DOUBLE PRECISION FUNCTION iau_DTDB ( DATE1, DATE2, : UT, ELONG, U, V ) *+ * - - - - - - - - - * i a u _ D T D B * - - - - - - - - - * * An approximation to TDB-TT, the difference between barycentric * dynamical time and terrestrial time, for an observer on the Earth. * * The different time scales - proper, coordinate and realized - are * related to each other: * * TAI <- physically realized * : * offset <- observed (nominally +32.184s) * : * TT <- terrestrial time * : * rate adjustment (L_G) <- definition of TT * : * TCG <- time scale for GCRS * : * "periodic" terms <- iau_DTDB is an implementation * : * rate adjustment (L_C) <- function of solar-system ephemeris * : * TCB <- time scale for BCRS * : * rate adjustment (-L_B) <- definition of TDB * : * TDB <- TCB scaled to track TT * : * "periodic" terms <- -iau_DTDB is an approximation * : * TT <- terrestrial time * * Adopted values for the various constants can be found in the IERS * Conventions (McCarthy & Petit 2003). * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * DATE1,DATE2 d date, TDB (Notes 1-3) * UT d universal time (UT1, fraction of one day) * ELONG d longitude (east positive, radians) * U d distance from Earth spin axis (km) * V d distance north of equatorial plane (km) * * Returned: * iau_DTDB d TDB-TT (seconds) * * Notes: * * 1) The date DATE1+DATE2 is a Julian Date, apportioned in any * convenient way between the arguments DATE1 and DATE2. For * example, JD(TDB)=2450123.7 could be expressed in any of these * ways, among others: * * DATE1 DATE2 * * 2450123.7D0 0D0 (JD method) * 2451545D0 -1421.3D0 (J2000 method) * 2400000.5D0 50123.2D0 (MJD method) * 2450123.5D0 0.2D0 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. * * Although the date is, formally, barycentric dynamical time (TDB), * the terrestrial dynamical time (TT) can be used with no practical * effect on the accuracy of the prediction. * * 2) TT can be regarded as a coordinate time that is realized as an * offset of 32.184s from International Atomic Time, TAI. TT is a * specific linear transformation of geocentric coordinate time TCG, * which is the time scale for the Geocentric Celestial Reference * System, GCRS. * * 3) TDB is a coordinate time, and is a specific linear transformation * of barycentric coordinate time TCB, which is the time scale for * the Barycentric Celestial Reference System, BCRS. * * 4) The difference TCG-TCB depends on the masses and positions of the * bodies of the solar system and the velocity of the Earth. It is * dominated by a rate difference, the residual being of a periodic * character. The latter, which is modeled by the present routine, * comprises a main (annual) sinusoidal term of amplitude * approximately 0.00166 seconds, plus planetary terms up to about * 20 microseconds, and lunar and diurnal terms up to 2 microseconds. * These effects come from the changing transverse Doppler effect * and gravitational red-shift as the observer (on the Earth's * surface) experiences variations in speed (with respect to the * BCRS) and gravitational potential. * * 5) TDB can be regarded as the same as TCB but with a rate adjustment * to keep it close to TT, which is convenient for many applications. * The history of successive attempts to define TDB is set out in * Resolution 3 adopted by the IAU General Assembly in 2006, which * defines a fixed TDB(TCB) transformation that is consistent with * contemporary solar-system ephemerides. Future ephemerides will * imply slightly changed transformations between TCG and TCB, which * could introduce a linear drift between TDB and TT; however, any * such drift is unlikely to exceed 1 nanosecond per century. * * 6) The geocentric TDB-TT model used in the present routine is that of * Fairhead & Bretagnon (1990), in its full form. It was originally * supplied by Fairhead (private communications with P.T.Wallace, * 1990) as a Fortran subroutine. The present routine contains an * adaptation of the Fairhead code. The numerical results are * essentially unaffected by the changes, the differences with * respect to the Fairhead & Bretagnon original being at the 1D-20 s * level. * * The topocentric part of the model is from Moyer (1981) and * Murray (1983), with fundamental arguments adapted from * Simon et al. 1994. It is an approximation to the expression * ( v / c ) . ( r / c ), where v is the barycentric velocity of * the Earth, r is the geocentric position of the observer and * c is the speed of light. * * By supplying zeroes for U and V, the topocentric part of the * model can be nullified, and the routine will return the Fairhead * & Bretagnon result alone. * * 7) During the interval 1950-2050, the absolute accuracy is better * than +/- 3 nanoseconds relative to time ephemerides obtained by * direct numerical integrations based on the JPL DE405 solar system * ephemeris. * * 8) It must be stressed that the present routine is merely a model, * and that numerical integration of solar-system ephemerides is the * definitive method for predicting the relationship between TCG and * TCB and hence between TT and TDB. * * References: * * Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247 * (1990). * * IAU 2006 Resolution 3. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Moyer, T.D., Cel.Mech., 23, 33 (1981). * * Murray, C.A., Vectorial Astrometry, Adam Hilger (1983). * * Seidelmann, P.K. et al., Explanatory Supplement to the * Astronomical Almanac, Chapter 2, University Science Books (1992). * * Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994). * * This revision: 2010 July 29 * * SOFA release 2017-04-20 * * Copyright (C) 2017 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, UT, ELONG, U, V * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Degrees to radians DOUBLE PRECISION DD2R PARAMETER ( DD2R = 1.745329251994329576923691D-2 ) * Reference epoch (J2000.0), JD DOUBLE PRECISION DJ00 PARAMETER ( DJ00 = 2451545D0 ) * Days per Julian millennium DOUBLE PRECISION DJM PARAMETER ( DJM = 365250D0 ) DOUBLE PRECISION T, TSOL, W, ELSUN, EMSUN, D, ELJ, ELS, : WT, W0, W1, W2, W3, W4, WF, WJ * * ===================== * Fairhead et al. model * ===================== * * 787 sets of three coefficients. * * Each set is amplitude (microseconds) * frequency (radians per Julian millennium since J2000.0), * phase (radians). * * Sets 1-474 are the T**0 terms, * " 475-679 " " T**1 " * " 680-764 " " T**2 " * " 765-784 " " T**3 " * " 785-787 " " T**4 " . * DOUBLE PRECISION FAIRHD(3,787) INTEGER I,J DATA ((FAIRHD(I,J),I=1,3),J= 1, 10) / : 1656.674564D-6, 6283.075849991D0, 6.240054195D0, : 22.417471D-6, 5753.384884897D0, 4.296977442D0, : 13.839792D-6, 12566.151699983D0, 6.196904410D0, : 4.770086D-6, 529.690965095D0, 0.444401603D0, : 4.676740D-6, 6069.776754553D0, 4.021195093D0, : 2.256707D-6, 213.299095438D0, 5.543113262D0, : 1.694205D-6, -3.523118349D0, 5.025132748D0, : 1.554905D-6, 77713.771467920D0, 5.198467090D0, : 1.276839D-6, 7860.419392439D0, 5.988822341D0, : 1.193379D-6, 5223.693919802D0, 3.649823730D0 / DATA ((FAIRHD(I,J),I=1,3),J= 11, 20) / : 1.115322D-6, 3930.209696220D0, 1.422745069D0, : 0.794185D-6, 11506.769769794D0, 2.322313077D0, : 0.447061D-6, 26.298319800D0, 3.615796498D0, : 0.435206D-6, -398.149003408D0, 4.349338347D0, : 0.600309D-6, 1577.343542448D0, 2.678271909D0, : 0.496817D-6, 6208.294251424D0, 5.696701824D0, : 0.486306D-6, 5884.926846583D0, 0.520007179D0, : 0.432392D-6, 74.781598567D0, 2.435898309D0, : 0.468597D-6, 6244.942814354D0, 5.866398759D0, : 0.375510D-6, 5507.553238667D0, 4.103476804D0 / DATA ((FAIRHD(I,J),I=1,3),J= 21, 30) / : 0.243085D-6, -775.522611324D0, 3.651837925D0, : 0.173435D-6, 18849.227549974D0, 6.153743485D0, : 0.230685D-6, 5856.477659115D0, 4.773852582D0, : 0.203747D-6, 12036.460734888D0, 4.333987818D0, : 0.143935D-6, -796.298006816D0, 5.957517795D0, : 0.159080D-6, 10977.078804699D0, 1.890075226D0, : 0.119979D-6, 38.133035638D0, 4.551585768D0, : 0.118971D-6, 5486.777843175D0, 1.914547226D0, : 0.116120D-6, 1059.381930189D0, 0.873504123D0, : 0.137927D-6, 11790.629088659D0, 1.135934669D0 / DATA ((FAIRHD(I,J),I=1,3),J= 31, 40) / : 0.098358D-6, 2544.314419883D0, 0.092793886D0, : 0.101868D-6, -5573.142801634D0, 5.984503847D0, : 0.080164D-6, 206.185548437D0, 2.095377709D0, : 0.079645D-6, 4694.002954708D0, 2.949233637D0, : 0.062617D-6, 20.775395492D0, 2.654394814D0, : 0.075019D-6, 2942.463423292D0, 4.980931759D0, : 0.064397D-6, 5746.271337896D0, 1.280308748D0, : 0.063814D-6, 5760.498431898D0, 4.167901731D0, : 0.048042D-6, 2146.165416475D0, 1.495846011D0, : 0.048373D-6, 155.420399434D0, 2.251573730D0 / DATA ((FAIRHD(I,J),I=1,3),J= 41, 50) / : 0.058844D-6, 426.598190876D0, 4.839650148D0, : 0.046551D-6, -0.980321068D0, 0.921573539D0, : 0.054139D-6, 17260.154654690D0, 3.411091093D0, : 0.042411D-6, 6275.962302991D0, 2.869567043D0, : 0.040184D-6, -7.113547001D0, 3.565975565D0, : 0.036564D-6, 5088.628839767D0, 3.324679049D0, : 0.040759D-6, 12352.852604545D0, 3.981496998D0, : 0.036507D-6, 801.820931124D0, 6.248866009D0, : 0.036955D-6, 3154.687084896D0, 5.071801441D0, : 0.042732D-6, 632.783739313D0, 5.720622217D0 / DATA ((FAIRHD(I,J),I=1,3),J= 51, 60) / : 0.042560D-6, 161000.685737473D0, 1.270837679D0, : 0.040480D-6, 15720.838784878D0, 2.546610123D0, : 0.028244D-6, -6286.598968340D0, 5.069663519D0, : 0.033477D-6, 6062.663207553D0, 4.144987272D0, : 0.034867D-6, 522.577418094D0, 5.210064075D0, : 0.032438D-6, 6076.890301554D0, 0.749317412D0, : 0.030215D-6, 7084.896781115D0, 3.389610345D0, : 0.029247D-6, -71430.695617928D0, 4.183178762D0, : 0.033529D-6, 9437.762934887D0, 2.404714239D0, : 0.032423D-6, 8827.390269875D0, 5.541473556D0 / DATA ((FAIRHD(I,J),I=1,3),J= 61, 70) / : 0.027567D-6, 6279.552731642D0, 5.040846034D0, : 0.029862D-6, 12139.553509107D0, 1.770181024D0, : 0.022509D-6, 10447.387839604D0, 1.460726241D0, : 0.020937D-6, 8429.241266467D0, 0.652303414D0, : 0.020322D-6, 419.484643875D0, 3.735430632D0, : 0.024816D-6, -1194.447010225D0, 1.087136918D0, : 0.025196D-6, 1748.016413067D0, 2.901883301D0, : 0.021691D-6, 14143.495242431D0, 5.952658009D0, : 0.017673D-6, 6812.766815086D0, 3.186129845D0, : 0.022567D-6, 6133.512652857D0, 3.307984806D0 / DATA ((FAIRHD(I,J),I=1,3),J= 71, 80) / : 0.016155D-6, 10213.285546211D0, 1.331103168D0, : 0.014751D-6, 1349.867409659D0, 4.308933301D0, : 0.015949D-6, -220.412642439D0, 4.005298270D0, : 0.015974D-6, -2352.866153772D0, 6.145309371D0, : 0.014223D-6, 17789.845619785D0, 2.104551349D0, : 0.017806D-6, 73.297125859D0, 3.475975097D0, : 0.013671D-6, -536.804512095D0, 5.971672571D0, : 0.011942D-6, 8031.092263058D0, 2.053414715D0, : 0.014318D-6, 16730.463689596D0, 3.016058075D0, : 0.012462D-6, 103.092774219D0, 1.737438797D0 / DATA ((FAIRHD(I,J),I=1,3),J= 81, 90) / : 0.010962D-6, 3.590428652D0, 2.196567739D0, : 0.015078D-6, 19651.048481098D0, 3.969480770D0, : 0.010396D-6, 951.718406251D0, 5.717799605D0, : 0.011707D-6, -4705.732307544D0, 2.654125618D0, : 0.010453D-6, 5863.591206116D0, 1.913704550D0, : 0.012420D-6, 4690.479836359D0, 4.734090399D0, : 0.011847D-6, 5643.178563677D0, 5.489005403D0, : 0.008610D-6, 3340.612426700D0, 3.661698944D0, : 0.011622D-6, 5120.601145584D0, 4.863931876D0, : 0.010825D-6, 553.569402842D0, 0.842715011D0 / DATA ((FAIRHD(I,J),I=1,3),J= 91,100) / : 0.008666D-6, -135.065080035D0, 3.293406547D0, : 0.009963D-6, 149.563197135D0, 4.870690598D0, : 0.009858D-6, 6309.374169791D0, 1.061816410D0, : 0.007959D-6, 316.391869657D0, 2.465042647D0, : 0.010099D-6, 283.859318865D0, 1.942176992D0, : 0.007147D-6, -242.728603974D0, 3.661486981D0, : 0.007505D-6, 5230.807466803D0, 4.920937029D0, : 0.008323D-6, 11769.853693166D0, 1.229392026D0, : 0.007490D-6, -6256.777530192D0, 3.658444681D0, : 0.009370D-6, 149854.400134205D0, 0.673880395D0 / DATA ((FAIRHD(I,J),I=1,3),J=101,110) / : 0.007117D-6, 38.027672636D0, 5.294249518D0, : 0.007857D-6, 12168.002696575D0, 0.525733528D0, : 0.007019D-6, 6206.809778716D0, 0.837688810D0, : 0.006056D-6, 955.599741609D0, 4.194535082D0, : 0.008107D-6, 13367.972631107D0, 3.793235253D0, : 0.006731D-6, 5650.292110678D0, 5.639906583D0, : 0.007332D-6, 36.648562930D0, 0.114858677D0, : 0.006366D-6, 4164.311989613D0, 2.262081818D0, : 0.006858D-6, 5216.580372801D0, 0.642063318D0, : 0.006919D-6, 6681.224853400D0, 6.018501522D0 / DATA ((FAIRHD(I,J),I=1,3),J=111,120) / : 0.006826D-6, 7632.943259650D0, 3.458654112D0, : 0.005308D-6, -1592.596013633D0, 2.500382359D0, : 0.005096D-6, 11371.704689758D0, 2.547107806D0, : 0.004841D-6, 5333.900241022D0, 0.437078094D0, : 0.005582D-6, 5966.683980335D0, 2.246174308D0, : 0.006304D-6, 11926.254413669D0, 2.512929171D0, : 0.006603D-6, 23581.258177318D0, 5.393136889D0, : 0.005123D-6, -1.484472708D0, 2.999641028D0, : 0.004648D-6, 1589.072895284D0, 1.275847090D0, : 0.005119D-6, 6438.496249426D0, 1.486539246D0 / DATA ((FAIRHD(I,J),I=1,3),J=121,130) / : 0.004521D-6, 4292.330832950D0, 6.140635794D0, : 0.005680D-6, 23013.539539587D0, 4.557814849D0, : 0.005488D-6, -3.455808046D0, 0.090675389D0, : 0.004193D-6, 7234.794256242D0, 4.869091389D0, : 0.003742D-6, 7238.675591600D0, 4.691976180D0, : 0.004148D-6, -110.206321219D0, 3.016173439D0, : 0.004553D-6, 11499.656222793D0, 5.554998314D0, : 0.004892D-6, 5436.993015240D0, 1.475415597D0, : 0.004044D-6, 4732.030627343D0, 1.398784824D0, : 0.004164D-6, 12491.370101415D0, 5.650931916D0 / DATA ((FAIRHD(I,J),I=1,3),J=131,140) / : 0.004349D-6, 11513.883316794D0, 2.181745369D0, : 0.003919D-6, 12528.018664345D0, 5.823319737D0, : 0.003129D-6, 6836.645252834D0, 0.003844094D0, : 0.004080D-6, -7058.598461315D0, 3.690360123D0, : 0.003270D-6, 76.266071276D0, 1.517189902D0, : 0.002954D-6, 6283.143160294D0, 4.447203799D0, : 0.002872D-6, 28.449187468D0, 1.158692983D0, : 0.002881D-6, 735.876513532D0, 0.349250250D0, : 0.003279D-6, 5849.364112115D0, 4.893384368D0, : 0.003625D-6, 6209.778724132D0, 1.473760578D0 / DATA ((FAIRHD(I,J),I=1,3),J=141,150) / : 0.003074D-6, 949.175608970D0, 5.185878737D0, : 0.002775D-6, 9917.696874510D0, 1.030026325D0, : 0.002646D-6, 10973.555686350D0, 3.918259169D0, : 0.002575D-6, 25132.303399966D0, 6.109659023D0, : 0.003500D-6, 263.083923373D0, 1.892100742D0, : 0.002740D-6, 18319.536584880D0, 4.320519510D0, : 0.002464D-6, 202.253395174D0, 4.698203059D0, : 0.002409D-6, 2.542797281D0, 5.325009315D0, : 0.003354D-6, -90955.551694697D0, 1.942656623D0, : 0.002296D-6, 6496.374945429D0, 5.061810696D0 / DATA ((FAIRHD(I,J),I=1,3),J=151,160) / : 0.003002D-6, 6172.869528772D0, 2.797822767D0, : 0.003202D-6, 27511.467873537D0, 0.531673101D0, : 0.002954D-6, -6283.008539689D0, 4.533471191D0, : 0.002353D-6, 639.897286314D0, 3.734548088D0, : 0.002401D-6, 16200.772724501D0, 2.605547070D0, : 0.003053D-6, 233141.314403759D0, 3.029030662D0, : 0.003024D-6, 83286.914269554D0, 2.355556099D0, : 0.002863D-6, 17298.182327326D0, 5.240963796D0, : 0.002103D-6, -7079.373856808D0, 5.756641637D0, : 0.002303D-6, 83996.847317911D0, 2.013686814D0 / DATA ((FAIRHD(I,J),I=1,3),J=161,170) / : 0.002303D-6, 18073.704938650D0, 1.089100410D0, : 0.002381D-6, 63.735898303D0, 0.759188178D0, : 0.002493D-6, 6386.168624210D0, 0.645026535D0, : 0.002366D-6, 3.932153263D0, 6.215885448D0, : 0.002169D-6, 11015.106477335D0, 4.845297676D0, : 0.002397D-6, 6243.458341645D0, 3.809290043D0, : 0.002183D-6, 1162.474704408D0, 6.179611691D0, : 0.002353D-6, 6246.427287062D0, 4.781719760D0, : 0.002199D-6, -245.831646229D0, 5.956152284D0, : 0.001729D-6, 3894.181829542D0, 1.264976635D0 / DATA ((FAIRHD(I,J),I=1,3),J=171,180) / : 0.001896D-6, -3128.388765096D0, 4.914231596D0, : 0.002085D-6, 35.164090221D0, 1.405158503D0, : 0.002024D-6, 14712.317116458D0, 2.752035928D0, : 0.001737D-6, 6290.189396992D0, 5.280820144D0, : 0.002229D-6, 491.557929457D0, 1.571007057D0, : 0.001602D-6, 14314.168113050D0, 4.203664806D0, : 0.002186D-6, 454.909366527D0, 1.402101526D0, : 0.001897D-6, 22483.848574493D0, 4.167932508D0, : 0.001825D-6, -3738.761430108D0, 0.545828785D0, : 0.001894D-6, 1052.268383188D0, 5.817167450D0 / DATA ((FAIRHD(I,J),I=1,3),J=181,190) / : 0.001421D-6, 20.355319399D0, 2.419886601D0, : 0.001408D-6, 10984.192351700D0, 2.732084787D0, : 0.001847D-6, 10873.986030480D0, 2.903477885D0, : 0.001391D-6, -8635.942003763D0, 0.593891500D0, : 0.001388D-6, -7.046236698D0, 1.166145902D0, : 0.001810D-6, -88860.057071188D0, 0.487355242D0, : 0.001288D-6, -1990.745017041D0, 3.913022880D0, : 0.001297D-6, 23543.230504682D0, 3.063805171D0, : 0.001335D-6, -266.607041722D0, 3.995764039D0, : 0.001376D-6, 10969.965257698D0, 5.152914309D0 / DATA ((FAIRHD(I,J),I=1,3),J=191,200) / : 0.001745D-6, 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((FAIRHD(I,J),I=1,3),J=611,620) / : 0.000241D-6, 12528.018664345D0, 3.832324536D0, : 0.000304D-6, 4686.889407707D0, 1.612348468D0, : 0.000259D-6, 16200.772724501D0, 3.470173146D0, : 0.000238D-6, 12139.553509107D0, 1.147977842D0, : 0.000236D-6, 6172.869528772D0, 3.776271728D0, : 0.000296D-6, -7058.598461315D0, 0.460368852D0, : 0.000306D-6, 10575.406682942D0, 0.554749016D0, : 0.000251D-6, 17298.182327326D0, 0.834332510D0, : 0.000290D-6, 4732.030627343D0, 4.759564091D0, : 0.000261D-6, 5884.926846583D0, 0.298259862D0 / DATA ((FAIRHD(I,J),I=1,3),J=621,630) / : 0.000249D-6, 5547.199336460D0, 3.749366406D0, : 0.000213D-6, 11712.955318231D0, 5.415666119D0, : 0.000223D-6, 4701.116501708D0, 2.703203558D0, : 0.000268D-6, -640.877607382D0, 0.283670793D0, : 0.000209D-6, 5636.065016677D0, 1.238477199D0, : 0.000193D-6, 10177.257679534D0, 1.943251340D0, : 0.000182D-6, 6283.143160294D0, 2.456157599D0, : 0.000184D-6, -227.526189440D0, 5.888038582D0, : 0.000182D-6, -6283.008539689D0, 0.241332086D0, : 0.000228D-6, -6284.056171060D0, 2.657323816D0 / DATA ((FAIRHD(I,J),I=1,3),J=631,640) / : 0.000166D-6, 7238.675591600D0, 5.930629110D0, : 0.000167D-6, 3097.883822726D0, 5.570955333D0, : 0.000159D-6, -323.505416657D0, 5.786670700D0, : 0.000154D-6, -4136.910433516D0, 1.517805532D0, : 0.000176D-6, 12029.347187887D0, 3.139266834D0, : 0.000167D-6, 12132.439962106D0, 3.556352289D0, : 0.000153D-6, 202.253395174D0, 1.463313961D0, : 0.000157D-6, 17267.268201691D0, 1.586837396D0, : 0.000142D-6, 83996.847317911D0, 0.022670115D0, : 0.000152D-6, 17260.154654690D0, 0.708528947D0 / DATA ((FAIRHD(I,J),I=1,3),J=641,650) / : 0.000144D-6, 6084.003848555D0, 5.187075177D0, : 0.000135D-6, 5756.566278634D0, 1.993229262D0, : 0.000134D-6, 5750.203491159D0, 3.457197134D0, : 0.000144D-6, 5326.786694021D0, 6.066193291D0, : 0.000160D-6, 11015.106477335D0, 1.710431974D0, : 0.000133D-6, 3634.621024518D0, 2.836451652D0, : 0.000134D-6, 18073.704938650D0, 5.453106665D0, : 0.000134D-6, 1162.474704408D0, 5.326898811D0, : 0.000128D-6, 5642.198242609D0, 2.511652591D0, : 0.000160D-6, 632.783739313D0, 5.628785365D0 / DATA ((FAIRHD(I,J),I=1,3),J=651,660) / : 0.000132D-6, 13916.019109642D0, 0.819294053D0, : 0.000122D-6, 14314.168113050D0, 5.677408071D0, : 0.000125D-6, 12359.966151546D0, 5.251984735D0, : 0.000121D-6, 5749.452731634D0, 2.210924603D0, : 0.000136D-6, -245.831646229D0, 1.646502367D0, : 0.000120D-6, 5757.317038160D0, 3.240883049D0, : 0.000134D-6, 12146.667056108D0, 3.059480037D0, : 0.000137D-6, 6206.809778716D0, 1.867105418D0, : 0.000141D-6, 17253.041107690D0, 2.069217456D0, : 0.000129D-6, -7477.522860216D0, 2.781469314D0 / DATA ((FAIRHD(I,J),I=1,3),J=661,670) / : 0.000116D-6, 5540.085789459D0, 4.281176991D0, : 0.000116D-6, 9779.108676125D0, 3.320925381D0, : 0.000129D-6, 5237.921013804D0, 3.497704076D0, : 0.000113D-6, 5959.570433334D0, 0.983210840D0, : 0.000122D-6, 6282.095528923D0, 2.674938860D0, : 0.000140D-6, -11.045700264D0, 4.957936982D0, : 0.000108D-6, 23543.230504682D0, 1.390113589D0, : 0.000106D-6, -12569.674818332D0, 0.429631317D0, : 0.000110D-6, -266.607041722D0, 5.501340197D0, : 0.000115D-6, 12559.038152982D0, 4.691456618D0 / DATA ((FAIRHD(I,J),I=1,3),J=671,680) / : 0.000134D-6, -2388.894020449D0, 0.577313584D0, : 0.000109D-6, 10440.274292604D0, 6.218148717D0, : 0.000102D-6, -543.918059096D0, 1.477842615D0, : 0.000108D-6, 21228.392023546D0, 2.237753948D0, : 0.000101D-6, -4535.059436924D0, 3.100492232D0, : 0.000103D-6, 76.266071276D0, 5.594294322D0, : 0.000104D-6, 949.175608970D0, 5.674287810D0, : 0.000101D-6, 13517.870106233D0, 2.196632348D0, : 0.000100D-6, 11933.367960670D0, 4.056084160D0, * T^2 : 4.322990D-6, 6283.075849991D0, 2.642893748D0 / DATA ((FAIRHD(I,J),I=1,3),J=681,690) / : 0.406495D-6, 0.000000000D0, 4.712388980D0, : 0.122605D-6, 12566.151699983D0, 2.438140634D0, : 0.019476D-6, 213.299095438D0, 1.642186981D0, : 0.016916D-6, 529.690965095D0, 4.510959344D0, : 0.013374D-6, -3.523118349D0, 1.502210314D0, : 0.008042D-6, 26.298319800D0, 0.478549024D0, : 0.007824D-6, 155.420399434D0, 5.254710405D0, : 0.004894D-6, 5746.271337896D0, 4.683210850D0, : 0.004875D-6, 5760.498431898D0, 0.759507698D0, : 0.004416D-6, 5223.693919802D0, 6.028853166D0 / DATA ((FAIRHD(I,J),I=1,3),J=691,700) / : 0.004088D-6, -7.113547001D0, 0.060926389D0, : 0.004433D-6, 77713.771467920D0, 3.627734103D0, : 0.003277D-6, 18849.227549974D0, 2.327912542D0, : 0.002703D-6, 6062.663207553D0, 1.271941729D0, : 0.003435D-6, -775.522611324D0, 0.747446224D0, : 0.002618D-6, 6076.890301554D0, 3.633715689D0, : 0.003146D-6, 206.185548437D0, 5.647874613D0, : 0.002544D-6, 1577.343542448D0, 6.232904270D0, : 0.002218D-6, -220.412642439D0, 1.309509946D0, : 0.002197D-6, 5856.477659115D0, 2.407212349D0 / DATA ((FAIRHD(I,J),I=1,3),J=701,710) / : 0.002897D-6, 5753.384884897D0, 5.863842246D0, : 0.001766D-6, 426.598190876D0, 0.754113147D0, : 0.001738D-6, -796.298006816D0, 2.714942671D0, : 0.001695D-6, 522.577418094D0, 2.629369842D0, : 0.001584D-6, 5507.553238667D0, 1.341138229D0, : 0.001503D-6, -242.728603974D0, 0.377699736D0, : 0.001552D-6, -536.804512095D0, 2.904684667D0, : 0.001370D-6, -398.149003408D0, 1.265599125D0, : 0.001889D-6, -5573.142801634D0, 4.413514859D0, : 0.001722D-6, 6069.776754553D0, 2.445966339D0 / DATA ((FAIRHD(I,J),I=1,3),J=711,720) / : 0.001124D-6, 1059.381930189D0, 5.041799657D0, : 0.001258D-6, 553.569402842D0, 3.849557278D0, : 0.000831D-6, 951.718406251D0, 2.471094709D0, : 0.000767D-6, 4694.002954708D0, 5.363125422D0, : 0.000756D-6, 1349.867409659D0, 1.046195744D0, : 0.000775D-6, -11.045700264D0, 0.245548001D0, : 0.000597D-6, 2146.165416475D0, 4.543268798D0, : 0.000568D-6, 5216.580372801D0, 4.178853144D0, : 0.000711D-6, 1748.016413067D0, 5.934271972D0, : 0.000499D-6, 12036.460734888D0, 0.624434410D0 / DATA ((FAIRHD(I,J),I=1,3),J=721,730) / : 0.000671D-6, -1194.447010225D0, 4.136047594D0, : 0.000488D-6, 5849.364112115D0, 2.209679987D0, : 0.000621D-6, 6438.496249426D0, 4.518860804D0, : 0.000495D-6, -6286.598968340D0, 1.868201275D0, : 0.000456D-6, 5230.807466803D0, 1.271231591D0, : 0.000451D-6, 5088.628839767D0, 0.084060889D0, : 0.000435D-6, 5643.178563677D0, 3.324456609D0, : 0.000387D-6, 10977.078804699D0, 4.052488477D0, : 0.000547D-6, 161000.685737473D0, 2.841633844D0, : 0.000522D-6, 3154.687084896D0, 2.171979966D0 / DATA ((FAIRHD(I,J),I=1,3),J=731,740) / : 0.000375D-6, 5486.777843175D0, 4.983027306D0, : 0.000421D-6, 5863.591206116D0, 4.546432249D0, : 0.000439D-6, 7084.896781115D0, 0.522967921D0, : 0.000309D-6, 2544.314419883D0, 3.172606705D0, : 0.000347D-6, 4690.479836359D0, 1.479586566D0, : 0.000317D-6, 801.820931124D0, 3.553088096D0, : 0.000262D-6, 419.484643875D0, 0.606635550D0, : 0.000248D-6, 6836.645252834D0, 3.014082064D0, : 0.000245D-6, -1592.596013633D0, 5.519526220D0, : 0.000225D-6, 4292.330832950D0, 2.877956536D0 / DATA ((FAIRHD(I,J),I=1,3),J=741,750) / : 0.000214D-6, 7234.794256242D0, 1.605227587D0, : 0.000205D-6, 5767.611978898D0, 0.625804796D0, : 0.000180D-6, 10447.387839604D0, 3.499954526D0, : 0.000229D-6, 199.072001436D0, 5.632304604D0, : 0.000214D-6, 639.897286314D0, 5.960227667D0, : 0.000175D-6, -433.711737877D0, 2.162417992D0, : 0.000209D-6, 515.463871093D0, 2.322150893D0, : 0.000173D-6, 6040.347246017D0, 2.556183691D0, : 0.000184D-6, 6309.374169791D0, 4.732296790D0, : 0.000227D-6, 149854.400134205D0, 5.385812217D0 / DATA ((FAIRHD(I,J),I=1,3),J=751,760) / : 0.000154D-6, 8031.092263058D0, 5.120720920D0, : 0.000151D-6, 5739.157790895D0, 4.815000443D0, : 0.000197D-6, 7632.943259650D0, 0.222827271D0, : 0.000197D-6, 74.781598567D0, 3.910456770D0, : 0.000138D-6, 6055.549660552D0, 1.397484253D0, : 0.000149D-6, -6127.655450557D0, 5.333727496D0, : 0.000137D-6, 3894.181829542D0, 4.281749907D0, : 0.000135D-6, 9437.762934887D0, 5.979971885D0, : 0.000139D-6, -2352.866153772D0, 4.715630782D0, : 0.000142D-6, 6812.766815086D0, 0.513330157D0 / DATA ((FAIRHD(I,J),I=1,3),J=761,770) / : 0.000120D-6, -4705.732307544D0, 0.194160689D0, : 0.000131D-6, -71430.695617928D0, 0.000379226D0, : 0.000124D-6, 6279.552731642D0, 2.122264908D0, : 0.000108D-6, -6256.777530192D0, 0.883445696D0, * T^3 : 0.143388D-6, 6283.075849991D0, 1.131453581D0, : 0.006671D-6, 12566.151699983D0, 0.775148887D0, : 0.001480D-6, 155.420399434D0, 0.480016880D0, : 0.000934D-6, 213.299095438D0, 6.144453084D0, : 0.000795D-6, 529.690965095D0, 2.941595619D0, : 0.000673D-6, 5746.271337896D0, 0.120415406D0 / DATA ((FAIRHD(I,J),I=1,3),J=771,780) / : 0.000672D-6, 5760.498431898D0, 5.317009738D0, : 0.000389D-6, -220.412642439D0, 3.090323467D0, : 0.000373D-6, 6062.663207553D0, 3.003551964D0, : 0.000360D-6, 6076.890301554D0, 1.918913041D0, : 0.000316D-6, -21.340641002D0, 5.545798121D0, : 0.000315D-6, -242.728603974D0, 1.884932563D0, : 0.000278D-6, 206.185548437D0, 1.266254859D0, : 0.000238D-6, -536.804512095D0, 4.532664830D0, : 0.000185D-6, 522.577418094D0, 4.578313856D0, : 0.000245D-6, 18849.227549974D0, 0.587467082D0 / DATA ((FAIRHD(I,J),I=1,3),J=781,787) / : 0.000180D-6, 426.598190876D0, 5.151178553D0, : 0.000200D-6, 553.569402842D0, 5.355983739D0, : 0.000141D-6, 5223.693919802D0, 1.336556009D0, : 0.000104D-6, 5856.477659115D0, 4.239842759D0, * T^4 : 0.003826D-6, 6283.075849991D0, 5.705257275D0, : 0.000303D-6, 12566.151699983D0, 5.407132842D0, : 0.000209D-6, 155.420399434D0, 1.989815753D0 / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Time since J2000.0 in Julian millennia. T = ( ( DATE1-DJ00 ) + DATE2 ) / DJM * ================= * Topocentric terms * ================= * Convert UT to local solar time in radians. TSOL = MOD(UT,1D0) * D2PI + ELONG * FUNDAMENTAL ARGUMENTS: Simon et al. 1994. * Combine time argument (millennia) with deg/arcsec factor. W = T / 3600D0 * Sun Mean Longitude. ELSUN = MOD(280.46645683D0 + 1296027711.03429D0 * W, 360D0) * DD2R * Sun Mean Anomaly. EMSUN = MOD(357.52910918D0 + 1295965810.481D0 * W, 360D0) * DD2R * Mean Elongation of Moon from Sun. D = MOD(297.85019547D0 + 16029616012.090D0 * W, 360D0) * DD2R * Mean Longitude of Jupiter. ELJ = MOD(34.35151874D0 + 109306899.89453D0 * W, 360D0) * DD2R * Mean Longitude of Saturn. ELS = MOD(50.07744430D0 + 44046398.47038D0 * W, 360D0) * DD2R * TOPOCENTRIC TERMS: Moyer 1981 and Murray 1983. WT = + 0.00029D-10 * U * SIN(TSOL + ELSUN - ELS) : + 0.00100D-10 * U * SIN(TSOL - 2D0*EMSUN) : + 0.00133D-10 * U * SIN(TSOL - D) : + 0.00133D-10 * U * SIN(TSOL + ELSUN - ELJ) : - 0.00229D-10 * U * SIN(TSOL + 2D0*ELSUN + EMSUN) : - 0.0220 D-10 * V * COS(ELSUN + EMSUN) : + 0.05312D-10 * U * SIN(TSOL - EMSUN) : - 0.13677D-10 * U * SIN(TSOL + 2D0*ELSUN) : - 1.3184 D-10 * V * COS(ELSUN) : + 3.17679D-10 * U * SIN(TSOL) * ===================== * Fairhead et al. model * ===================== * T**0 W0 = 0D0 DO 10 J=474,1,-1 W0 = W0 + FAIRHD(1,J) * SIN(FAIRHD(2,J)*T + FAIRHD(3,J)) 10 CONTINUE * T**1 W1 = 0D0 DO 11 J=679,475,-1 W1 = W1 + FAIRHD(1,J) * SIN(FAIRHD(2,J)*T + FAIRHD(3,J)) 11 CONTINUE * T**2 W2 = 0D0 DO 12 J=764,680,-1 W2 = W2 + FAIRHD(1,J) * SIN(FAIRHD(2,J)*T + FAIRHD(3,J)) 12 CONTINUE * T**3 W3 = 0D0 DO 13 J=784,765,-1 W3 = W3 + FAIRHD(1,J) * SIN(FAIRHD(2,J)*T + FAIRHD(3,J)) 13 CONTINUE * T**4 W4 = 0D0 DO 14 J=787,785,-1 W4 = W4 + FAIRHD(1,J) * SIN(FAIRHD(2,J)*T + FAIRHD(3,J)) 14 CONTINUE * Multiply by powers of T and combine. WF = T * ( T * ( T * ( T * W4 + W3 ) + W2 ) + W1 ) + W0 * Adjustments to use JPL planetary masses instead of IAU. WJ = 0.00065D-6 * SIN(6069.776754D0*T + 4.021194D0) + : 0.00033D-6 * SIN( 213.299095D0*T + 5.543132D0) + : ( -0.00196D-6 * SIN(6208.294251D0*T + 5.696701D0) ) + : ( -0.00173D-6 * SIN( 74.781599D0*T + 2.435900D0) ) + : 0.03638D-6 * T * T * ============ * Final result * ============ * TDB-TT in seconds. iau_DTDB = WT + WF + WJ * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2017 * Standards Of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. 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The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END