Module: Horologium::Data::BarycentricModel
- Defined in:
- lib/horologium/data/barycentric_model.rb,
sig/horologium/data/barycentric_model.rbs
Overview
The difference TDB - TT, in seconds, from the Fairhead & Bretagnon (1990) series that ERFA uses. TDB keeps almost the rate of TT, apart from periodic terms that come from the Earth's motion through the Sun's gravity. The largest is an annual term of about 1.7 milliseconds, and the two scales never drift more than about 2 milliseconds apart.
The value is geocentric. The full model has a further part that depends on where on the Earth the observer stands, worth a few microseconds. Horologium leaves it out and reads the difference at the Earth's centre.
The series is floating-point at any precision. Read at :exact the
difference is stored faithfully as a Rational, but the model itself
stays a float computation: :exact keeps the arithmetic that follows
it, not the model.
Ported from ERFA's dtdb.c, which derives from IAU SOFA. The
amplitudes below are in microseconds. See
https://github.com/liberfa/erfa.
Constant Summary collapse
- J2000 =
The Julian Date of J2000.0, where the series starts counting.
2_451_545.0- DAYS_PER_MILLENNIUM =
The days in a Julian millennium, the unit the series counts in.
365_250.0- TERMS_BY_POWER =
The periodic terms, grouped by the power of t they carry, from t^0 to t^4. Each term is an amplitude in microseconds, a frequency, and a phase. Ported verbatim from ERFA's dtdb.c (Fairhead & Bretagnon 1990).
[ # t^0 (474 terms) [ [1656.674564, 6283.075849991, 6.240054195], [22.417471, 5753.384884897, 4.296977442], [13.839792, 12566.151699983, 6.196904410], [4.770086, 529.690965095, 0.444401603], [4.676740, 6069.776754553, 4.021195093], [2.256707, 213.299095438, 5.543113262], [1.694205, -3.523118349, 5.025132748], [1.554905, 77713.771467920, 5.198467090], [1.276839, 7860.419392439, 5.988822341], [1.193379, 5223.693919802, 3.649823730], [1.115322, 3930.209696220, 1.422745069], [0.794185, 11506.769769794, 2.322313077], [0.447061, 26.298319800, 3.615796498], [0.435206, -398.149003408, 4.349338347], [0.600309, 1577.343542448, 2.678271909], [0.496817, 6208.294251424, 5.696701824], [0.486306, 5884.926846583, 0.520007179], [0.432392, 74.781598567, 2.435898309], [0.468597, 6244.942814354, 5.866398759], [0.375510, 5507.553238667, 4.103476804], [0.243085, -775.522611324, 3.651837925], [0.173435, 18849.227549974, 6.153743485], [0.230685, 5856.477659115, 4.773852582], [0.203747, 12036.460734888, 4.333987818], [0.143935, -796.298006816, 5.957517795], [0.159080, 10977.078804699, 1.890075226], [0.119979, 38.133035638, 4.551585768], [0.118971, 5486.777843175, 1.914547226], [0.116120, 1059.381930189, 0.873504123], [0.137927, 11790.629088659, 1.135934669], [0.098358, 2544.314419883, 0.092793886], [0.101868, -5573.142801634, 5.984503847], [0.080164, 206.185548437, 2.095377709], [0.079645, 4694.002954708, 2.949233637], [0.062617, 20.775395492, 2.654394814], [0.075019, 2942.463423292, 4.980931759], [0.064397, 5746.271337896, 1.280308748], [0.063814, 5760.498431898, 4.167901731], [0.048042, 2146.165416475, 1.495846011], [0.048373, 155.420399434, 2.251573730], [0.058844, 426.598190876, 4.839650148], [0.046551, -0.980321068, 0.921573539], [0.054139, 17260.154654690, 3.411091093], [0.042411, 6275.962302991, 2.869567043], [0.040184, -7.113547001, 3.565975565], [0.036564, 5088.628839767, 3.324679049], [0.040759, 12352.852604545, 3.981496998], [0.036507, 801.820931124, 6.248866009], [0.036955, 3154.687084896, 5.071801441], [0.042732, 632.783739313, 5.720622217], [0.042560, 161000.685737473, 1.270837679], [0.040480, 15720.838784878, 2.546610123], [0.028244, -6286.598968340, 5.069663519], [0.033477, 6062.663207553, 4.144987272], [0.034867, 522.577418094, 5.210064075], [0.032438, 6076.890301554, 0.749317412], [0.030215, 7084.896781115, 3.389610345], [0.029247, -71430.695617928, 4.183178762], [0.033529, 9437.762934887, 2.404714239], [0.032423, 8827.390269875, 5.541473556], [0.027567, 6279.552731642, 5.040846034], [0.029862, 12139.553509107, 1.770181024], [0.022509, 10447.387839604, 1.460726241], [0.020937, 8429.241266467, 0.652303414], [0.020322, 419.484643875, 3.735430632], [0.024816, -1194.447010225, 1.087136918], [0.025196, 1748.016413067, 2.901883301], [0.021691, 14143.495242431, 5.952658009], [0.017673, 6812.766815086, 3.186129845], [0.022567, 6133.512652857, 3.307984806], [0.016155, 10213.285546211, 1.331103168], [0.014751, 1349.867409659, 4.308933301], [0.015949, -220.412642439, 4.005298270], [0.015974, -2352.866153772, 6.145309371], [0.014223, 17789.845619785, 2.104551349], [0.017806, 73.297125859, 3.475975097], [0.013671, -536.804512095, 5.971672571], [0.011942, 8031.092263058, 2.053414715], [0.014318, 16730.463689596, 3.016058075], [0.012462, 103.092774219, 1.737438797], [0.010962, 3.590428652, 2.196567739], [0.015078, 19651.048481098, 3.969480770], [0.010396, 951.718406251, 5.717799605], [0.011707, -4705.732307544, 2.654125618], [0.010453, 5863.591206116, 1.913704550], [0.012420, 4690.479836359, 4.734090399], [0.011847, 5643.178563677, 5.489005403], [0.008610, 3340.612426700, 3.661698944], [0.011622, 5120.601145584, 4.863931876], [0.010825, 553.569402842, 0.842715011], [0.008666, -135.065080035, 3.293406547], [0.009963, 149.563197135, 4.870690598], [0.009858, 6309.374169791, 1.061816410], [0.007959, 316.391869657, 2.465042647], [0.010099, 283.859318865, 1.942176992], [0.007147, -242.728603974, 3.661486981], [0.007505, 5230.807466803, 4.920937029], [0.008323, 11769.853693166, 1.229392026], [0.007490, -6256.777530192, 3.658444681], [0.009370, 149854.400134205, 0.673880395], [0.007117, 38.027672636, 5.294249518], [0.007857, 12168.002696575, 0.525733528], [0.007019, 6206.809778716, 0.837688810], [0.006056, 955.599741609, 4.194535082], [0.008107, 13367.972631107, 3.793235253], [0.006731, 5650.292110678, 5.639906583], [0.007332, 36.648562930, 0.114858677], [0.006366, 4164.311989613, 2.262081818], [0.006858, 5216.580372801, 0.642063318], [0.006919, 6681.224853400, 6.018501522], [0.006826, 7632.943259650, 3.458654112], [0.005308, -1592.596013633, 2.500382359], [0.005096, 11371.704689758, 2.547107806], [0.004841, 5333.900241022, 0.437078094], [0.005582, 5966.683980335, 2.246174308], [0.006304, 11926.254413669, 2.512929171], [0.006603, 23581.258177318, 5.393136889], [0.005123, -1.484472708, 2.999641028], [0.004648, 1589.072895284, 1.275847090], [0.005119, 6438.496249426, 1.486539246], [0.004521, 4292.330832950, 6.140635794], [0.005680, 23013.539539587, 4.557814849], [0.005488, -3.455808046, 0.090675389], [0.004193, 7234.794256242, 4.869091389], [0.003742, 7238.675591600, 4.691976180], [0.004148, -110.206321219, 3.016173439], [0.004553, 11499.656222793, 5.554998314], [0.004892, 5436.993015240, 1.475415597], [0.004044, 4732.030627343, 1.398784824], [0.004164, 12491.370101415, 5.650931916], [0.004349, 11513.883316794, 2.181745369], [0.003919, 12528.018664345, 5.823319737], [0.003129, 6836.645252834, 0.003844094], [0.004080, -7058.598461315, 3.690360123], [0.003270, 76.266071276, 1.517189902], [0.002954, 6283.143160294, 4.447203799], [0.002872, 28.449187468, 1.158692983], [0.002881, 735.876513532, 0.349250250], [0.003279, 5849.364112115, 4.893384368], [0.003625, 6209.778724132, 1.473760578], [0.003074, 949.175608970, 5.185878737], [0.002775, 9917.696874510, 1.030026325], [0.002646, 10973.555686350, 3.918259169], [0.002575, 25132.303399966, 6.109659023], [0.003500, 263.083923373, 1.892100742], [0.002740, 18319.536584880, 4.320519510], [0.002464, 202.253395174, 4.698203059], [0.002409, 2.542797281, 5.325009315], [0.003354, -90955.551694697, 1.942656623], [0.002296, 6496.374945429, 5.061810696], [0.003002, 6172.869528772, 2.797822767], [0.003202, 27511.467873537, 0.531673101], [0.002954, -6283.008539689, 4.533471191], [0.002353, 639.897286314, 3.734548088], [0.002401, 16200.772724501, 2.605547070], [0.003053, 233141.314403759, 3.029030662], [0.003024, 83286.914269554, 2.355556099], [0.002863, 17298.182327326, 5.240963796], [0.002103, -7079.373856808, 5.756641637], [0.002303, 83996.847317911, 2.013686814], [0.002303, 18073.704938650, 1.089100410], [0.002381, 63.735898303, 0.759188178], [0.002493, 6386.168624210, 0.645026535], [0.002366, 3.932153263, 6.215885448], [0.002169, 11015.106477335, 4.845297676], [0.002397, 6243.458341645, 3.809290043], [0.002183, 1162.474704408, 6.179611691], [0.002353, 6246.427287062, 4.781719760], [0.002199, -245.831646229, 5.956152284], [0.001729, 3894.181829542, 1.264976635], [0.001896, -3128.388765096, 4.914231596], [0.002085, 35.164090221, 1.405158503], [0.002024, 14712.317116458, 2.752035928], [0.001737, 6290.189396992, 5.280820144], [0.002229, 491.557929457, 1.571007057], [0.001602, 14314.168113050, 4.203664806], [0.002186, 454.909366527, 1.402101526], [0.001897, 22483.848574493, 4.167932508], [0.001825, -3738.761430108, 0.545828785], [0.001894, 1052.268383188, 5.817167450], [0.001421, 20.355319399, 2.419886601], [0.001408, 10984.192351700, 2.732084787], [0.001847, 10873.986030480, 2.903477885], [0.001391, -8635.942003763, 0.593891500], [0.001388, -7.046236698, 1.166145902], [0.001810, -88860.057071188, 0.487355242], [0.001288, -1990.745017041, 3.913022880], [0.001297, 23543.230504682, 3.063805171], [0.001335, -266.607041722, 3.995764039], [0.001376, 10969.965257698, 5.152914309], [0.001745, 244287.600007027, 3.626395673], [0.001649, 31441.677569757, 1.952049260], [0.001416, 9225.539273283, 4.996408389], [0.001238, 4804.209275927, 5.503379738], [0.001472, 4590.910180489, 4.164913291], [0.001169, 6040.347246017, 5.841719038], [0.001039, 5540.085789459, 2.769753519], [0.001004, -170.672870619, 0.755008103], [0.001284, 10575.406682942, 5.306538209], [0.001278, 71.812653151, 4.713486491], [0.001321, 18209.330263660, 2.624866359], [0.001297, 21228.392023546, 0.382603541], [0.000954, 6282.095528923, 0.882213514], [0.001145, 6058.731054289, 1.169483931], [0.000979, 5547.199336460, 5.448375984], [0.000987, -6262.300454499, 2.656486959], [0.001070, -154717.609887482, 1.827624012], [0.000991, 4701.116501708, 4.387001801], [0.001155, -14.227094002, 3.042700750], [0.001176, 277.034993741, 3.335519004], [0.000890, 13916.019109642, 5.601498297], [0.000884, -1551.045222648, 1.088831705], [0.000876, 5017.508371365, 3.969902609], [0.000806, 15110.466119866, 5.142876744], [0.000773, -4136.910433516, 0.022067765], [0.001077, 175.166059800, 1.844913056], [0.000954, -6284.056171060, 0.968480906], [0.000737, 5326.786694021, 4.923831588], [0.000845, -433.711737877, 4.749245231], [0.000819, 8662.240323563, 5.991247817], [0.000852, 199.072001436, 2.189604979], [0.000723, 17256.631536341, 6.068719637], [0.000940, 6037.244203762, 6.197428148], [0.000885, 11712.955318231, 3.280414875], [0.000706, 12559.038152982, 2.824848947], [0.000732, 2379.164473572, 2.501813417], [0.000764, -6127.655450557, 2.236346329], [0.000908, 131.541961686, 2.521257490], [0.000907, 35371.887265976, 3.370195967], [0.000673, 1066.495477190, 3.876512374], [0.000814, 17654.780539750, 4.627122566], [0.000630, 36.027866677, 0.156368499], [0.000798, 515.463871093, 5.151962502], [0.000798, 148.078724426, 5.909225055], [0.000806, 309.278322656, 6.054064447], [0.000607, -39.617508346, 2.839021623], [0.000601, 412.371096874, 3.984225404], [0.000646, 11403.676995575, 3.852959484], [0.000704, 13521.751441591, 2.300991267], [0.000603, -65147.619767937, 4.140083146], [0.000609, 10177.257679534, 0.437122327], [0.000631, 5767.611978898, 4.026532329], [0.000576, 11087.285125918, 4.760293101], [0.000674, 14945.316173554, 6.270510511], [0.000726, 5429.879468239, 6.039606892], [0.000710, 28766.924424484, 5.672617711], [0.000647, 11856.218651625, 3.397132627], [0.000678, -5481.254918868, 6.249666675], [0.000618, 22003.914634870, 2.466427018], [0.000738, 6134.997125565, 2.242668890], [0.000660, 625.670192312, 5.864091907], [0.000694, 3496.032826134, 2.668309141], [0.000531, 6489.261398429, 1.681888780], [0.000611, -143571.324284214, 2.424978312], [0.000575, 12043.574281889, 4.216492400], [0.000553, 12416.588502848, 4.772158039], [0.000689, 4686.889407707, 6.224271088], [0.000495, 7342.457780181, 3.817285811], [0.000567, 3634.621024518, 1.649264690], [0.000515, 18635.928454536, 3.945345892], [0.000486, -323.505416657, 4.061673868], [0.000662, 25158.601719765, 1.794058369], [0.000509, 846.082834751, 3.053874588], [0.000472, -12569.674818332, 5.112133338], [0.000461, 6179.983075773, 0.513669325], [0.000641, 83467.156352816, 3.210727723], [0.000520, 10344.295065386, 2.445597761], [0.000493, 18422.629359098, 1.676939306], [0.000478, 1265.567478626, 5.487314569], [0.000472, -18.159247265, 1.999707589], [0.000559, 11190.377900137, 5.783236356], [0.000494, 9623.688276691, 3.022645053], [0.000463, 5739.157790895, 1.411223013], [0.000432, 16858.482532933, 1.179256434], [0.000574, 72140.628666286, 1.758191830], [0.000484, 17267.268201691, 3.290589143], [0.000550, 4907.302050146, 0.864024298], [0.000399, 14.977853527, 2.094441910], [0.000491, 224.344795702, 0.878372791], [0.000432, 20426.571092422, 6.003829241], [0.000481, 5749.452731634, 4.309591964], [0.000480, 5757.317038160, 1.142348571], [0.000485, 6702.560493867, 0.210580917], [0.000426, 6055.549660552, 4.274476529], [0.000480, 5959.570433334, 5.031351030], [0.000466, 12562.628581634, 4.959581597], [0.000520, 39302.096962196, 4.788002889], [0.000458, 12132.439962106, 1.880103788], [0.000470, 12029.347187887, 1.405611197], [0.000416, -7477.522860216, 1.082356330], [0.000449, 11609.862544012, 4.179989585], [0.000465, 17253.041107690, 0.353496295], [0.000362, -4535.059436924, 1.583849576], [0.000383, 21954.157609398, 3.747376371], [0.000389, 17.252277143, 1.395753179], [0.000331, 18052.929543158, 0.566790582], [0.000430, 13517.870106233, 0.685827538], [0.000368, -5756.908003246, 0.731374317], [0.000330, 10557.594160824, 3.710043680], [0.000332, 20199.094959633, 1.652901407], [0.000384, 11933.367960670, 5.827781531], [0.000387, 10454.501386605, 2.541182564], [0.000325, 15671.081759407, 2.178850542], [0.000318, 138.517496871, 2.253253037], [0.000305, 9388.005909415, 0.578340206], [0.000352, 5749.861766548, 3.000297967], [0.000311, 6915.859589305, 1.693574249], [0.000297, 24072.921469776, 1.997249392], [0.000363, -640.877607382, 5.071820966], [0.000323, 12592.450019783, 1.072262823], [0.000341, 12146.667056108, 4.700657997], [0.000290, 9779.108676125, 1.812320441], [0.000342, 6132.028180148, 4.322238614], [0.000329, 6268.848755990, 3.033827743], [0.000374, 17996.031168222, 3.388716544], [0.000285, -533.214083444, 4.687313233], [0.000338, 6065.844601290, 0.877776108], [0.000276, 24.298513841, 0.770299429], [0.000336, -2388.894020449, 5.353796034], [0.000290, 3097.883822726, 4.075291557], [0.000318, 709.933048357, 5.941207518], [0.000271, 13095.842665077, 3.208912203], [0.000331, 6073.708907816, 4.007881169], [0.000292, 742.990060533, 2.714333592], [0.000362, 29088.811415985, 3.215977013], [0.000280, 12359.966151546, 0.710872502], [0.000267, 10440.274292604, 4.730108488], [0.000262, 838.969287750, 1.327720272], [0.000250, 16496.361396202, 0.898769761], [0.000325, 20597.243963041, 0.180044365], [0.000268, 6148.010769956, 5.152666276], [0.000284, 5636.065016677, 5.655385808], [0.000301, 6080.822454817, 2.135396205], [0.000294, -377.373607916, 3.708784168], [0.000236, 2118.763860378, 1.733578756], [0.000234, 5867.523359379, 5.575209112], [0.000268, -226858.238553767, 0.069432392], [0.000265, 167283.761587465, 4.369302826], [0.000280, 28237.233459389, 5.304829118], [0.000292, 12345.739057544, 4.096094132], [0.000223, 19800.945956225, 3.069327406], [0.000301, 43232.306658416, 6.205311188], [0.000264, 18875.525869774, 1.417263408], [0.000304, -1823.175188677, 3.409035232], [0.000301, 109.945688789, 0.510922054], [0.000260, 813.550283960, 2.389438934], [0.000299, 316428.228673312, 5.384595078], [0.000211, 5756.566278634, 3.789392838], [0.000209, 5750.203491159, 1.661943545], [0.000240, 12489.885628707, 5.684549045], [0.000216, 6303.851245484, 3.862942261], [0.000203, 1581.959348283, 5.549853589], [0.000200, 5642.198242609, 1.016115785], [0.000197, -70.849445304, 4.690702525], [0.000227, 6287.008003254, 2.911891613], [0.000197, 533.623118358, 1.048982898], [0.000205, -6279.485421340, 1.829362730], [0.000209, -10988.808157535, 2.636140084], [0.000208, -227.526189440, 4.127883842], [0.000191, 415.552490612, 4.401165650], [0.000190, 29296.615389579, 4.175658539], [0.000264, 66567.485864652, 4.601102551], [0.000256, -3646.350377354, 0.506364778], [0.000188, 13119.721102825, 2.032195842], [0.000185, -209.366942175, 4.694756586], [0.000198, 25934.124331089, 3.832703118], [0.000195, 4061.219215394, 3.308463427], [0.000234, 5113.487598583, 1.716090661], [0.000188, 1478.866574064, 5.686865780], [0.000222, 11823.161639450, 1.942386641], [0.000181, 10770.893256262, 1.999482059], [0.000171, 6546.159773364, 1.182807992], [0.000206, 70.328180442, 5.934076062], [0.000169, 20995.392966449, 2.169080622], [0.000191, 10660.686935042, 5.405515999], [0.000228, 33019.021112205, 4.656985514], [0.000184, -4933.208440333, 3.327476868], [0.000220, -135.625325010, 1.765430262], [0.000166, 23141.558382925, 3.454132746], [0.000191, 6144.558353121, 5.020393445], [0.000180, 6084.003848555, 0.602182191], [0.000163, 17782.732072784, 4.960593133], [0.000225, 16460.333529525, 2.596451817], [0.000222, 5905.702242076, 3.731990323], [0.000204, 227.476132789, 5.636192701], [0.000159, 16737.577236597, 3.600691544], [0.000200, 6805.653268085, 0.868220961], [0.000187, 11919.140866668, 2.629456641], [0.000161, 127.471796607, 2.862574720], [0.000205, 6286.666278643, 1.742882331], [0.000189, 153.778810485, 4.812372643], [0.000168, 16723.350142595, 0.027860588], [0.000149, 11720.068865232, 0.659721876], [0.000189, 5237.921013804, 5.245313000], [0.000143, 6709.674040867, 4.317625647], [0.000146, 4487.817406270, 4.815297007], [0.000144, -664.756045130, 5.381366880], [0.000175, 5127.714692584, 4.728443327], [0.000162, 6254.626662524, 1.435132069], [0.000187, 47162.516354635, 1.354371923], [0.000146, 11080.171578918, 3.369695406], [0.000180, -348.924420448, 2.490902145], [0.000148, 151.047669843, 3.799109588], [0.000157, 6197.248551160, 1.284375887], [0.000167, 146.594251718, 0.759969109], [0.000133, -5331.357443741, 5.409701889], [0.000154, 95.979227218, 3.366890614], [0.000148, -6418.140930027, 3.384104996], [0.000128, -6525.804453965, 3.803419985], [0.000130, 11293.470674356, 0.939039445], [0.000152, -5729.506447149, 0.734117523], [0.000138, 210.117701700, 2.564216078], [0.000123, 6066.595360816, 4.517099537], [0.000140, 18451.078546566, 0.642049130], [0.000126, 11300.584221356, 3.485280663], [0.000119, 10027.903195729, 3.217431161], [0.000151, 4274.518310832, 4.404359108], [0.000117, 6072.958148291, 0.366324650], [0.000165, -7668.637425143, 4.298212528], [0.000117, -6245.048177356, 5.379518958], [0.000130, -5888.449964932, 4.527681115], [0.000121, -543.918059096, 6.109429504], [0.000162, 9683.594581116, 5.720092446], [0.000141, 6219.339951688, 0.679068671], [0.000118, 22743.409379516, 4.881123092], [0.000129, 1692.165669502, 0.351407289], [0.000126, 5657.405657679, 5.146592349], [0.000114, 728.762966531, 0.520791814], [0.000120, 52.596639600, 0.948516300], [0.000115, 65.220371012, 3.504914846], [0.000126, 5881.403728234, 5.577502482], [0.000158, 163096.180360983, 2.957128968], [0.000134, 12341.806904281, 2.598576764], [0.000151, 16627.370915377, 3.985702050], [0.000109, 1368.660252845, 0.014730471], [0.000131, 6211.263196841, 0.085077024], [0.000146, 5792.741760812, 0.708426604], [0.000146, -77.750543984, 3.121576600], [0.000107, 5341.013788022, 0.288231904], [0.000138, 6281.591377283, 2.797450317], [0.000113, -6277.552925684, 2.788904128], [0.000115, -525.758811831, 5.895222200], [0.000138, 6016.468808270, 6.096188999], [0.000139, 23539.707386333, 2.028195445], [0.000146, -4176.041342449, 4.660008502], [0.000107, 16062.184526117, 4.066520001], [0.000142, 83783.548222473, 2.936315115], [0.000128, 9380.959672717, 3.223844306], [0.000135, 6205.325306007, 1.638054048], [0.000101, 2699.734819318, 5.481603249], [0.000104, -568.821874027, 2.205734493], [0.000103, 6321.103522627, 2.440421099], [0.000119, 6321.208885629, 2.547496264], [0.000138, 1975.492545856, 2.314608466], [0.000121, 137.033024162, 4.539108237], [0.000123, 19402.796952817, 4.538074405], [0.000119, 22805.735565994, 2.869040566], [0.000133, 64471.991241142, 6.056405489], [0.000129, -85.827298831, 2.540635083], [0.000131, 13613.804277336, 4.005732868], [0.000104, 9814.604100291, 1.959967212], [0.000112, 16097.679950283, 3.589026260], [0.000123, 2107.034507542, 1.728627253], [0.000121, 36949.230808424, 6.072332087], [0.000108, -12539.853380183, 3.716133846], [0.000113, -7875.671863624, 2.725771122], [0.000109, 4171.425536614, 4.033338079], [0.000101, 6247.911759770, 3.441347021], [0.000113, 7330.728427345, 0.656372122], [0.000113, 51092.726050855, 2.791483066], [0.000106, 5621.842923210, 1.815323326], [0.000101, 111.430161497, 5.711033677], [0.000103, 909.818733055, 2.812745443], [0.000101, 1790.642637886, 1.965746028] ], # t^1 (205 terms) [ [102.156724, 6283.075849991, 4.249032005], [1.706807, 12566.151699983, 4.205904248], [0.269668, 213.299095438, 3.400290479], [0.265919, 529.690965095, 5.836047367], [0.210568, -3.523118349, 6.262738348], [0.077996, 5223.693919802, 4.670344204], [0.054764, 1577.343542448, 4.534800170], [0.059146, 26.298319800, 1.083044735], [0.034420, -398.149003408, 5.980077351], [0.032088, 18849.227549974, 4.162913471], [0.033595, 5507.553238667, 5.980162321], [0.029198, 5856.477659115, 0.623811863], [0.027764, 155.420399434, 3.745318113], [0.025190, 5746.271337896, 2.980330535], [0.022997, -796.298006816, 1.174411803], [0.024976, 5760.498431898, 2.467913690], [0.021774, 206.185548437, 3.854787540], [0.017925, -775.522611324, 1.092065955], [0.013794, 426.598190876, 2.699831988], [0.013276, 6062.663207553, 5.845801920], [0.011774, 12036.460734888, 2.292832062], [0.012869, 6076.890301554, 5.333425680], [0.012152, 1059.381930189, 6.222874454], [0.011081, -7.113547001, 5.154724984], [0.010143, 4694.002954708, 4.044013795], [0.009357, 5486.777843175, 3.416081409], [0.010084, 522.577418094, 0.749320262], [0.008587, 10977.078804699, 2.777152598], [0.008628, 6275.962302991, 4.562060226], [0.008158, -220.412642439, 5.806891533], [0.007746, 2544.314419883, 1.603197066], [0.007670, 2146.165416475, 3.000200440], [0.007098, 74.781598567, 0.443725817], [0.006180, -536.804512095, 1.302642751], [0.005818, 5088.628839767, 4.827723531], [0.004945, -6286.598968340, 0.268305170], [0.004774, 1349.867409659, 5.808636673], [0.004687, -242.728603974, 5.154890570], [0.006089, 1748.016413067, 4.403765209], [0.005975, -1194.447010225, 2.583472591], [0.004229, 951.718406251, 0.931172179], [0.005264, 553.569402842, 2.336107252], [0.003049, 5643.178563677, 1.362634430], [0.002974, 6812.766815086, 1.583012668], [0.003403, -2352.866153772, 2.552189886], [0.003030, 419.484643875, 5.286473844], [0.003210, -7.046236698, 1.863796539], [0.003058, 9437.762934887, 4.226420633], [0.002589, 12352.852604545, 1.991935820], [0.002927, 5216.580372801, 2.319951253], [0.002425, 5230.807466803, 3.084752833], [0.002656, 3154.687084896, 2.487447866], [0.002445, 10447.387839604, 2.347139160], [0.002990, 4690.479836359, 6.235872050], [0.002890, 5863.591206116, 0.095197563], [0.002498, 6438.496249426, 2.994779800], [0.001889, 8031.092263058, 3.569003717], [0.002567, 801.820931124, 3.425611498], [0.001803, -71430.695617928, 2.192295512], [0.001782, 3.932153263, 5.180433689], [0.001694, -4705.732307544, 4.641779174], [0.001704, -1592.596013633, 3.997097652], [0.001735, 5849.364112115, 0.417558428], [0.001643, 8429.241266467, 2.180619584], [0.001680, 38.133035638, 4.164529426], [0.002045, 7084.896781115, 0.526323854], [0.001458, 4292.330832950, 1.356098141], [0.001437, 20.355319399, 3.895439360], [0.001738, 6279.552731642, 0.087484036], [0.001367, 14143.495242431, 3.987576591], [0.001344, 7234.794256242, 0.090454338], [0.001438, 11499.656222793, 0.974387904], [0.001257, 6836.645252834, 1.509069366], [0.001358, 11513.883316794, 0.495572260], [0.001628, 7632.943259650, 4.968445721], [0.001169, 103.092774219, 2.838496795], [0.001162, 4164.311989613, 3.408387778], [0.001092, 6069.776754553, 3.617942651], [0.001008, 17789.845619785, 0.286350174], [0.001008, 639.897286314, 1.610762073], [0.000918, 10213.285546211, 5.532798067], [0.001011, -6256.777530192, 0.661826484], [0.000753, 16730.463689596, 3.905030235], [0.000737, 11926.254413669, 4.641956361], [0.000694, 3340.612426700, 2.111120332], [0.000701, 3894.181829542, 2.760823491], [0.000689, -135.065080035, 4.768800780], [0.000700, 13367.972631107, 5.760439898], [0.000664, 6040.347246017, 1.051215840], [0.000654, 5650.292110678, 4.911332503], [0.000788, 6681.224853400, 4.699648011], [0.000628, 5333.900241022, 5.024608847], [0.000755, -110.206321219, 4.370971253], [0.000628, 6290.189396992, 3.660478857], [0.000635, 25132.303399966, 4.121051532], [0.000534, 5966.683980335, 1.173284524], [0.000543, -433.711737877, 0.345585464], [0.000517, -1990.745017041, 5.414571768], [0.000504, 5767.611978898, 2.328281115], [0.000485, 5753.384884897, 1.685874771], [0.000463, 7860.419392439, 5.297703006], [0.000604, 515.463871093, 0.591998446], [0.000443, 12168.002696575, 4.830881244], [0.000570, 199.072001436, 3.899190272], [0.000465, 10969.965257698, 0.476681802], [0.000424, -7079.373856808, 1.112242763], [0.000427, 735.876513532, 1.994214480], [0.000478, -6127.655450557, 3.778025483], [0.000414, 10973.555686350, 5.441088327], [0.000512, 1589.072895284, 0.107123853], [0.000378, 10984.192351700, 0.915087231], [0.000402, 11371.704689758, 4.107281715], [0.000453, 9917.696874510, 1.917490952], [0.000395, 149.563197135, 2.763124165], [0.000371, 5739.157790895, 3.112111866], [0.000350, 11790.629088659, 0.440639857], [0.000356, 6133.512652857, 5.444568842], [0.000344, 412.371096874, 5.676832684], [0.000383, 955.599741609, 5.559734846], [0.000333, 6496.374945429, 0.261537984], [0.000340, 6055.549660552, 5.975534987], [0.000334, 1066.495477190, 2.335063907], [0.000399, 11506.769769794, 5.321230910], [0.000314, 18319.536584880, 2.313312404], [0.000424, 1052.268383188, 1.211961766], [0.000307, 63.735898303, 3.169551388], [0.000329, 29.821438149, 6.106912080], [0.000357, 6309.374169791, 4.223760346], [0.000312, -3738.761430108, 2.180556645], [0.000301, 309.278322656, 1.499984572], [0.000268, 12043.574281889, 2.447520648], [0.000257, 12491.370101415, 3.662331761], [0.000290, 625.670192312, 1.272834584], [0.000256, 5429.879468239, 1.913426912], [0.000339, 3496.032826134, 4.165930011], [0.000283, 3930.209696220, 4.325565754], [0.000241, 12528.018664345, 3.832324536], [0.000304, 4686.889407707, 1.612348468], [0.000259, 16200.772724501, 3.470173146], [0.000238, 12139.553509107, 1.147977842], [0.000236, 6172.869528772, 3.776271728], [0.000296, -7058.598461315, 0.460368852], [0.000306, 10575.406682942, 0.554749016], [0.000251, 17298.182327326, 0.834332510], [0.000290, 4732.030627343, 4.759564091], [0.000261, 5884.926846583, 0.298259862], [0.000249, 5547.199336460, 3.749366406], [0.000213, 11712.955318231, 5.415666119], [0.000223, 4701.116501708, 2.703203558], [0.000268, -640.877607382, 0.283670793], [0.000209, 5636.065016677, 1.238477199], [0.000193, 10177.257679534, 1.943251340], [0.000182, 6283.143160294, 2.456157599], [0.000184, -227.526189440, 5.888038582], [0.000182, -6283.008539689, 0.241332086], [0.000228, -6284.056171060, 2.657323816], [0.000166, 7238.675591600, 5.930629110], [0.000167, 3097.883822726, 5.570955333], [0.000159, -323.505416657, 5.786670700], [0.000154, -4136.910433516, 1.517805532], [0.000176, 12029.347187887, 3.139266834], [0.000167, 12132.439962106, 3.556352289], [0.000153, 202.253395174, 1.463313961], [0.000157, 17267.268201691, 1.586837396], [0.000142, 83996.847317911, 0.022670115], [0.000152, 17260.154654690, 0.708528947], [0.000144, 6084.003848555, 5.187075177], [0.000135, 5756.566278634, 1.993229262], [0.000134, 5750.203491159, 3.457197134], [0.000144, 5326.786694021, 6.066193291], [0.000160, 11015.106477335, 1.710431974], [0.000133, 3634.621024518, 2.836451652], [0.000134, 18073.704938650, 5.453106665], [0.000134, 1162.474704408, 5.326898811], [0.000128, 5642.198242609, 2.511652591], [0.000160, 632.783739313, 5.628785365], [0.000132, 13916.019109642, 0.819294053], [0.000122, 14314.168113050, 5.677408071], [0.000125, 12359.966151546, 5.251984735], [0.000121, 5749.452731634, 2.210924603], [0.000136, -245.831646229, 1.646502367], [0.000120, 5757.317038160, 3.240883049], [0.000134, 12146.667056108, 3.059480037], [0.000137, 6206.809778716, 1.867105418], [0.000141, 17253.041107690, 2.069217456], [0.000129, -7477.522860216, 2.781469314], [0.000116, 5540.085789459, 4.281176991], [0.000116, 9779.108676125, 3.320925381], [0.000129, 5237.921013804, 3.497704076], [0.000113, 5959.570433334, 0.983210840], [0.000122, 6282.095528923, 2.674938860], [0.000140, -11.045700264, 4.957936982], [0.000108, 23543.230504682, 1.390113589], [0.000106, -12569.674818332, 0.429631317], [0.000110, -266.607041722, 5.501340197], [0.000115, 12559.038152982, 4.691456618], [0.000134, -2388.894020449, 0.577313584], [0.000109, 10440.274292604, 6.218148717], [0.000102, -543.918059096, 1.477842615], [0.000108, 21228.392023546, 2.237753948], [0.000101, -4535.059436924, 3.100492232], [0.000103, 76.266071276, 5.594294322], [0.000104, 949.175608970, 5.674287810], [0.000101, 13517.870106233, 2.196632348], [0.000100, 11933.367960670, 4.056084160] ], # t^2 (85 terms) [ [4.322990, 6283.075849991, 2.642893748], [0.406495, 0.000000000, 4.712388980], [0.122605, 12566.151699983, 2.438140634], [0.019476, 213.299095438, 1.642186981], [0.016916, 529.690965095, 4.510959344], [0.013374, -3.523118349, 1.502210314], [0.008042, 26.298319800, 0.478549024], [0.007824, 155.420399434, 5.254710405], [0.004894, 5746.271337896, 4.683210850], [0.004875, 5760.498431898, 0.759507698], [0.004416, 5223.693919802, 6.028853166], [0.004088, -7.113547001, 0.060926389], [0.004433, 77713.771467920, 3.627734103], [0.003277, 18849.227549974, 2.327912542], [0.002703, 6062.663207553, 1.271941729], [0.003435, -775.522611324, 0.747446224], [0.002618, 6076.890301554, 3.633715689], [0.003146, 206.185548437, 5.647874613], [0.002544, 1577.343542448, 6.232904270], [0.002218, -220.412642439, 1.309509946], [0.002197, 5856.477659115, 2.407212349], [0.002897, 5753.384884897, 5.863842246], [0.001766, 426.598190876, 0.754113147], [0.001738, -796.298006816, 2.714942671], [0.001695, 522.577418094, 2.629369842], [0.001584, 5507.553238667, 1.341138229], [0.001503, -242.728603974, 0.377699736], [0.001552, -536.804512095, 2.904684667], [0.001370, -398.149003408, 1.265599125], [0.001889, -5573.142801634, 4.413514859], [0.001722, 6069.776754553, 2.445966339], [0.001124, 1059.381930189, 5.041799657], [0.001258, 553.569402842, 3.849557278], [0.000831, 951.718406251, 2.471094709], [0.000767, 4694.002954708, 5.363125422], [0.000756, 1349.867409659, 1.046195744], [0.000775, -11.045700264, 0.245548001], [0.000597, 2146.165416475, 4.543268798], [0.000568, 5216.580372801, 4.178853144], [0.000711, 1748.016413067, 5.934271972], [0.000499, 12036.460734888, 0.624434410], [0.000671, -1194.447010225, 4.136047594], [0.000488, 5849.364112115, 2.209679987], [0.000621, 6438.496249426, 4.518860804], [0.000495, -6286.598968340, 1.868201275], [0.000456, 5230.807466803, 1.271231591], [0.000451, 5088.628839767, 0.084060889], [0.000435, 5643.178563677, 3.324456609], [0.000387, 10977.078804699, 4.052488477], [0.000547, 161000.685737473, 2.841633844], [0.000522, 3154.687084896, 2.171979966], [0.000375, 5486.777843175, 4.983027306], [0.000421, 5863.591206116, 4.546432249], [0.000439, 7084.896781115, 0.522967921], [0.000309, 2544.314419883, 3.172606705], [0.000347, 4690.479836359, 1.479586566], [0.000317, 801.820931124, 3.553088096], [0.000262, 419.484643875, 0.606635550], [0.000248, 6836.645252834, 3.014082064], [0.000245, -1592.596013633, 5.519526220], [0.000225, 4292.330832950, 2.877956536], [0.000214, 7234.794256242, 1.605227587], [0.000205, 5767.611978898, 0.625804796], [0.000180, 10447.387839604, 3.499954526], [0.000229, 199.072001436, 5.632304604], [0.000214, 639.897286314, 5.960227667], [0.000175, -433.711737877, 2.162417992], [0.000209, 515.463871093, 2.322150893], [0.000173, 6040.347246017, 2.556183691], [0.000184, 6309.374169791, 4.732296790], [0.000227, 149854.400134205, 5.385812217], [0.000154, 8031.092263058, 5.120720920], [0.000151, 5739.157790895, 4.815000443], [0.000197, 7632.943259650, 0.222827271], [0.000197, 74.781598567, 3.910456770], [0.000138, 6055.549660552, 1.397484253], [0.000149, -6127.655450557, 5.333727496], [0.000137, 3894.181829542, 4.281749907], [0.000135, 9437.762934887, 5.979971885], [0.000139, -2352.866153772, 4.715630782], [0.000142, 6812.766815086, 0.513330157], [0.000120, -4705.732307544, 0.194160689], [0.000131, -71430.695617928, 0.000379226], [0.000124, 6279.552731642, 2.122264908], [0.000108, -6256.777530192, 0.883445696] ], # t^3 (20 terms) [ [0.143388, 6283.075849991, 1.131453581], [0.006671, 12566.151699983, 0.775148887], [0.001480, 155.420399434, 0.480016880], [0.000934, 213.299095438, 6.144453084], [0.000795, 529.690965095, 2.941595619], [0.000673, 5746.271337896, 0.120415406], [0.000672, 5760.498431898, 5.317009738], [0.000389, -220.412642439, 3.090323467], [0.000373, 6062.663207553, 3.003551964], [0.000360, 6076.890301554, 1.918913041], [0.000316, -21.340641002, 5.545798121], [0.000315, -242.728603974, 1.884932563], [0.000278, 206.185548437, 1.266254859], [0.000238, -536.804512095, 4.532664830], [0.000185, 522.577418094, 4.578313856], [0.000245, 18849.227549974, 0.587467082], [0.000180, 426.598190876, 5.151178553], [0.000200, 553.569402842, 5.355983739], [0.000141, 5223.693919802, 1.336556009], [0.000104, 5856.477659115, 4.239842759] ], # t^4 (3 terms) [ [0.003826, 6283.075849991, 5.705257275], [0.000303, 12566.151699983, 5.407132842], [0.000209, 155.420399434, 1.989815753] ] ].freeze
Class Method Summary collapse
-
.tdb_minus_tt(tt_julian_date) ⇒ Float
The difference TDB - TT at a TT Julian Date, in seconds.
Class Method Details
.tdb_minus_tt(tt_julian_date) ⇒ Float
The difference TDB - TT at a TT Julian Date, in seconds.
The same series serves both directions. TDB and TT never diverge by more than about two milliseconds, so reading it at a TDB Julian Date instead moves the result by far less than a nanosecond.
44 45 46 47 |
# File 'lib/horologium/data/barycentric_model.rb', line 44 def tdb_minus_tt(tt_julian_date) t = (tt_julian_date - J2000) / DAYS_PER_MILLENNIUM (periodic(t) + mass_adjustment(t)) * 1e-6 end |