 0.00000000081*cos(1.90858992196 + 29088.811415985*$t);
$R1 += 0.00000000075*cos(3.40955892978 + 5481.2549188676*$t);
$R1 += 0.00000000069*cos(4.49936170873 + 17256.6315363414*$t);
$R1 += 0.00000000088*cos(1.10098454357 + 11769.8536931664*$t);
$R1 += 0.00000000066*cos(2.78285801977 + 536.8045120954*$t);
$R1 += 0.00000000068*cos(3.88179770758 + 17260.1546546904*$t);
$R1 += 0.00000000084*cos(1.59303306354 + 9380.9596727172*$t);
$R1 += 0.00000000088*cos(3.88076636762 + 7477.522860216*$t);
$R1 += 0.00000000061*cos(6.17558202197 + 11087.2851259184*$t);
$R1 += 0.00000000060*cos(4.34824715818 + 6206.8097787158*$t);
$R1 += 0.00000000082*cos(4.59843208943 + 9388.0059094152*$t);
$R1 += 0.00000000079*cos(1.63131230601 + 4933.2084403326*$t);
$R1 += 0.00000000078*cos(4.20905757484 + 5729.506447149*$t);
$R1 += 0.00000000057*cos(5.48157926651 + 18319.5365848796*$t);
$R1 += 0.00000000060*cos(1.01261781084 + 12721.572099417*$t);
$R1 += 0.00000000056*cos(1.63031935692 + 15720.8387848784*$t);
$R1 += 0.00000000055*cos(0.24926735018 + 15110.4661198662*$t);
$R1 += 0.00000000061*cos(5.93059279661 + 12539.853380183*$t);
$R1 += 0.00000000055*cos(4.84298966314 + 13095.8426650774*$t);
$R1 += 0.00000000067*cos(6.11690589247 + 8662.240323563*$t);
$R1 += 0.00000000054*cos(5.73750638571 + 3634.6210245184*$t);
$R1 += 0.00000000074*cos(1.05466745829 + 16460.33352952499*$t);
$R1 += 0.00000000053*cos(2.29084335688 + 16062.1845261168*$t);
$R1 += 0.00000000064*cos(2.13513767927 + 7875.6718636242*$t);
$R1 += 0.00000000067*cos(0.07096807518 + 14945.3161735544*$t);
$R1 += 0.00000000051*cos(2.31511194429 + 6262.7205305926*$t);
$R1 += 0.00000000057*cos(5.77055471237 + 12043.574281889*$t);
$R1 += 0.00000000056*cos(4.41980790431 + 4701.1165017084*$t);
$R1 += 0.00000000059*cos(5.87963500073 + 5331.3574437408*$t);
$R1 += 0.00000000058*cos(2.30546168628 + 955.5997416086*$t);
$R1 += 0.00000000049*cos(1.93839278478 + 5333.9002410216*$t);
$R1 += 0.00000000048*cos(2.69973662261 + 6709.6740408674*$t);
$R1 += 0.00000000064*cos(1.64379897981 + 6262.300454499*$t);
$R1 += 0.00000000046*cos(3.98449608961 + 98068.53671630539*$t);
$R1 += 0.00000000050*cos(3.68875893005 + 12323.4230960088*$t);
$R1 += 0.00000000045*cos(3.30068569697 + 22003.9146348698*$t);
$R1 += 0.00000000047*cos(1.26317154881 + 11919.140866668*$t);
$R1 += 0.00000000045*cos(0.89150445122 + 51868.2486621788*$t);
$R1 += 0.00000000043*cos(1.61526242998 + 6277.552925684*$t);
$R1 += 0.00000000043*cos(5.74295325645 + 11403.676995575*$t);
$R1 += 0.00000000044*cos(3.43070646822 + 10021.8372800994*$t);
$R1 += 0.00000000056*cos(0.02481833774 + 15671.0817594066*$t);
$R1 += 0.00000000055*cos(3.14274403422 + 33019.0211122046*$t);
$R1 += 0.00000000045*cos(3.00877289177 + 8982.810669309*$t);
$R1 += 0.00000000046*cos(0.73303568429 + 6303.4311693902*$t);
$R1 += 0.00000000049*cos(1.60455690285 + 6303.8512454838*$t);
$R1 += 0.00000000045*cos(0.40210030323 + 6805.6532680852*$t);
$R1 += 0.00000000053*cos(0.94869680175 + 10988.808157535*$t);
$R1 += 0.00000000041*cos(1.61122384329 + 6819.8803620868*$t);
$R1 += 0.00000000055*cos(0.89439119424 + 11933.3679606696*$t);
$R1 += 0.00000000045*cos(3.88495384656 + 60530.4889857418*$t);
$R1 += 0.00000000040*cos(4.75740908001 + 38526.574350872*$t);
$R1 += 0.00000000040*cos(1.49921251887 + 18451.07854656599*$t);
$R1 += 0.00000000040*cos(3.77498297228 + 26087.9031415742*$t);
$R1 += 0.00000000051*cos(1.70258603562 + 1551.045222648*$t);
$R1 += 0.00000000039*cos(2.97100699926 + 2118.7638603784*$t);
$R1 += 0.00000000053*cos(5.19854123078 + 77713.7714681205*$t);
$R1 += 0.00000000047*cos(4.26356628717 + 21424.4666443034*$t);
$R1 += 0.00000000037*cos(0.62902722802 + 24356.7807886416*$t);
$R1 += 0.00000000036*cos(0.11087914947 + 10344.2950653858*$t);
$R1 += 0.00000000036*cos(0.77037556319 + 12029.3471878874*$t);
$R1 += 0.00000000035*cos(3.30933994515 + 24072.9214697764*$t);
$R1 += 0.00000000035*cos(5.93650887012 + 31570.7996493912*$t);
$R1 += 0.00000000036*cos(2.15108874765 + 30774.5016425748*$t);
$R1 += 0.00000000036*cos(1.75078825382 + 16207.886271502*$t);
$R1 += 0.00000000033*cos(5.06264177921 + 226858.23855437008*$t);
$R1 += 0.00000000034*cos(6.16891378800 + 24491.4257925834*$t);
$R1 += 0.00000000035*cos(3.19120695549 + 32217.2001810808*$t);
$R1 += 0.00000000034*cos(2.31528650443 + 55798.4583583984*$t);
$R1 += 0.00000000032*cos(4.21446357042 + 15664.03552270859*$t);
$R1 += 0.00000000039*cos(1.24979117796 + 6418.1409300268*$t);
$R1 += 0.00000000037*cos(4.11943655770 + 2787.0430238574*$t);
$R1 += 0.00000000032*cos(1.62887710890 + 639.897286314*$t);
$R1 += 0.00000000038*cos(5.89832942685 + 640.8776073822*$t);
$R1 += 0.00000000032*cos(1.72442327688 + 27433.88921587499*$t);
$R1 += 0.00000000031*cos(2.78828943753 + 12139.5535091068*$t);
$R1 += 0.00000000035*cos(4.44608896525 + 18202.21671665939*$t);
$R1 += 0.00000000034*cos(3.96287980676 + 18216.443810661*$t);
$R1 += 0.00000000033*cos(4.73611335874 + 16723.350142595*$t);
$R1 += 0.00000000034*cos(1.43910280005 + 49515.382508407*$t);
$R1 += 0.00000000031*cos(0.23302920161 + 23581.2581773176*$t);
$R1 += 0.00000000029*cos(2.02633840220 + 11609.8625440122*$t);
$R1 += 0.00000000030*cos(2.54923230240 + 9924.8104215106*$t);
$R1 += 0.00000000032*cos(4.91793198558 + 11300.5842213564*$t);
$R1 += 0.00000000028*cos(0.26187189577 + 13521.7514415914*$t);
$R1 += 0.00000000028*cos(3.84568936822 + 2699.7348193176*$t);
$R1 += 0.00000000029*cos(1.83149729794 + 29822.7832363242*$t);
$R1 += 0.00000000033*cos(4.60320094415 + 19004.6479494084*$t);
$R1 += 0.00000000027*cos(4.46183450287 + 6702.5604938666*$t);
$R1 += 0.00000000030*cos(4.46494072240 + 36147.4098773004*$t);
$R1 += 0.00000000027*cos(0.03211931363 + 6279.7894925736*$t);
$R1 += 0.00000000026*cos(5.46497324333 + 6245.0481773556*$t);
$R1 += 0.00000000035*cos(4.52695674113 + 36949.2308084242*$t);
$R1 += 0.00000000027*cos(3.52528177609 + 10770.8932562618*$t);
$R1 += 0.00000000026*cos(1.48499438453 + 11080.1715789176*$t);
$R1 += 0.00000000035*cos(2.82154380962 + 19402.7969528166*$t);
$R1 += 0.00000000025*cos(2.46339998836 + 6279.4854213396*$t);
$R1 += 0.00000000026*cos(4.97688894643 + 16737.5772365966*$t);
$R1 += 0.00000000026*cos(2.36136541526 + 17996.0311682222*$t);
$R1 += 0.00000000029*cos(4.15148654061 + 45892.73043315699*$t);
$R1 += 0.00000000026*cos(4.50714272714 + 17796.9591667858*$t);
$R1 += 0.00000000027*cos(4.72625223674 + 1066.49547719*$t);
$R1 += 0.00000000025*cos(2.89309528854 + 6286.6662786432*$t);
$R1 += 0.00000000027*cos(0.37462444357 + 12964.300703391*$t);
$R1 += 0.00000000029*cos(4.94860010533 + 5863.5912061162*$t);
$R1 += 0.00000000031*cos(3.93096113577 + 29864.334027309*$t);
$R1 += 0.00000000024*cos(6.14987193584 + 18606.4989460002*$t);
$R1 += 0.00000000024*cos(3.74225964547 + 29026.48522950779*$t);
$R1 += 0.00000000025*cos(5.70460621565 + 27707.5424942948*$t);
$R1 += 0.00000000025*cos(5.33928840652 + 15141.390794312*$t);
$R1 += 0.00000000027*cos(3.02320897140 + 6286.3622074092*$t);
$R1 += 0.00000000023*cos(0.28364955406 + 5327.4761083828*$t);
$R1 += 0.00000000026*cos(1.34240461687 + 18875.525869774*$t);
$R1 += 0.00000000024*cos(1.33998410121 + 19800.9459562248*$t);
$R1 += 0.00000000025*cos(6.00172494004 + 6489.2613984286*$t);
$R1 += 0.00000000022*cos(1.81777974484 + 6288.5987742988*$t);
$R1 += 0.00000000022*cos(3.58603606640 + 6915.8595893046*$t);
$R1 += 0.00000000029*cos(2.09564449439 + 15265.8865193004*$t);
$R1 += 0.00000000022*cos(1.02173599251 + 11925.2740926006*$t);
$R1 += 0.00000000022*cos(4.74660932338 + 28230.18722269139*$t);
$R1 += 0.00000000021*cos(2.30688751432 + 5999.2165311262*$t);
$R1 += 0.00000000021*cos(3.22654944430 + 25934.1243310894*$t);
$R1 += 0.00000000021*cos(3.04956726238 + 6566.9351688566*$t);
$R1 += 0.00000000027*cos(5.35653084499 + 33794.5437235286*$t);
$R1 += 0.00000000028*cos(3.91168324815 + 18208.349942592*$t);
$R1 += 0.00000000020*cos(1.52296293311 + 135.0650800354*$t);
$R1 += 0.00000000022*cos(4.66462839521 + 13362.4497067992*$t);
$R1 += 0.00000000019*cos(1.78121167862 + 156137.47598479928*$t);
$R1 += 0.00000000019*cos(2.99969102221 + 19651.048481098*$t);
$R1 += 0.00000000019*cos(2.86664273362 + 18422.62935909819*$t);
$R1 += 0.00000000025*cos(0.94995632141 + 31415.379249957*$t);
$R1 += 0.00000000019*cos(4.71432851499 + 77690.75950573849*$t);
$R1 += 0.00000000019*cos(2.54227398241 + 77736.78343050249*$t);
$R1 += 0.00000000020*cos(5.91915117116 + 48739.859897083*$t);
return $R1*$t;
}



function Earth_R2($t) // 139 terms of order 2
{
$R2 = 0.00004359385*cos(5.78455133738 + 6283.0758499914*$t);
$R2 += 0.00000123633*cos(5.57934722157 + 12566.1516999828*$t);
$R2 -= 0.00000012341;
$R2 += 0.00000008792*cos(3.62777733395 + 77713.7714681205*$t);
$R2 += 0.00000005689*cos(1.86958905084 + 5573.1428014331*$t);
$R2 += 0.00000003301*cos(5.47027913302 + 18849.2275499742*$t);
$R2 += 0.00000001471*cos(4.48028885617 + 5507.5532386674*$t);
$R2 += 0.00000001013*cos(2.81456417694 + 5223.6939198022*$t);
$R2 += 0.00000000854*cos(3.10878241236 + 1577.3435424478*$t);
$R2 += 0.00000001102*cos(2.84173992403 + 161000.6857376741*$t);
$R2 += 0.00000000648*cos(5.47349498544 + 775.522611324*$t);
$R2 += 0.00000000609*cos(1.37969434104 + 6438.4962494256*$t);
$R2 += 0.00000000499*cos(4.41649242250 + 6286.5989683404*$t);
$R2 += 0.00000000417*cos(0.90242451175 + 10977.078804699*$t);
$R2 += 0.00000000402*cos(3.20376585290 + 5088.6288397668*$t);
$R2 += 0.00000000351*cos(1.81079227770 + 5486.777843175*$t);
$R2 += 0.00000000467*cos(3.65753702738 + 7084.8967811152*$t);
$R2 += 0.00000000458*cos(5.38585314743 + 149854.40013480789*$t);
$R2 += 0.00000000304*cos(3.51701098693 + 796.2980068164*$t);
$R2 += 0.00000000266*cos(6.17413982699 + 6836.6452528338*$t);
$R2 += 0.00000000279*cos(1.84120501086 + 4694.0029547076*$t);
$R2 += 0.00000000260*cos(1.41629543251 + 2146.1654164752*$t);
$R2 += 0.00000000266*cos(3.13832905677 + 71430.69561812909*$t);
$R2 += 0.00000000321*cos(5.35313367048 + 3154.6870848956*$t);
$R2 += 0.00000000238*cos(2.17720020018 + 155.4203994342*$t);
$R2 += 0.00000000293*cos(4.61501268144 + 4690.4798363586*$t);
$R2 += 0.00000000229*cos(4.75969588070 + 7234.794256242*$t);
$R2 += 0.00000000211*cos(0.21868065485 + 4705.7323075436*$t);
$R2 += 0.00000000201*cos(4.21905743357 + 1349.8674096588*$t);
$R2 += 0.00000000195*cos(4.57808285364 + 529.6909650946*$t);
$R2 += 0.00000000253*cos(2.81496293039 + 1748.016413067*$t);
$R2 += 0.00000000182*cos(5.70454011389 + 6040.3472460174*$t);
$R2 += 0.00000000179*cos(6.02897097053 + 4292.3308329504*$t);
$R2 += 0.00000000186*cos(1.58690991244 + 6309.3741697912*$t);
$R2 += 0.00000000170*cos(2.90220009715 + 9437.762934887*$t);
$R2 += 0.00000000166*cos(1.99984925026 + 8031.0922630584*$t);
$R2 += 0.00000000158*cos(0.04783713552 + 2544.3144198834*$t);
$R2 += 0.00000000197*cos(2.01083639502 + 1194.4470102246*$t);
$R2 += 0.00000000165*cos(5.78372596778 + 83996.84731811189*$t);
$R2 += 0.00000000214*cos(3.38285934319 + 7632.9432596502*$t);
$R2 += 0.00000000140*cos(0.36401486094 + 10447.3878396044*$t);
$R2 += 0.00000000151*cos(0.95153163031 + 6127.6554505572*$t);
$R2 += 0.00000000136*cos(1.48426306582 + 2352.8661537718*$t);
$R2 += 0.00000000127*cos(5.48475435134 + 951.7184062506*$t);
$R2 += 0.00000000126*cos(5.26866506592 + 6279.5527316424*$t);
$R2 += 0.00000000125*cos(3.75754889288 + 6812.766815086*$t);
$R2 += 0.00000000101*cos(4.95015746147 + 398.1490034082*$t);
$R2 += 0.00000000102*cos(0.68468295277 + 1592.5960136328*$t);
$R2 += 0.00000000100*cos(1.14568935785 + 3894.1818295422*$t);
$R2 += 0.00000000129*cos(0.76540016965 + 553.5694028424*$t);
$R2 += 0.00000000109*cos(5.41063597567 + 6256.7775301916*$t);
$R2 += 0.00000000075*cos(5.84804322893 + 242.728603974*$t);
$R2 += 0.00000000095*cos(1.94452244083 + 11856.2186514245*$t);
$R2 += 0.00000000077*cos(0.69373708195 + 8429.2412664666*$t);
$R2 += 0.00000000100*cos(5.19725292131 + 244287.60000722769*$t);
$R2 += 0.00000000080*cos(6.18440483705 + 1059.3819301892*$t);
$R2 += 0.00000000069*cos(5.25699888595 + 14143.4952424306*$t);
$R2 += 0.00000000085*cos(5.39484725499 + 25132.3033999656*$t);
$R2 += 0.00000000066*cos(0.51779993906 + 801.8209311238*$t);
$R2 += 0.00000000055*cos(5.16878202461 + 7058.5984613154*$t);
$R2 += 0.00000000051*cos(3.88759155247 + 12036.4607348882*$t);
$R2 += 0.00000000050*cos(5.57636570536 + 6290.1893969922*$t);
$R2 += 0.00000000061*cos(2.24359003264 + 8635.9420037632*$t);
$R2 += 0.00000000050*cos(5.54441900966 + 1990.745017041*$t);
$R2 += 0.00000000056*cos(4.00301078040 + 13367.9726311066*$t);
$R2 += 0.00000000052*cos(4.13138898038 + 7860.4193924392*$t);
$R2 += 0.00000000052*cos(3.90943054011 + 26.2983197998*$t);
$R2 += 0.00000000041*cos(3.57128482780 + 7079.3738568078*$t);
$R2 += 0.00000000056*cos(2.76959005761 + 90955.5516944961*$t);
$R2 += 0.00000000042*cos(1.91461189199 + 7477.522860216*$t);
$R2 += 0.00000000042*cos(0.42728171713 + 10213.285546211*$t);
$R2 += 0.00000000042*cos(1.09413724455 + 709.9330485583*$t);
$R2 += 0.00000000039*cos(3.93298068961 + 10973.55568635*$t);
$R2 += 0.00000000038*cos(6.17935925345 + 9917.6968745098*$t);
$R2 += 0.00000000049*cos(0.83021145241 + 11506.7697697936*$t);
$R2 += 0.00000000053*cos(1.45828359397 + 233141.31440436149*$t);
$R2 += 0.00000000047*cos(6.21568666789 + 6681.2248533996*$t);
$R2 += 0.00000000037*cos(0.36359309980 + 10177.2576795336*$t);
$R2 += 0.00000000035*cos(3.33024911524 + 5643.1785636774*$t);
$R2 += 0.00000000034*cos(5.63446915337 + 6525.8044539654*$t);
$R2 += 0.00000000035*cos(5.36033855038 + 25158.6017197654*$t);
$R2 += 0.00000000034*cos(5.36319798321 + 4933.2084403326*$t);
$R2 += 0.00000000033*cos(4.24722336872 + 12569.6748183318*$t);
$R2 += 0.00000000043*cos(5.26370903404 + 10575.4066829418*$t);
$R2 += 0.00000000042*cos(5.08837645072 + 11015.1064773348*$t);
$R2 += 0.00000000040*cos(1.98334703186 + 6284.0561710596*$t);
$R2 += 0.00000000042*cos(4.22496037505 + 88860.05707098669*$t);
$R2 += 0.00000000029*cos(3.19088628170 + 11926.2544136688*$t);
$R2 += 0.00000000029*cos(0.15217616684 + 12168.0026965746*$t);
$R2 += 0.00000000030*cos(1.61904744136 + 9779.1086761254*$t);
$R2 += 0.00000000027*cos(0.76388991416 + 1589.0728952838*$t);
$R2 += 0.00000000036*cos(2.74712003443 + 3738.761430108*$t);
$R2 += 0.00000000033*cos(3.08807829566 + 3930.2096962196*$t);
$R2 += 0.00000000031*cos(5.34906619513 + 143571.32428481648*$t);
$R2 += 0.00000000025*cos(0.10240267494 + 22483.84857449259*$t);
$R2 += 0.00000000030*cos(3.47110495524 + 14945.3161735544*$t);
$R2 += 0.00000000024*cos(1.10425016019 + 4535.0594369244*$t);
$R2 += 0.00000000024*cos(1.58037259780 + 6496.3749454294*$t);
$R2 += 0.00000000023*cos(3.87710321433 + 6275.9623029906*$t);
$R2 += 0.00000000025*cos(3.94529778970 + 3128.3887650958*$t);
$R2 += 0.00000000023*cos(3.44685609601 + 4136.9104335162*$t);
$R2 += 0.00000000023*cos(3.83156029849 + 5753.3848848968*$t);
$R2 += 0.00000000022*cos(1.86956128067 + 16730.4636895958*$t);
$R2 += 0.00000000025*cos(2.42188933855 + 5729.506447149*$t);
$R2 += 0.00000000020*cos(1.78208352927 + 17789.845619785*$t);
$R2 += 0.00000000021*cos(4.30363087400 + 16858.4825329332*$t);
$R2 += 0.00000000021*cos(0.49258939822 + 29088.811415985*$t);
$R2 += 0.00000000025*cos(1.33030250444 + 6282.0955289232*$t);
$R2 += 0.00000000027*cos(2.54785812264 + 3496.032826134*$t);
$R2 += 0.00000000022*cos(1.11232521950 + 12721.572099417*$t);
$R2 += 0.00000000021*cos(5.97759081637 + 7.1135470008*$t);
$R2 += 0.00000000019*cos(0.80292033311 + 16062.1845261168*$t);
$R2 += 0.00000000023*cos(4.12454848769 + 2388.8940204492*$t);
$R2 += 0.00000000022*cos(4.92663152168 + 18875.525869774*$t);
$R2 += 0.00000000023*cos(5.68902059771 + 16460.33352952499*$t);
$R2 += 0.00000000023*cos(4.97346265647 + 17260.1546546904*$t);
$R2 += 0.00000000023*cos(3.03021283729 + 66567.48586525429*$t);
$R2 += 0.00000000016*cos(3.89740925257 + 5331.3574437408*$t);
$R2 += 0.00000000017*cos(3.08268671348 + 154717.60988768269*$t);
$R2 += 0.00000000016*cos(3.95085099736 + 3097.88382272579*$t);
$R2 += 0.00000000016*cos(3.99041783945 + 6283.14316029419*$t);
$R2 += 0.00000000020*cos(6.10644140189 + 167283.76158766549*$t);
$R2 += 0.00000000015*cos(4.09775914607 + 11712.9553182308*$t);
$R2 += 0.00000000016*cos(5.71769940700 + 17298.1823273262*$t);
$R2 += 0.00000000016*cos(3.28894009404 + 5884.9268465832*$t);
$R2 += 0.00000000015*cos(5.64785377164 + 12559.038152982*$t);
$R2 += 0.00000000016*cos(4.43452080930 + 6283.0085396886*$t);
$R2 += 0.00000000014*cos(2.31721603062 + 5481.2549188676*$t);
$R2 += 0.00000000014*cos(4.43479032305 + 13517.8701062334*$t);
$R2 += 0.00000000014*cos(4.73209312936 + 7342.4577801806*$t);
$R2 += 0.00000000012*cos(0.64705975463 + 18073.7049386502*$t);
$R2 += 0.00000000011*cos(1.51443332200 + 16200.7727245012*$t);
$R2 += 0.00000000011*cos(0.88708889185 + 21228.3920235458*$t);
$R2 += 0.00000000014*cos(4.50116508534 + 640.8776073822*$t);
$R2 += 0.00000000011*cos(4.64339996198 + 11790.6290886588*$t);
$R2 += 0.00000000011*cos(1.31064298246 + 4164.311989613*$t);
$R2 += 0.00000000009*cos(3.02238989305 + 23543.23050468179*$t);
$R2 += 0.00000000009*cos(2.04999402381 + 22003.9146348698*$t);
$R2 += 0.00000000009*cos(4.91488110218 + 213.299095438*$t);
return $R2*$t*$t;
}



function Earth_R3($t) // 27 terms of order 3
{
$R3 = 0.00000144595*cos(4.27319435148 + 6283.0758499914*$t);
$R3 += 0.00000006729*cos(3.91697608662 + 12566.1516999828*$t);
$R3 += 0.00000000774;
$R3 += 0.00000000247*cos(3.73019298781 + 18849.2275499742*$t);
$R3 += 0.00000000036*cos(2.80081409050 + 6286.5989683404*$t);
$R3 += 0.00000000033*cos(5.62216602775 + 6127.6554505572*$t);
$R3 += 0.00000000019*cos(3.71292621802 + 6438.4962494256*$t);
$R3 += 0.00000000016*cos(4.26011484232 + 6525.8044539654*$t);
$R3 += 0.00000000016*cos(3.50416887054 + 6256.7775301916*$t);
$R3 += 0.00000000014*cos(3.62127621114 + 25132.3033999656*$t);
$R3 += 0.00000000011*cos(4.39200958819 + 4705.7323075436*$t);
$R3 += 0.00000000011*cos(5.22327127059 + 6040.3472460174*$t);
$R3 += 0.00000000010*cos(4.28045254647 + 83996.84731811189*$t);
$R3 += 0.00000000009*cos(1.56864096494 + 5507.5532386674*$t);
$R3 += 0.00000000011*cos(1.37795688024 + 6309.3741697912*$t);
$R3 += 0.00000000010*cos(5.19937959068 + 71430.69561812909*$t);
$R3 += 0.00000000009*cos(0.47275199930 + 6279.5527316424*$t);
$R3 += 0.00000000009*cos(0.74642756529 + 5729.506447149*$t);
$R3 += 0.00000000007*cos(2.97374891560 + 775.522611324*$t);
$R3 += 0.00000000007*cos(3.28615691021 + 7058.5984613154*$t);
$R3 += 0.00000000007*cos(2.19184402142 + 6812.766815086*$t);
$R3 += 0.00000000005*cos(3.15419034438 + 529.6909650946*$t);
$R3 += 0.00000000006*cos(4.54725567047 + 1059.3819301892*$t);
$R3 += 0.00000000005*cos(1.51104406936 + 7079.3738568078*$t);
$R3 += 0.00000000007*cos(2.98052059053 + 6681.2248533996*$t);
$R3 += 0.00000000005*cos(2.30961231391 + 12036.4607348882*$t);
$R3 += 0.00000000005*cos(3.71102966917 + 6290.1893969922*$t);
return $R3*$t*$t*$t;
}



function Earth_R4($t) // 10 terms of order 4
{
$R4 = 0.00000003858*cos(2.56384387339 + 6283.0758499914*$t);
$R4 += 0.00000000306*cos(2.26769501230 + 12566.1516999828*$t);
$R4 += 0.00000000053*cos(3.44031471924 + 5573.1428014331*$t);
$R4 += 0.00000000015*cos(2.04794573436 + 18849.2275499742*$t);
$R4 += 0.00000000013*cos(2.05688873673 + 77713.7714681205*$t);
$R4 += 0.00000000007*cos(4.41218854480 + 161000.6857376741*$t);
$R4 += 0.00000000005*cos(5.26154653107 + 6438.4962494256*$t);
$R4 += 0.00000000005*cos(4.07695126049 + 6127.6554505572*$t);
$R4 += 0.00000000006*cos(3.81514213664 + 149854.40013480789*$t);
$R4 += 0.00000000003*cos(1.28175749811 + 6286.5989683404*$t);
return $R4*$t*$t*$t*$t;
}



function Earth_R5($t) // 3 terms of order 5
{
$R5 = 0.00000000086*cos(1.21579741687 + 6283.0758499914*$t);
$R5 += 0.00000000012*cos(0.65617264033 + 12566.1516999828*$t);
$R5 += 0.00000000001*cos(0.38068797142 + 18849.2275499742*$t);
return $R5*$t*$t*$t*$t*$t;
}


?>

Tại sao tôi lại đưa tính toán lên đây. Lý do, chính tôi cũng đã gặp quả đắng khi sử dụng các kết luận của ông Hồ Ngọc Đức. Các tính toán rất phức tạp, nhưng ông Đức đã vất đi các hạng tử bậc cao của khai triển taylor, khiến cho các sai số nảy sinh.
Hệ quả, rất nhiều trường hợp bị sai sót 3-6 phút khi tính toán.
Có bạn hỏi, 6 phút thì sao?
Vâng, nếu mà ta tính lịch thái ất, 10 triệu năm cho số tích tuế, lại là vấn đề không nhỏ đâu.

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#3 MikeDo

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Gửi vào 01/12/2016 - 18:24

Tại sao lúc này, không thấy mấy lão chém gió vào sửa nhỉ? Cộng đồng đang rất cần cơ mà.

#4 quanphuc2015

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Gửi vào 01/12/2016 - 19:01

Ạ đi rồi mới chém

#5 tranthevu

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Gửi vào 16/12/2016 - 15:14

 MikeDo, on 01/12/2016 - 18:24, said:

Tại sao lúc này, không thấy mấy lão chém gió vào sửa nhỉ? Cộng đồng đang rất cần cơ mà.
Vì mảng này đại ca đúng la sư phụ...

#6 health

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Gửi vào 10/10/2019 - 07:54

Mikedo không biết lập trình. Đưa code đó vào chạy đến mùa quít mới ra kết quả. Bài toán cần đặt trong bối cảnh ứng dụng của nó.

#7 minhminh

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Gửi vào 10/10/2019 - 11:09

Lập trình tính toán chi cho mệt
Xuống China town tìm mua quyển Tinh mệnh vạn niên lịch
Chỉ cần biết chữ Hán đủ để xem lịch là được .

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#8 MikeDo

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Gửi vào 10/10/2019 - 11:15

 health, on 10/10/2019 - 07:54, said:

Mikedo không biết lập trình. Đưa code đó vào chạy đến mùa quít mới ra kết quả. Bài toán cần đặt trong bối cảnh ứng dụng của nó.
bạn nghĩhay nhỉ. Tôi làm gd công ty về khoa học máy tính chuyên về AI và ML, sao lại không biết code.
Tất cả các thuật toán độ phức tạp tuyến tính đều không cần phải quá quan tâm về thời gian chạy.

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#9 health

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Gửi vào 10/10/2019 - 15:44

 MikeDo, on 10/10/2019 - 11:15, said:

bạn nghĩhay nhỉ. Tôi làm gd công ty về khoa học máy tính chuyên về AI và ML, sao lại không biết code.
Tất cả các thuật toán độ phức tạp tuyến tính đều không cần phải quá quan tâm về thời gian chạy.
Một bài toán lịch viết cho triệu người truy cập. Với một bài toán Machine Learning viết cho 1 người truy cập nó khác hẳn nhau.

#10 CaiLonCoCa

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Gửi vào 11/10/2019 - 15:41

 health, on 10/10/2019 - 15:44, said:


Một bài toán lịch viết cho triệu người truy cập. Với một bài toán Machine Learning viết cho 1 người truy cập nó khác hẳn nhau.
Chém kinh quá.
Nếu có một bộ sưu tập các lá số tử vi.
Một tập các cách cục của tử vi.
Và một tập các sự kiện của các hồ sơ bên trên ( thời điểm lập gia đình, thăng chức,trúng số, mổ xẻ).
Tập các phân loại cho các lá số bên trên ( ví dụ đứng top 10% trong lĩnh vực, giàu top 20 thế giới, sát nhân, nạn nhân, kết hôn nhiều lần...)

Liệu món khai phá dữ liệu có thể làm được những điều này không -helpme:
Nghiệm lý lại các cách cục.
Gợi ý cách cục mới.

Ngoài ra:
Giả sử có bộ sưu tập lá số tử vi và có dữ liệu xếp hạng trong lĩnh vực thể thao của 10000 hồ sơ.(***)

Nếu trong 100 ứng viên, muốn tuyển chọn 10 người có khả năng top đầu trong lĩnh vực thể thao( không phải 10 người top đầu trong 100 ứng viên)

Nếu dùng tử vi thì xem từng người và kết luận luôn.Làm sao kết hợp (***) để ra kết quả tốt hơn.

#11 sailormoon1

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Gửi vào 15/10/2019 - 11:44

Ngày xưa em cũng có ý nghĩ sưu tầm ls, phân loại, train... nhưng em bỏ ngay suy nghĩ ko thực tế đấy vì dữ liệu không bao giờ đủ là thứ nhất, có quá nhiều lỗ hổng trong kiến thức tử vi là thứ hai, thứ ba là vấn đề sự tương tác/dynamics (aka point #1).
Hoặc là có cả ba hoặc là ko có cái nào hết.
Thuật toán quan trọng nhưng dữ liệu còn quan trọng hơn, muốn sưu tầm thì cũng có thể crawl web như astro nhưng độ khả tín kiểm chứng ntn? Câu trả lời là giấy khai sinh CHÍNH XÁC. Vậy nên từ hồi xưa em đã nói cần sự hệ thống hóa ngày giờ tháng sinh đẻ của cả 1 quốc gia (bộ tâm linh? ) để khai phá tiềm năng của 1 dân tộc. Nhưng đây là con dao hai lưỡi, vô cùng nguy hiểm.
Nếu dữ liệu đủ lớn thì có thể dự đoán đến độ chính xác nào đấy. Nhưng nhắc đến độ chính xác thì phải nói đến xác suất thống kê và hiểu tường tận về risk management & randomness, điều mà ngày nay chưa 1 ai làm được.
Còn đã ko hiểu cặn kẽ mà làm bừa thì hậu quả khôn lường, tốt nhất là tránh xa

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#12 CaiLonCoCa

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Gửi vào 15/10/2019 - 15:14

 sailormoon1, on 15/10/2019 - 11:44, said:

Ngày xưa em cũng có ý nghĩ sưu tầm ls, phân loại, train... nhưng em bỏ ngay suy nghĩ ko thực tế đấy vì dữ liệu không bao giờ đủ là thứ nhất, có quá nhiều lỗ hổng trong kiến thức tử vi là thứ hai, thứ ba là vấn đề sự tương tác/dynamics (aka point #1).
Hoặc là có cả ba hoặc là ko có cái nào hết.
Thuật toán quan trọng nhưng dữ liệu còn quan trọng hơn, muốn sưu tầm thì cũng có thể crawl web như astro nhưng độ khả tín kiểm chứng ntn? Câu trả lời là giấy khai sinh CHÍNH XÁC. Vậy nên từ hồi xưa em đã nói cần sự hệ thống hóa ngày giờ tháng sinh đẻ của cả 1 quốc gia (bộ tâm linh? ) để khai phá tiềm năng của 1 dân tộc. Nhưng đây là con dao hai lưỡi, vô cùng nguy hiểm.
Nếu dữ liệu đủ lớn thì có thể dự đoán đến độ chính xác nào đấy. Nhưng nhắc đến độ chính xác thì phải nói đến xác suất thống kê và hiểu tường tận về risk management & randomness, điều mà ngày nay chưa 1 ai làm được.
Còn đã ko hiểu cặn kẽ mà làm bừa thì hậu quả khôn lường, tốt nhất là tránh xa
Dữ liệu quý như vàng, chả thế mà mấy bô lão ôm vài hồ sơ có thể ngâm cứu cả đời =)).
Mong bạn nói rõ hơn về randomness và "vấn đề sự tương tác/dynamics".
Bạn có chấp nhận những hồ sơ của astro có độ khả tín AA không?Các hồ sơ này ghi theo giấy khai sinh hay hồ sơ sinh.

Không cần các kiến thức chuyên sâu, cũng có thể thực hiện được những điều này:
Mình ví dụ môn cân xương tính số.Rất nhiều hồ sơ có ngày tháng năm sinh khác nhau, khi cân xương tính số đều cho về A lượng và B chỉ.Nếu trong bộ dữ liệu có nhiều hồ sơ A lượng B chỉ mà cuộc đời không như lời giải đoán.Thì có thể loại bỏ luôn lời giải của môn cân xương tính số cho các hồ sơ có A lượng B chỉ.
Đối với một cách cục Tử vi, nếu có nhiều hồ sơ không diễn ra như lời giải của cách cục.Có thể thấy ngay cách cục này chưa đầy đủ hoặc thậm chí sai bét.Nếu may mắn từ sự khác biệt giữa các hồ sơ, có thể tìm ra một số cách cục đầy đủ nhờ bổ sung thêm yếu tố vào cách cục gốc.






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