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 <- 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 <- -DTDB is an approximation
:
TT <- terrestrial time
Adopted values for the various constants can be found in the IERS Conventions (McCarthy & Petit 2003).
Status: support routine.
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.
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.
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.
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.
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.
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.
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.
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.
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).
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in) | :: | date1 | date, TDB (Notes 1-3) |
||
| real(kind=wp), | intent(in) | :: | date2 | date, TDB (Notes 1-3) |
||
| real(kind=wp), | intent(in) | :: | ut | universal time (UT1, fraction of one day) |
||
| real(kind=wp), | intent(in) | :: | elong | longitude (east positive, radians) |
||
| real(kind=wp), | intent(in) | :: | u | distance from Earth spin axis (km) |
||
| real(kind=wp), | intent(in) | :: | v | distance north of equatorial plane (km) |
TDB-TT (seconds)
function DTDB ( date1, date2, ut, elong, u, v ) result(TDB_minus_TT)
implicit none
real(wp),intent(in) :: date1 !! date, TDB (Notes 1-3)
real(wp),intent(in) :: date2 !! date, TDB (Notes 1-3)
real(wp),intent(in) :: ut !! universal time (UT1, fraction of one day)
real(wp),intent(in) :: elong !! longitude (east positive, radians)
real(wp),intent(in) :: u !! distance from Earth spin axis (km)
real(wp),intent(in) :: v !! distance north of equatorial plane (km)
real(wp) :: TDB_minus_TT !! TDB-TT (seconds)
! Degrees to radians
real(wp),parameter :: dd2r = 1.745329251994329576923691e-2_wp
! Days per Julian millennium
real(wp),parameter :: djm = 365250.0_wp
real(wp) :: t, tsol, w, elsun, emsun, d, elj, els, &
wt, w0, w1, w2, w3, w4, wf, wj
integer :: j
!
! =====================
! 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 " .
!
!real(wp) :: fairhd(3,787)
!integer :: i,j
real(wp),dimension(3,787),parameter :: fairhd = reshape([ &
1656.674564e-6_wp, 6283.075849991_wp, 6.240054195_wp, &
22.417471e-6_wp, 5753.384884897_wp, 4.296977442_wp, &
13.839792e-6_wp, 12566.151699983_wp, 6.196904410_wp, &
4.770086e-6_wp, 529.690965095_wp, 0.444401603_wp, &
4.676740e-6_wp, 6069.776754553_wp, 4.021195093_wp, &
2.256707e-6_wp, 213.299095438_wp, 5.543113262_wp, &
1.694205e-6_wp, -3.523118349_wp, 5.025132748_wp, &
1.554905e-6_wp, 77713.771467920_wp, 5.198467090_wp, &
1.276839e-6_wp, 7860.419392439_wp, 5.988822341_wp, &
1.193379e-6_wp, 5223.693919802_wp, 3.649823730_wp, &
1.115322e-6_wp, 3930.209696220_wp, 1.422745069_wp, &
0.794185e-6_wp, 11506.769769794_wp, 2.322313077_wp, &
0.447061e-6_wp, 26.298319800_wp, 3.615796498_wp, &
0.435206e-6_wp, -398.149003408_wp, 4.349338347_wp, &
0.600309e-6_wp, 1577.343542448_wp, 2.678271909_wp, &
0.496817e-6_wp, 6208.294251424_wp, 5.696701824_wp, &
0.486306e-6_wp, 5884.926846583_wp, 0.520007179_wp, &
0.432392e-6_wp, 74.781598567_wp, 2.435898309_wp, &
0.468597e-6_wp, 6244.942814354_wp, 5.866398759_wp, &
0.375510e-6_wp, 5507.553238667_wp, 4.103476804_wp, &
0.243085e-6_wp, -775.522611324_wp, 3.651837925_wp, &
0.173435e-6_wp, 18849.227549974_wp, 6.153743485_wp, &
0.230685e-6_wp, 5856.477659115_wp, 4.773852582_wp, &
0.203747e-6_wp, 12036.460734888_wp, 4.333987818_wp, &
0.143935e-6_wp, -796.298006816_wp, 5.957517795_wp, &
0.159080e-6_wp, 10977.078804699_wp, 1.890075226_wp, &
0.119979e-6_wp, 38.133035638_wp, 4.551585768_wp, &
0.118971e-6_wp, 5486.777843175_wp, 1.914547226_wp, &
0.116120e-6_wp, 1059.381930189_wp, 0.873504123_wp, &
0.137927e-6_wp, 11790.629088659_wp, 1.135934669_wp, &
0.098358e-6_wp, 2544.314419883_wp, 0.092793886_wp, &
0.101868e-6_wp, -5573.142801634_wp, 5.984503847_wp, &
0.080164e-6_wp, 206.185548437_wp, 2.095377709_wp, &
0.079645e-6_wp, 4694.002954708_wp, 2.949233637_wp, &
0.062617e-6_wp, 20.775395492_wp, 2.654394814_wp, &
0.075019e-6_wp, 2942.463423292_wp, 4.980931759_wp, &
0.064397e-6_wp, 5746.271337896_wp, 1.280308748_wp, &
0.063814e-6_wp, 5760.498431898_wp, 4.167901731_wp, &
0.048042e-6_wp, 2146.165416475_wp, 1.495846011_wp, &
0.048373e-6_wp, 155.420399434_wp, 2.251573730_wp, &
0.058844e-6_wp, 426.598190876_wp, 4.839650148_wp, &
0.046551e-6_wp, -0.980321068_wp, 0.921573539_wp, &
0.054139e-6_wp, 17260.154654690_wp, 3.411091093_wp, &
0.042411e-6_wp, 6275.962302991_wp, 2.869567043_wp, &
0.040184e-6_wp, -7.113547001_wp, 3.565975565_wp, &
0.036564e-6_wp, 5088.628839767_wp, 3.324679049_wp, &
0.040759e-6_wp, 12352.852604545_wp, 3.981496998_wp, &
0.036507e-6_wp, 801.820931124_wp, 6.248866009_wp, &
0.036955e-6_wp, 3154.687084896_wp, 5.071801441_wp, &
0.042732e-6_wp, 632.783739313_wp, 5.720622217_wp, &
0.042560e-6_wp, 161000.685737473_wp, 1.270837679_wp, &
0.040480e-6_wp, 15720.838784878_wp, 2.546610123_wp, &
0.028244e-6_wp, -6286.598968340_wp, 5.069663519_wp, &
0.033477e-6_wp, 6062.663207553_wp, 4.144987272_wp, &
0.034867e-6_wp, 522.577418094_wp, 5.210064075_wp, &
0.032438e-6_wp, 6076.890301554_wp, 0.749317412_wp, &
0.030215e-6_wp, 7084.896781115_wp, 3.389610345_wp, &
0.029247e-6_wp, -71430.695617928_wp, 4.183178762_wp, &
0.033529e-6_wp, 9437.762934887_wp, 2.404714239_wp, &
0.032423e-6_wp, 8827.390269875_wp, 5.541473556_wp, &
0.027567e-6_wp, 6279.552731642_wp, 5.040846034_wp, &
0.029862e-6_wp, 12139.553509107_wp, 1.770181024_wp, &
0.022509e-6_wp, 10447.387839604_wp, 1.460726241_wp, &
0.020937e-6_wp, 8429.241266467_wp, 0.652303414_wp, &
0.020322e-6_wp, 419.484643875_wp, 3.735430632_wp, &
0.024816e-6_wp, -1194.447010225_wp, 1.087136918_wp, &
0.025196e-6_wp, 1748.016413067_wp, 2.901883301_wp, &
0.021691e-6_wp, 14143.495242431_wp, 5.952658009_wp, &
0.017673e-6_wp, 6812.766815086_wp, 3.186129845_wp, &
0.022567e-6_wp, 6133.512652857_wp, 3.307984806_wp, &
0.016155e-6_wp, 10213.285546211_wp, 1.331103168_wp, &
0.014751e-6_wp, 1349.867409659_wp, 4.308933301_wp, &
0.015949e-6_wp, -220.412642439_wp, 4.005298270_wp, &
0.015974e-6_wp, -2352.866153772_wp, 6.145309371_wp, &
0.014223e-6_wp, 17789.845619785_wp, 2.104551349_wp, &
0.017806e-6_wp, 73.297125859_wp, 3.475975097_wp, &
0.013671e-6_wp, -536.804512095_wp, 5.971672571_wp, &
0.011942e-6_wp, 8031.092263058_wp, 2.053414715_wp, &
0.014318e-6_wp, 16730.463689596_wp, 3.016058075_wp, &
0.012462e-6_wp, 103.092774219_wp, 1.737438797_wp, &
0.010962e-6_wp, 3.590428652_wp, 2.196567739_wp, &
0.015078e-6_wp, 19651.048481098_wp, 3.969480770_wp, &
0.010396e-6_wp, 951.718406251_wp, 5.717799605_wp, &
0.011707e-6_wp, -4705.732307544_wp, 2.654125618_wp, &
0.010453e-6_wp, 5863.591206116_wp, 1.913704550_wp, &
0.012420e-6_wp, 4690.479836359_wp, 4.734090399_wp, &
0.011847e-6_wp, 5643.178563677_wp, 5.489005403_wp, &
0.008610e-6_wp, 3340.612426700_wp, 3.661698944_wp, &
0.011622e-6_wp, 5120.601145584_wp, 4.863931876_wp, &
0.010825e-6_wp, 553.569402842_wp, 0.842715011_wp, &
0.008666e-6_wp, -135.065080035_wp, 3.293406547_wp, &
0.009963e-6_wp, 149.563197135_wp, 4.870690598_wp, &
0.009858e-6_wp, 6309.374169791_wp, 1.061816410_wp, &
0.007959e-6_wp, 316.391869657_wp, 2.465042647_wp, &
0.010099e-6_wp, 283.859318865_wp, 1.942176992_wp, &
0.007147e-6_wp, -242.728603974_wp, 3.661486981_wp, &
0.007505e-6_wp, 5230.807466803_wp, 4.920937029_wp, &
0.008323e-6_wp, 11769.853693166_wp, 1.229392026_wp, &
0.007490e-6_wp, -6256.777530192_wp, 3.658444681_wp, &
0.009370e-6_wp, 149854.400134205_wp, 0.673880395_wp, &
0.007117e-6_wp, 38.027672636_wp, 5.294249518_wp, &
0.007857e-6_wp, 12168.002696575_wp, 0.525733528_wp, &
0.007019e-6_wp, 6206.809778716_wp, 0.837688810_wp, &
0.006056e-6_wp, 955.599741609_wp, 4.194535082_wp, &
0.008107e-6_wp, 13367.972631107_wp, 3.793235253_wp, &
0.006731e-6_wp, 5650.292110678_wp, 5.639906583_wp, &
0.007332e-6_wp, 36.648562930_wp, 0.114858677_wp, &
0.006366e-6_wp, 4164.311989613_wp, 2.262081818_wp, &
0.006858e-6_wp, 5216.580372801_wp, 0.642063318_wp, &
0.006919e-6_wp, 6681.224853400_wp, 6.018501522_wp, &
0.006826e-6_wp, 7632.943259650_wp, 3.458654112_wp, &
0.005308e-6_wp, -1592.596013633_wp, 2.500382359_wp, &
0.005096e-6_wp, 11371.704689758_wp, 2.547107806_wp, &
0.004841e-6_wp, 5333.900241022_wp, 0.437078094_wp, &
0.005582e-6_wp, 5966.683980335_wp, 2.246174308_wp, &
0.006304e-6_wp, 11926.254413669_wp, 2.512929171_wp, &
0.006603e-6_wp, 23581.258177318_wp, 5.393136889_wp, &
0.005123e-6_wp, -1.484472708_wp, 2.999641028_wp, &
0.004648e-6_wp, 1589.072895284_wp, 1.275847090_wp, &
0.005119e-6_wp, 6438.496249426_wp, 1.486539246_wp, &
0.004521e-6_wp, 4292.330832950_wp, 6.140635794_wp, &
0.005680e-6_wp, 23013.539539587_wp, 4.557814849_wp, &
0.005488e-6_wp, -3.455808046_wp, 0.090675389_wp, &
0.004193e-6_wp, 7234.794256242_wp, 4.869091389_wp, &
0.003742e-6_wp, 7238.675591600_wp, 4.691976180_wp, &
0.004148e-6_wp, -110.206321219_wp, 3.016173439_wp, &
0.004553e-6_wp, 11499.656222793_wp, 5.554998314_wp, &
0.004892e-6_wp, 5436.993015240_wp, 1.475415597_wp, &
0.004044e-6_wp, 4732.030627343_wp, 1.398784824_wp, &
0.004164e-6_wp, 12491.370101415_wp, 5.650931916_wp, &
0.004349e-6_wp, 11513.883316794_wp, 2.181745369_wp, &
0.003919e-6_wp, 12528.018664345_wp, 5.823319737_wp, &
0.003129e-6_wp, 6836.645252834_wp, 0.003844094_wp, &
0.004080e-6_wp, -7058.598461315_wp, 3.690360123_wp, &
0.003270e-6_wp, 76.266071276_wp, 1.517189902_wp, &
0.002954e-6_wp, 6283.143160294_wp, 4.447203799_wp, &
0.002872e-6_wp, 28.449187468_wp, 1.158692983_wp, &
0.002881e-6_wp, 735.876513532_wp, 0.349250250_wp, &
0.003279e-6_wp, 5849.364112115_wp, 4.893384368_wp, &
0.003625e-6_wp, 6209.778724132_wp, 1.473760578_wp, &
0.003074e-6_wp, 949.175608970_wp, 5.185878737_wp, &
0.002775e-6_wp, 9917.696874510_wp, 1.030026325_wp, &
0.002646e-6_wp, 10973.555686350_wp, 3.918259169_wp, &
0.002575e-6_wp, 25132.303399966_wp, 6.109659023_wp, &
0.003500e-6_wp, 263.083923373_wp, 1.892100742_wp, &
0.002740e-6_wp, 18319.536584880_wp, 4.320519510_wp, &
0.002464e-6_wp, 202.253395174_wp, 4.698203059_wp, &
0.002409e-6_wp, 2.542797281_wp, 5.325009315_wp, &
0.003354e-6_wp, -90955.551694697_wp, 1.942656623_wp, &
0.002296e-6_wp, 6496.374945429_wp, 5.061810696_wp, &
0.003002e-6_wp, 6172.869528772_wp, 2.797822767_wp, &
0.003202e-6_wp, 27511.467873537_wp, 0.531673101_wp, &
0.002954e-6_wp, -6283.008539689_wp, 4.533471191_wp, &
0.002353e-6_wp, 639.897286314_wp, 3.734548088_wp, &
0.002401e-6_wp, 16200.772724501_wp, 2.605547070_wp, &
0.003053e-6_wp, 233141.314403759_wp, 3.029030662_wp, &
0.003024e-6_wp, 83286.914269554_wp, 2.355556099_wp, &
0.002863e-6_wp, 17298.182327326_wp, 5.240963796_wp, &
0.002103e-6_wp, -7079.373856808_wp, 5.756641637_wp, &
0.002303e-6_wp, 83996.847317911_wp, 2.013686814_wp, &
0.002303e-6_wp, 18073.704938650_wp, 1.089100410_wp, &
0.002381e-6_wp, 63.735898303_wp, 0.759188178_wp, &
0.002493e-6_wp, 6386.168624210_wp, 0.645026535_wp, &
0.002366e-6_wp, 3.932153263_wp, 6.215885448_wp, &
0.002169e-6_wp, 11015.106477335_wp, 4.845297676_wp, &
0.002397e-6_wp, 6243.458341645_wp, 3.809290043_wp, &
0.002183e-6_wp, 1162.474704408_wp, 6.179611691_wp, &
0.002353e-6_wp, 6246.427287062_wp, 4.781719760_wp, &
0.002199e-6_wp, -245.831646229_wp, 5.956152284_wp, &
0.001729e-6_wp, 3894.181829542_wp, 1.264976635_wp, &
0.001896e-6_wp, -3128.388765096_wp, 4.914231596_wp, &
0.002085e-6_wp, 35.164090221_wp, 1.405158503_wp, &
0.002024e-6_wp, 14712.317116458_wp, 2.752035928_wp, &
0.001737e-6_wp, 6290.189396992_wp, 5.280820144_wp, &
0.002229e-6_wp, 491.557929457_wp, 1.571007057_wp, &
0.001602e-6_wp, 14314.168113050_wp, 4.203664806_wp, &
0.002186e-6_wp, 454.909366527_wp, 1.402101526_wp, &
0.001897e-6_wp, 22483.848574493_wp, 4.167932508_wp, &
0.001825e-6_wp, -3738.761430108_wp, 0.545828785_wp, &
0.001894e-6_wp, 1052.268383188_wp, 5.817167450_wp, &
0.001421e-6_wp, 20.355319399_wp, 2.419886601_wp, &
0.001408e-6_wp, 10984.192351700_wp, 2.732084787_wp, &
0.001847e-6_wp, 10873.986030480_wp, 2.903477885_wp, &
0.001391e-6_wp, -8635.942003763_wp, 0.593891500_wp, &
0.001388e-6_wp, -7.046236698_wp, 1.166145902_wp, &
0.001810e-6_wp, -88860.057071188_wp, 0.487355242_wp, &
0.001288e-6_wp, -1990.745017041_wp, 3.913022880_wp, &
0.001297e-6_wp, 23543.230504682_wp, 3.063805171_wp, &
0.001335e-6_wp, -266.607041722_wp, 3.995764039_wp, &
0.001376e-6_wp, 10969.965257698_wp, 5.152914309_wp, &
0.001745e-6_wp, 244287.600007027_wp, 3.626395673_wp, &
0.001649e-6_wp, 31441.677569757_wp, 1.952049260_wp, &
0.001416e-6_wp, 9225.539273283_wp, 4.996408389_wp, &
0.001238e-6_wp, 4804.209275927_wp, 5.503379738_wp, &
0.001472e-6_wp, 4590.910180489_wp, 4.164913291_wp, &
0.001169e-6_wp, 6040.347246017_wp, 5.841719038_wp, &
0.001039e-6_wp, 5540.085789459_wp, 2.769753519_wp, &
0.001004e-6_wp, -170.672870619_wp, 0.755008103_wp, &
0.001284e-6_wp, 10575.406682942_wp, 5.306538209_wp, &
0.001278e-6_wp, 71.812653151_wp, 4.713486491_wp, &
0.001321e-6_wp, 18209.330263660_wp, 2.624866359_wp, &
0.001297e-6_wp, 21228.392023546_wp, 0.382603541_wp, &
0.000954e-6_wp, 6282.095528923_wp, 0.882213514_wp, &
0.001145e-6_wp, 6058.731054289_wp, 1.169483931_wp, &
0.000979e-6_wp, 5547.199336460_wp, 5.448375984_wp, &
0.000987e-6_wp, -6262.300454499_wp, 2.656486959_wp, &
0.001070e-6_wp, -154717.609887482_wp, 1.827624012_wp, &
0.000991e-6_wp, 4701.116501708_wp, 4.387001801_wp, &
0.001155e-6_wp, -14.227094002_wp, 3.042700750_wp, &
0.001176e-6_wp, 277.034993741_wp, 3.335519004_wp, &
0.000890e-6_wp, 13916.019109642_wp, 5.601498297_wp, &
0.000884e-6_wp, -1551.045222648_wp, 1.088831705_wp, &
0.000876e-6_wp, 5017.508371365_wp, 3.969902609_wp, &
0.000806e-6_wp, 15110.466119866_wp, 5.142876744_wp, &
0.000773e-6_wp, -4136.910433516_wp, 0.022067765_wp, &
0.001077e-6_wp, 175.166059800_wp, 1.844913056_wp, &
0.000954e-6_wp, -6284.056171060_wp, 0.968480906_wp, &
0.000737e-6_wp, 5326.786694021_wp, 4.923831588_wp, &
0.000845e-6_wp, -433.711737877_wp, 4.749245231_wp, &
0.000819e-6_wp, 8662.240323563_wp, 5.991247817_wp, &
0.000852e-6_wp, 199.072001436_wp, 2.189604979_wp, &
0.000723e-6_wp, 17256.631536341_wp, 6.068719637_wp, &
0.000940e-6_wp, 6037.244203762_wp, 6.197428148_wp, &
0.000885e-6_wp, 11712.955318231_wp, 3.280414875_wp, &
0.000706e-6_wp, 12559.038152982_wp, 2.824848947_wp, &
0.000732e-6_wp, 2379.164473572_wp, 2.501813417_wp, &
0.000764e-6_wp, -6127.655450557_wp, 2.236346329_wp, &
0.000908e-6_wp, 131.541961686_wp, 2.521257490_wp, &
0.000907e-6_wp, 35371.887265976_wp, 3.370195967_wp, &
0.000673e-6_wp, 1066.495477190_wp, 3.876512374_wp, &
0.000814e-6_wp, 17654.780539750_wp, 4.627122566_wp, &
0.000630e-6_wp, 36.027866677_wp, 0.156368499_wp, &
0.000798e-6_wp, 515.463871093_wp, 5.151962502_wp, &
0.000798e-6_wp, 148.078724426_wp, 5.909225055_wp, &
0.000806e-6_wp, 309.278322656_wp, 6.054064447_wp, &
0.000607e-6_wp, -39.617508346_wp, 2.839021623_wp, &
0.000601e-6_wp, 412.371096874_wp, 3.984225404_wp, &
0.000646e-6_wp, 11403.676995575_wp, 3.852959484_wp, &
0.000704e-6_wp, 13521.751441591_wp, 2.300991267_wp, &
0.000603e-6_wp, -65147.619767937_wp, 4.140083146_wp, &
0.000609e-6_wp, 10177.257679534_wp, 0.437122327_wp, &
0.000631e-6_wp, 5767.611978898_wp, 4.026532329_wp, &
0.000576e-6_wp, 11087.285125918_wp, 4.760293101_wp, &
0.000674e-6_wp, 14945.316173554_wp, 6.270510511_wp, &
0.000726e-6_wp, 5429.879468239_wp, 6.039606892_wp, &
0.000710e-6_wp, 28766.924424484_wp, 5.672617711_wp, &
0.000647e-6_wp, 11856.218651625_wp, 3.397132627_wp, &
0.000678e-6_wp, -5481.254918868_wp, 6.249666675_wp, &
0.000618e-6_wp, 22003.914634870_wp, 2.466427018_wp, &
0.000738e-6_wp, 6134.997125565_wp, 2.242668890_wp, &
0.000660e-6_wp, 625.670192312_wp, 5.864091907_wp, &
0.000694e-6_wp, 3496.032826134_wp, 2.668309141_wp, &
0.000531e-6_wp, 6489.261398429_wp, 1.681888780_wp, &
0.000611e-6_wp, -143571.324284214_wp, 2.424978312_wp, &
0.000575e-6_wp, 12043.574281889_wp, 4.216492400_wp, &
0.000553e-6_wp, 12416.588502848_wp, 4.772158039_wp, &
0.000689e-6_wp, 4686.889407707_wp, 6.224271088_wp, &
0.000495e-6_wp, 7342.457780181_wp, 3.817285811_wp, &
0.000567e-6_wp, 3634.621024518_wp, 1.649264690_wp, &
0.000515e-6_wp, 18635.928454536_wp, 3.945345892_wp, &
0.000486e-6_wp, -323.505416657_wp, 4.061673868_wp, &
0.000662e-6_wp, 25158.601719765_wp, 1.794058369_wp, &
0.000509e-6_wp, 846.082834751_wp, 3.053874588_wp, &
0.000472e-6_wp, -12569.674818332_wp, 5.112133338_wp, &
0.000461e-6_wp, 6179.983075773_wp, 0.513669325_wp, &
0.000641e-6_wp, 83467.156352816_wp, 3.210727723_wp, &
0.000520e-6_wp, 10344.295065386_wp, 2.445597761_wp, &
0.000493e-6_wp, 18422.629359098_wp, 1.676939306_wp, &
0.000478e-6_wp, 1265.567478626_wp, 5.487314569_wp, &
0.000472e-6_wp, -18.159247265_wp, 1.999707589_wp, &
0.000559e-6_wp, 11190.377900137_wp, 5.783236356_wp, &
0.000494e-6_wp, 9623.688276691_wp, 3.022645053_wp, &
0.000463e-6_wp, 5739.157790895_wp, 1.411223013_wp, &
0.000432e-6_wp, 16858.482532933_wp, 1.179256434_wp, &
0.000574e-6_wp, 72140.628666286_wp, 1.758191830_wp, &
0.000484e-6_wp, 17267.268201691_wp, 3.290589143_wp, &
0.000550e-6_wp, 4907.302050146_wp, 0.864024298_wp, &
0.000399e-6_wp, 14.977853527_wp, 2.094441910_wp, &
0.000491e-6_wp, 224.344795702_wp, 0.878372791_wp, &
0.000432e-6_wp, 20426.571092422_wp, 6.003829241_wp, &
0.000481e-6_wp, 5749.452731634_wp, 4.309591964_wp, &
0.000480e-6_wp, 5757.317038160_wp, 1.142348571_wp, &
0.000485e-6_wp, 6702.560493867_wp, 0.210580917_wp, &
0.000426e-6_wp, 6055.549660552_wp, 4.274476529_wp, &
0.000480e-6_wp, 5959.570433334_wp, 5.031351030_wp, &
0.000466e-6_wp, 12562.628581634_wp, 4.959581597_wp, &
0.000520e-6_wp, 39302.096962196_wp, 4.788002889_wp, &
0.000458e-6_wp, 12132.439962106_wp, 1.880103788_wp, &
0.000470e-6_wp, 12029.347187887_wp, 1.405611197_wp, &
0.000416e-6_wp, -7477.522860216_wp, 1.082356330_wp, &
0.000449e-6_wp, 11609.862544012_wp, 4.179989585_wp, &
0.000465e-6_wp, 17253.041107690_wp, 0.353496295_wp, &
0.000362e-6_wp, -4535.059436924_wp, 1.583849576_wp, &
0.000383e-6_wp, 21954.157609398_wp, 3.747376371_wp, &
0.000389e-6_wp, 17.252277143_wp, 1.395753179_wp, &
0.000331e-6_wp, 18052.929543158_wp, 0.566790582_wp, &
0.000430e-6_wp, 13517.870106233_wp, 0.685827538_wp, &
0.000368e-6_wp, -5756.908003246_wp, 0.731374317_wp, &
0.000330e-6_wp, 10557.594160824_wp, 3.710043680_wp, &
0.000332e-6_wp, 20199.094959633_wp, 1.652901407_wp, &
0.000384e-6_wp, 11933.367960670_wp, 5.827781531_wp, &
0.000387e-6_wp, 10454.501386605_wp, 2.541182564_wp, &
0.000325e-6_wp, 15671.081759407_wp, 2.178850542_wp, &
0.000318e-6_wp, 138.517496871_wp, 2.253253037_wp, &
0.000305e-6_wp, 9388.005909415_wp, 0.578340206_wp, &
0.000352e-6_wp, 5749.861766548_wp, 3.000297967_wp, &
0.000311e-6_wp, 6915.859589305_wp, 1.693574249_wp, &
0.000297e-6_wp, 24072.921469776_wp, 1.997249392_wp, &
0.000363e-6_wp, -640.877607382_wp, 5.071820966_wp, &
0.000323e-6_wp, 12592.450019783_wp, 1.072262823_wp, &
0.000341e-6_wp, 12146.667056108_wp, 4.700657997_wp, &
0.000290e-6_wp, 9779.108676125_wp, 1.812320441_wp, &
0.000342e-6_wp, 6132.028180148_wp, 4.322238614_wp, &
0.000329e-6_wp, 6268.848755990_wp, 3.033827743_wp, &
0.000374e-6_wp, 17996.031168222_wp, 3.388716544_wp, &
0.000285e-6_wp, -533.214083444_wp, 4.687313233_wp, &
0.000338e-6_wp, 6065.844601290_wp, 0.877776108_wp, &
0.000276e-6_wp, 24.298513841_wp, 0.770299429_wp, &
0.000336e-6_wp, -2388.894020449_wp, 5.353796034_wp, &
0.000290e-6_wp, 3097.883822726_wp, 4.075291557_wp, &
0.000318e-6_wp, 709.933048357_wp, 5.941207518_wp, &
0.000271e-6_wp, 13095.842665077_wp, 3.208912203_wp, &
0.000331e-6_wp, 6073.708907816_wp, 4.007881169_wp, &
0.000292e-6_wp, 742.990060533_wp, 2.714333592_wp, &
0.000362e-6_wp, 29088.811415985_wp, 3.215977013_wp, &
0.000280e-6_wp, 12359.966151546_wp, 0.710872502_wp, &
0.000267e-6_wp, 10440.274292604_wp, 4.730108488_wp, &
0.000262e-6_wp, 838.969287750_wp, 1.327720272_wp, &
0.000250e-6_wp, 16496.361396202_wp, 0.898769761_wp, &
0.000325e-6_wp, 20597.243963041_wp, 0.180044365_wp, &
0.000268e-6_wp, 6148.010769956_wp, 5.152666276_wp, &
0.000284e-6_wp, 5636.065016677_wp, 5.655385808_wp, &
0.000301e-6_wp, 6080.822454817_wp, 2.135396205_wp, &
0.000294e-6_wp, -377.373607916_wp, 3.708784168_wp, &
0.000236e-6_wp, 2118.763860378_wp, 1.733578756_wp, &
0.000234e-6_wp, 5867.523359379_wp, 5.575209112_wp, &
0.000268e-6_wp, -226858.238553767_wp, 0.069432392_wp, &
0.000265e-6_wp, 167283.761587465_wp, 4.369302826_wp, &
0.000280e-6_wp, 28237.233459389_wp, 5.304829118_wp, &
0.000292e-6_wp, 12345.739057544_wp, 4.096094132_wp, &
0.000223e-6_wp, 19800.945956225_wp, 3.069327406_wp, &
0.000301e-6_wp, 43232.306658416_wp, 6.205311188_wp, &
0.000264e-6_wp, 18875.525869774_wp, 1.417263408_wp, &
0.000304e-6_wp, -1823.175188677_wp, 3.409035232_wp, &
0.000301e-6_wp, 109.945688789_wp, 0.510922054_wp, &
0.000260e-6_wp, 813.550283960_wp, 2.389438934_wp, &
0.000299e-6_wp, 316428.228673312_wp, 5.384595078_wp, &
0.000211e-6_wp, 5756.566278634_wp, 3.789392838_wp, &
0.000209e-6_wp, 5750.203491159_wp, 1.661943545_wp, &
0.000240e-6_wp, 12489.885628707_wp, 5.684549045_wp, &
0.000216e-6_wp, 6303.851245484_wp, 3.862942261_wp, &
0.000203e-6_wp, 1581.959348283_wp, 5.549853589_wp, &
0.000200e-6_wp, 5642.198242609_wp, 1.016115785_wp, &
0.000197e-6_wp, -70.849445304_wp, 4.690702525_wp, &
0.000227e-6_wp, 6287.008003254_wp, 2.911891613_wp, &
0.000197e-6_wp, 533.623118358_wp, 1.048982898_wp, &
0.000205e-6_wp, -6279.485421340_wp, 1.829362730_wp, &
0.000209e-6_wp, -10988.808157535_wp, 2.636140084_wp, &
0.000208e-6_wp, -227.526189440_wp, 4.127883842_wp, &
0.000191e-6_wp, 415.552490612_wp, 4.401165650_wp, &
0.000190e-6_wp, 29296.615389579_wp, 4.175658539_wp, &
0.000264e-6_wp, 66567.485864652_wp, 4.601102551_wp, &
0.000256e-6_wp, -3646.350377354_wp, 0.506364778_wp, &
0.000188e-6_wp, 13119.721102825_wp, 2.032195842_wp, &
0.000185e-6_wp, -209.366942175_wp, 4.694756586_wp, &
0.000198e-6_wp, 25934.124331089_wp, 3.832703118_wp, &
0.000195e-6_wp, 4061.219215394_wp, 3.308463427_wp, &
0.000234e-6_wp, 5113.487598583_wp, 1.716090661_wp, &
0.000188e-6_wp, 1478.866574064_wp, 5.686865780_wp, &
0.000222e-6_wp, 11823.161639450_wp, 1.942386641_wp, &
0.000181e-6_wp, 10770.893256262_wp, 1.999482059_wp, &
0.000171e-6_wp, 6546.159773364_wp, 1.182807992_wp, &
0.000206e-6_wp, 70.328180442_wp, 5.934076062_wp, &
0.000169e-6_wp, 20995.392966449_wp, 2.169080622_wp, &
0.000191e-6_wp, 10660.686935042_wp, 5.405515999_wp, &
0.000228e-6_wp, 33019.021112205_wp, 4.656985514_wp, &
0.000184e-6_wp, -4933.208440333_wp, 3.327476868_wp, &
0.000220e-6_wp, -135.625325010_wp, 1.765430262_wp, &
0.000166e-6_wp, 23141.558382925_wp, 3.454132746_wp, &
0.000191e-6_wp, 6144.558353121_wp, 5.020393445_wp, &
0.000180e-6_wp, 6084.003848555_wp, 0.602182191_wp, &
0.000163e-6_wp, 17782.732072784_wp, 4.960593133_wp, &
0.000225e-6_wp, 16460.333529525_wp, 2.596451817_wp, &
0.000222e-6_wp, 5905.702242076_wp, 3.731990323_wp, &
0.000204e-6_wp, 227.476132789_wp, 5.636192701_wp, &
0.000159e-6_wp, 16737.577236597_wp, 3.600691544_wp, &
0.000200e-6_wp, 6805.653268085_wp, 0.868220961_wp, &
0.000187e-6_wp, 11919.140866668_wp, 2.629456641_wp, &
0.000161e-6_wp, 127.471796607_wp, 2.862574720_wp, &
0.000205e-6_wp, 6286.666278643_wp, 1.742882331_wp, &
0.000189e-6_wp, 153.778810485_wp, 4.812372643_wp, &
0.000168e-6_wp, 16723.350142595_wp, 0.027860588_wp, &
0.000149e-6_wp, 11720.068865232_wp, 0.659721876_wp, &
0.000189e-6_wp, 5237.921013804_wp, 5.245313000_wp, &
0.000143e-6_wp, 6709.674040867_wp, 4.317625647_wp, &
0.000146e-6_wp, 4487.817406270_wp, 4.815297007_wp, &
0.000144e-6_wp, -664.756045130_wp, 5.381366880_wp, &
0.000175e-6_wp, 5127.714692584_wp, 4.728443327_wp, &
0.000162e-6_wp, 6254.626662524_wp, 1.435132069_wp, &
0.000187e-6_wp, 47162.516354635_wp, 1.354371923_wp, &
0.000146e-6_wp, 11080.171578918_wp, 3.369695406_wp, &
0.000180e-6_wp, -348.924420448_wp, 2.490902145_wp, &
0.000148e-6_wp, 151.047669843_wp, 3.799109588_wp, &
0.000157e-6_wp, 6197.248551160_wp, 1.284375887_wp, &
0.000167e-6_wp, 146.594251718_wp, 0.759969109_wp, &
0.000133e-6_wp, -5331.357443741_wp, 5.409701889_wp, &
0.000154e-6_wp, 95.979227218_wp, 3.366890614_wp, &
0.000148e-6_wp, -6418.140930027_wp, 3.384104996_wp, &
0.000128e-6_wp, -6525.804453965_wp, 3.803419985_wp, &
0.000130e-6_wp, 11293.470674356_wp, 0.939039445_wp, &
0.000152e-6_wp, -5729.506447149_wp, 0.734117523_wp, &
0.000138e-6_wp, 210.117701700_wp, 2.564216078_wp, &
0.000123e-6_wp, 6066.595360816_wp, 4.517099537_wp, &
0.000140e-6_wp, 18451.078546566_wp, 0.642049130_wp, &
0.000126e-6_wp, 11300.584221356_wp, 3.485280663_wp, &
0.000119e-6_wp, 10027.903195729_wp, 3.217431161_wp, &
0.000151e-6_wp, 4274.518310832_wp, 4.404359108_wp, &
0.000117e-6_wp, 6072.958148291_wp, 0.366324650_wp, &
0.000165e-6_wp, -7668.637425143_wp, 4.298212528_wp, &
0.000117e-6_wp, -6245.048177356_wp, 5.379518958_wp, &
0.000130e-6_wp, -5888.449964932_wp, 4.527681115_wp, &
0.000121e-6_wp, -543.918059096_wp, 6.109429504_wp, &
0.000162e-6_wp, 9683.594581116_wp, 5.720092446_wp, &
0.000141e-6_wp, 6219.339951688_wp, 0.679068671_wp, &
0.000118e-6_wp, 22743.409379516_wp, 4.881123092_wp, &
0.000129e-6_wp, 1692.165669502_wp, 0.351407289_wp, &
0.000126e-6_wp, 5657.405657679_wp, 5.146592349_wp, &
0.000114e-6_wp, 728.762966531_wp, 0.520791814_wp, &
0.000120e-6_wp, 52.596639600_wp, 0.948516300_wp, &
0.000115e-6_wp, 65.220371012_wp, 3.504914846_wp, &
0.000126e-6_wp, 5881.403728234_wp, 5.577502482_wp, &
0.000158e-6_wp, 163096.180360983_wp, 2.957128968_wp, &
0.000134e-6_wp, 12341.806904281_wp, 2.598576764_wp, &
0.000151e-6_wp, 16627.370915377_wp, 3.985702050_wp, &
0.000109e-6_wp, 1368.660252845_wp, 0.014730471_wp, &
0.000131e-6_wp, 6211.263196841_wp, 0.085077024_wp, &
0.000146e-6_wp, 5792.741760812_wp, 0.708426604_wp, &
0.000146e-6_wp, -77.750543984_wp, 3.121576600_wp, &
0.000107e-6_wp, 5341.013788022_wp, 0.288231904_wp, &
0.000138e-6_wp, 6281.591377283_wp, 2.797450317_wp, &
0.000113e-6_wp, -6277.552925684_wp, 2.788904128_wp, &
0.000115e-6_wp, -525.758811831_wp, 5.895222200_wp, &
0.000138e-6_wp, 6016.468808270_wp, 6.096188999_wp, &
0.000139e-6_wp, 23539.707386333_wp, 2.028195445_wp, &
0.000146e-6_wp, -4176.041342449_wp, 4.660008502_wp, &
0.000107e-6_wp, 16062.184526117_wp, 4.066520001_wp, &
0.000142e-6_wp, 83783.548222473_wp, 2.936315115_wp, &
0.000128e-6_wp, 9380.959672717_wp, 3.223844306_wp, &
0.000135e-6_wp, 6205.325306007_wp, 1.638054048_wp, &
0.000101e-6_wp, 2699.734819318_wp, 5.481603249_wp, &
0.000104e-6_wp, -568.821874027_wp, 2.205734493_wp, &
0.000103e-6_wp, 6321.103522627_wp, 2.440421099_wp, &
0.000119e-6_wp, 6321.208885629_wp, 2.547496264_wp, &
0.000138e-6_wp, 1975.492545856_wp, 2.314608466_wp, &
0.000121e-6_wp, 137.033024162_wp, 4.539108237_wp, &
0.000123e-6_wp, 19402.796952817_wp, 4.538074405_wp, &
0.000119e-6_wp, 22805.735565994_wp, 2.869040566_wp, &
0.000133e-6_wp, 64471.991241142_wp, 6.056405489_wp, &
0.000129e-6_wp, -85.827298831_wp, 2.540635083_wp, &
0.000131e-6_wp, 13613.804277336_wp, 4.005732868_wp, &
0.000104e-6_wp, 9814.604100291_wp, 1.959967212_wp, &
0.000112e-6_wp, 16097.679950283_wp, 3.589026260_wp, &
0.000123e-6_wp, 2107.034507542_wp, 1.728627253_wp, &
0.000121e-6_wp, 36949.230808424_wp, 6.072332087_wp, &
0.000108e-6_wp, -12539.853380183_wp, 3.716133846_wp, &
0.000113e-6_wp, -7875.671863624_wp, 2.725771122_wp, &
0.000109e-6_wp, 4171.425536614_wp, 4.033338079_wp, &
0.000101e-6_wp, 6247.911759770_wp, 3.441347021_wp, &
0.000113e-6_wp, 7330.728427345_wp, 0.656372122_wp, &
0.000113e-6_wp, 51092.726050855_wp, 2.791483066_wp, &
0.000106e-6_wp, 5621.842923210_wp, 1.815323326_wp, &
0.000101e-6_wp, 111.430161497_wp, 5.711033677_wp, &
0.000103e-6_wp, 909.818733055_wp, 2.812745443_wp, &
0.000101e-6_wp, 1790.642637886_wp, 1.965746028_wp, &
102.156724e-6_wp, 6283.075849991_wp, 4.249032005_wp, & ! T
1.706807e-6_wp, 12566.151699983_wp, 4.205904248_wp, &
0.269668e-6_wp, 213.299095438_wp, 3.400290479_wp, &
0.265919e-6_wp, 529.690965095_wp, 5.836047367_wp, &
0.210568e-6_wp, -3.523118349_wp, 6.262738348_wp, &
0.077996e-6_wp, 5223.693919802_wp, 4.670344204_wp, &
0.054764e-6_wp, 1577.343542448_wp, 4.534800170_wp, &
0.059146e-6_wp, 26.298319800_wp, 1.083044735_wp, &
0.034420e-6_wp, -398.149003408_wp, 5.980077351_wp, &
0.032088e-6_wp, 18849.227549974_wp, 4.162913471_wp, &
0.033595e-6_wp, 5507.553238667_wp, 5.980162321_wp, &
0.029198e-6_wp, 5856.477659115_wp, 0.623811863_wp, &
0.027764e-6_wp, 155.420399434_wp, 3.745318113_wp, &
0.025190e-6_wp, 5746.271337896_wp, 2.980330535_wp, &
0.022997e-6_wp, -796.298006816_wp, 1.174411803_wp, &
0.024976e-6_wp, 5760.498431898_wp, 2.467913690_wp, &
0.021774e-6_wp, 206.185548437_wp, 3.854787540_wp, &
0.017925e-6_wp, -775.522611324_wp, 1.092065955_wp, &
0.013794e-6_wp, 426.598190876_wp, 2.699831988_wp, &
0.013276e-6_wp, 6062.663207553_wp, 5.845801920_wp, &
0.011774e-6_wp, 12036.460734888_wp, 2.292832062_wp, &
0.012869e-6_wp, 6076.890301554_wp, 5.333425680_wp, &
0.012152e-6_wp, 1059.381930189_wp, 6.222874454_wp, &
0.011081e-6_wp, -7.113547001_wp, 5.154724984_wp, &
0.010143e-6_wp, 4694.002954708_wp, 4.044013795_wp, &
0.009357e-6_wp, 5486.777843175_wp, 3.416081409_wp, &
0.010084e-6_wp, 522.577418094_wp, 0.749320262_wp, &
0.008587e-6_wp, 10977.078804699_wp, 2.777152598_wp, &
0.008628e-6_wp, 6275.962302991_wp, 4.562060226_wp, &
0.008158e-6_wp, -220.412642439_wp, 5.806891533_wp, &
0.007746e-6_wp, 2544.314419883_wp, 1.603197066_wp, &
0.007670e-6_wp, 2146.165416475_wp, 3.000200440_wp, &
0.007098e-6_wp, 74.781598567_wp, 0.443725817_wp, &
0.006180e-6_wp, -536.804512095_wp, 1.302642751_wp, &
0.005818e-6_wp, 5088.628839767_wp, 4.827723531_wp, &
0.004945e-6_wp, -6286.598968340_wp, 0.268305170_wp, &
0.004774e-6_wp, 1349.867409659_wp, 5.808636673_wp, &
0.004687e-6_wp, -242.728603974_wp, 5.154890570_wp, &
0.006089e-6_wp, 1748.016413067_wp, 4.403765209_wp, &
0.005975e-6_wp, -1194.447010225_wp, 2.583472591_wp, &
0.004229e-6_wp, 951.718406251_wp, 0.931172179_wp, &
0.005264e-6_wp, 553.569402842_wp, 2.336107252_wp, &
0.003049e-6_wp, 5643.178563677_wp, 1.362634430_wp, &
0.002974e-6_wp, 6812.766815086_wp, 1.583012668_wp, &
0.003403e-6_wp, -2352.866153772_wp, 2.552189886_wp, &
0.003030e-6_wp, 419.484643875_wp, 5.286473844_wp, &
0.003210e-6_wp, -7.046236698_wp, 1.863796539_wp, &
0.003058e-6_wp, 9437.762934887_wp, 4.226420633_wp, &
0.002589e-6_wp, 12352.852604545_wp, 1.991935820_wp, &
0.002927e-6_wp, 5216.580372801_wp, 2.319951253_wp, &
0.002425e-6_wp, 5230.807466803_wp, 3.084752833_wp, &
0.002656e-6_wp, 3154.687084896_wp, 2.487447866_wp, &
0.002445e-6_wp, 10447.387839604_wp, 2.347139160_wp, &
0.002990e-6_wp, 4690.479836359_wp, 6.235872050_wp, &
0.002890e-6_wp, 5863.591206116_wp, 0.095197563_wp, &
0.002498e-6_wp, 6438.496249426_wp, 2.994779800_wp, &
0.001889e-6_wp, 8031.092263058_wp, 3.569003717_wp, &
0.002567e-6_wp, 801.820931124_wp, 3.425611498_wp, &
0.001803e-6_wp, -71430.695617928_wp, 2.192295512_wp, &
0.001782e-6_wp, 3.932153263_wp, 5.180433689_wp, &
0.001694e-6_wp, -4705.732307544_wp, 4.641779174_wp, &
0.001704e-6_wp, -1592.596013633_wp, 3.997097652_wp, &
0.001735e-6_wp, 5849.364112115_wp, 0.417558428_wp, &
0.001643e-6_wp, 8429.241266467_wp, 2.180619584_wp, &
0.001680e-6_wp, 38.133035638_wp, 4.164529426_wp, &
0.002045e-6_wp, 7084.896781115_wp, 0.526323854_wp, &
0.001458e-6_wp, 4292.330832950_wp, 1.356098141_wp, &
0.001437e-6_wp, 20.355319399_wp, 3.895439360_wp, &
0.001738e-6_wp, 6279.552731642_wp, 0.087484036_wp, &
0.001367e-6_wp, 14143.495242431_wp, 3.987576591_wp, &
0.001344e-6_wp, 7234.794256242_wp, 0.090454338_wp, &
0.001438e-6_wp, 11499.656222793_wp, 0.974387904_wp, &
0.001257e-6_wp, 6836.645252834_wp, 1.509069366_wp, &
0.001358e-6_wp, 11513.883316794_wp, 0.495572260_wp, &
0.001628e-6_wp, 7632.943259650_wp, 4.968445721_wp, &
0.001169e-6_wp, 103.092774219_wp, 2.838496795_wp, &
0.001162e-6_wp, 4164.311989613_wp, 3.408387778_wp, &
0.001092e-6_wp, 6069.776754553_wp, 3.617942651_wp, &
0.001008e-6_wp, 17789.845619785_wp, 0.286350174_wp, &
0.001008e-6_wp, 639.897286314_wp, 1.610762073_wp, &
0.000918e-6_wp, 10213.285546211_wp, 5.532798067_wp, &
0.001011e-6_wp, -6256.777530192_wp, 0.661826484_wp, &
0.000753e-6_wp, 16730.463689596_wp, 3.905030235_wp, &
0.000737e-6_wp, 11926.254413669_wp, 4.641956361_wp, &
0.000694e-6_wp, 3340.612426700_wp, 2.111120332_wp, &
0.000701e-6_wp, 3894.181829542_wp, 2.760823491_wp, &
0.000689e-6_wp, -135.065080035_wp, 4.768800780_wp, &
0.000700e-6_wp, 13367.972631107_wp, 5.760439898_wp, &
0.000664e-6_wp, 6040.347246017_wp, 1.051215840_wp, &
0.000654e-6_wp, 5650.292110678_wp, 4.911332503_wp, &
0.000788e-6_wp, 6681.224853400_wp, 4.699648011_wp, &
0.000628e-6_wp, 5333.900241022_wp, 5.024608847_wp, &
0.000755e-6_wp, -110.206321219_wp, 4.370971253_wp, &
0.000628e-6_wp, 6290.189396992_wp, 3.660478857_wp, &
0.000635e-6_wp, 25132.303399966_wp, 4.121051532_wp, &
0.000534e-6_wp, 5966.683980335_wp, 1.173284524_wp, &
0.000543e-6_wp, -433.711737877_wp, 0.345585464_wp, &
0.000517e-6_wp, -1990.745017041_wp, 5.414571768_wp, &
0.000504e-6_wp, 5767.611978898_wp, 2.328281115_wp, &
0.000485e-6_wp, 5753.384884897_wp, 1.685874771_wp, &
0.000463e-6_wp, 7860.419392439_wp, 5.297703006_wp, &
0.000604e-6_wp, 515.463871093_wp, 0.591998446_wp, &
0.000443e-6_wp, 12168.002696575_wp, 4.830881244_wp, &
0.000570e-6_wp, 199.072001436_wp, 3.899190272_wp, &
0.000465e-6_wp, 10969.965257698_wp, 0.476681802_wp, &
0.000424e-6_wp, -7079.373856808_wp, 1.112242763_wp, &
0.000427e-6_wp, 735.876513532_wp, 1.994214480_wp, &
0.000478e-6_wp, -6127.655450557_wp, 3.778025483_wp, &
0.000414e-6_wp, 10973.555686350_wp, 5.441088327_wp, &
0.000512e-6_wp, 1589.072895284_wp, 0.107123853_wp, &
0.000378e-6_wp, 10984.192351700_wp, 0.915087231_wp, &
0.000402e-6_wp, 11371.704689758_wp, 4.107281715_wp, &
0.000453e-6_wp, 9917.696874510_wp, 1.917490952_wp, &
0.000395e-6_wp, 149.563197135_wp, 2.763124165_wp, &
0.000371e-6_wp, 5739.157790895_wp, 3.112111866_wp, &
0.000350e-6_wp, 11790.629088659_wp, 0.440639857_wp, &
0.000356e-6_wp, 6133.512652857_wp, 5.444568842_wp, &
0.000344e-6_wp, 412.371096874_wp, 5.676832684_wp, &
0.000383e-6_wp, 955.599741609_wp, 5.559734846_wp, &
0.000333e-6_wp, 6496.374945429_wp, 0.261537984_wp, &
0.000340e-6_wp, 6055.549660552_wp, 5.975534987_wp, &
0.000334e-6_wp, 1066.495477190_wp, 2.335063907_wp, &
0.000399e-6_wp, 11506.769769794_wp, 5.321230910_wp, &
0.000314e-6_wp, 18319.536584880_wp, 2.313312404_wp, &
0.000424e-6_wp, 1052.268383188_wp, 1.211961766_wp, &
0.000307e-6_wp, 63.735898303_wp, 3.169551388_wp, &
0.000329e-6_wp, 29.821438149_wp, 6.106912080_wp, &
0.000357e-6_wp, 6309.374169791_wp, 4.223760346_wp, &
0.000312e-6_wp, -3738.761430108_wp, 2.180556645_wp, &
0.000301e-6_wp, 309.278322656_wp, 1.499984572_wp, &
0.000268e-6_wp, 12043.574281889_wp, 2.447520648_wp, &
0.000257e-6_wp, 12491.370101415_wp, 3.662331761_wp, &
0.000290e-6_wp, 625.670192312_wp, 1.272834584_wp, &
0.000256e-6_wp, 5429.879468239_wp, 1.913426912_wp, &
0.000339e-6_wp, 3496.032826134_wp, 4.165930011_wp, &
0.000283e-6_wp, 3930.209696220_wp, 4.325565754_wp, &
0.000241e-6_wp, 12528.018664345_wp, 3.832324536_wp, &
0.000304e-6_wp, 4686.889407707_wp, 1.612348468_wp, &
0.000259e-6_wp, 16200.772724501_wp, 3.470173146_wp, &
0.000238e-6_wp, 12139.553509107_wp, 1.147977842_wp, &
0.000236e-6_wp, 6172.869528772_wp, 3.776271728_wp, &
0.000296e-6_wp, -7058.598461315_wp, 0.460368852_wp, &
0.000306e-6_wp, 10575.406682942_wp, 0.554749016_wp, &
0.000251e-6_wp, 17298.182327326_wp, 0.834332510_wp, &
0.000290e-6_wp, 4732.030627343_wp, 4.759564091_wp, &
0.000261e-6_wp, 5884.926846583_wp, 0.298259862_wp, &
0.000249e-6_wp, 5547.199336460_wp, 3.749366406_wp, &
0.000213e-6_wp, 11712.955318231_wp, 5.415666119_wp, &
0.000223e-6_wp, 4701.116501708_wp, 2.703203558_wp, &
0.000268e-6_wp, -640.877607382_wp, 0.283670793_wp, &
0.000209e-6_wp, 5636.065016677_wp, 1.238477199_wp, &
0.000193e-6_wp, 10177.257679534_wp, 1.943251340_wp, &
0.000182e-6_wp, 6283.143160294_wp, 2.456157599_wp, &
0.000184e-6_wp, -227.526189440_wp, 5.888038582_wp, &
0.000182e-6_wp, -6283.008539689_wp, 0.241332086_wp, &
0.000228e-6_wp, -6284.056171060_wp, 2.657323816_wp, &
0.000166e-6_wp, 7238.675591600_wp, 5.930629110_wp, &
0.000167e-6_wp, 3097.883822726_wp, 5.570955333_wp, &
0.000159e-6_wp, -323.505416657_wp, 5.786670700_wp, &
0.000154e-6_wp, -4136.910433516_wp, 1.517805532_wp, &
0.000176e-6_wp, 12029.347187887_wp, 3.139266834_wp, &
0.000167e-6_wp, 12132.439962106_wp, 3.556352289_wp, &
0.000153e-6_wp, 202.253395174_wp, 1.463313961_wp, &
0.000157e-6_wp, 17267.268201691_wp, 1.586837396_wp, &
0.000142e-6_wp, 83996.847317911_wp, 0.022670115_wp, &
0.000152e-6_wp, 17260.154654690_wp, 0.708528947_wp, &
0.000144e-6_wp, 6084.003848555_wp, 5.187075177_wp, &
0.000135e-6_wp, 5756.566278634_wp, 1.993229262_wp, &
0.000134e-6_wp, 5750.203491159_wp, 3.457197134_wp, &
0.000144e-6_wp, 5326.786694021_wp, 6.066193291_wp, &
0.000160e-6_wp, 11015.106477335_wp, 1.710431974_wp, &
0.000133e-6_wp, 3634.621024518_wp, 2.836451652_wp, &
0.000134e-6_wp, 18073.704938650_wp, 5.453106665_wp, &
0.000134e-6_wp, 1162.474704408_wp, 5.326898811_wp, &
0.000128e-6_wp, 5642.198242609_wp, 2.511652591_wp, &
0.000160e-6_wp, 632.783739313_wp, 5.628785365_wp, &
0.000132e-6_wp, 13916.019109642_wp, 0.819294053_wp, &
0.000122e-6_wp, 14314.168113050_wp, 5.677408071_wp, &
0.000125e-6_wp, 12359.966151546_wp, 5.251984735_wp, &
0.000121e-6_wp, 5749.452731634_wp, 2.210924603_wp, &
0.000136e-6_wp, -245.831646229_wp, 1.646502367_wp, &
0.000120e-6_wp, 5757.317038160_wp, 3.240883049_wp, &
0.000134e-6_wp, 12146.667056108_wp, 3.059480037_wp, &
0.000137e-6_wp, 6206.809778716_wp, 1.867105418_wp, &
0.000141e-6_wp, 17253.041107690_wp, 2.069217456_wp, &
0.000129e-6_wp, -7477.522860216_wp, 2.781469314_wp, &
0.000116e-6_wp, 5540.085789459_wp, 4.281176991_wp, &
0.000116e-6_wp, 9779.108676125_wp, 3.320925381_wp, &
0.000129e-6_wp, 5237.921013804_wp, 3.497704076_wp, &
0.000113e-6_wp, 5959.570433334_wp, 0.983210840_wp, &
0.000122e-6_wp, 6282.095528923_wp, 2.674938860_wp, &
0.000140e-6_wp, -11.045700264_wp, 4.957936982_wp, &
0.000108e-6_wp, 23543.230504682_wp, 1.390113589_wp, &
0.000106e-6_wp, -12569.674818332_wp, 0.429631317_wp, &
0.000110e-6_wp, -266.607041722_wp, 5.501340197_wp, &
0.000115e-6_wp, 12559.038152982_wp, 4.691456618_wp, &
0.000134e-6_wp, -2388.894020449_wp, 0.577313584_wp, &
0.000109e-6_wp, 10440.274292604_wp, 6.218148717_wp, &
0.000102e-6_wp, -543.918059096_wp, 1.477842615_wp, &
0.000108e-6_wp, 21228.392023546_wp, 2.237753948_wp, &
0.000101e-6_wp, -4535.059436924_wp, 3.100492232_wp, &
0.000103e-6_wp, 76.266071276_wp, 5.594294322_wp, &
0.000104e-6_wp, 949.175608970_wp, 5.674287810_wp, &
0.000101e-6_wp, 13517.870106233_wp, 2.196632348_wp, &
0.000100e-6_wp, 11933.367960670_wp, 4.056084160_wp, &
4.322990e-6_wp, 6283.075849991_wp, 2.642893748_wp, & ! T^2
0.406495e-6_wp, 0.000000000_wp, 4.712388980_wp, &
0.122605e-6_wp, 12566.151699983_wp, 2.438140634_wp, &
0.019476e-6_wp, 213.299095438_wp, 1.642186981_wp, &
0.016916e-6_wp, 529.690965095_wp, 4.510959344_wp, &
0.013374e-6_wp, -3.523118349_wp, 1.502210314_wp, &
0.008042e-6_wp, 26.298319800_wp, 0.478549024_wp, &
0.007824e-6_wp, 155.420399434_wp, 5.254710405_wp, &
0.004894e-6_wp, 5746.271337896_wp, 4.683210850_wp, &
0.004875e-6_wp, 5760.498431898_wp, 0.759507698_wp, &
0.004416e-6_wp, 5223.693919802_wp, 6.028853166_wp, &
0.004088e-6_wp, -7.113547001_wp, 0.060926389_wp, &
0.004433e-6_wp, 77713.771467920_wp, 3.627734103_wp, &
0.003277e-6_wp, 18849.227549974_wp, 2.327912542_wp, &
0.002703e-6_wp, 6062.663207553_wp, 1.271941729_wp, &
0.003435e-6_wp, -775.522611324_wp, 0.747446224_wp, &
0.002618e-6_wp, 6076.890301554_wp, 3.633715689_wp, &
0.003146e-6_wp, 206.185548437_wp, 5.647874613_wp, &
0.002544e-6_wp, 1577.343542448_wp, 6.232904270_wp, &
0.002218e-6_wp, -220.412642439_wp, 1.309509946_wp, &
0.002197e-6_wp, 5856.477659115_wp, 2.407212349_wp, &
0.002897e-6_wp, 5753.384884897_wp, 5.863842246_wp, &
0.001766e-6_wp, 426.598190876_wp, 0.754113147_wp, &
0.001738e-6_wp, -796.298006816_wp, 2.714942671_wp, &
0.001695e-6_wp, 522.577418094_wp, 2.629369842_wp, &
0.001584e-6_wp, 5507.553238667_wp, 1.341138229_wp, &
0.001503e-6_wp, -242.728603974_wp, 0.377699736_wp, &
0.001552e-6_wp, -536.804512095_wp, 2.904684667_wp, &
0.001370e-6_wp, -398.149003408_wp, 1.265599125_wp, &
0.001889e-6_wp, -5573.142801634_wp, 4.413514859_wp, &
0.001722e-6_wp, 6069.776754553_wp, 2.445966339_wp, &
0.001124e-6_wp, 1059.381930189_wp, 5.041799657_wp, &
0.001258e-6_wp, 553.569402842_wp, 3.849557278_wp, &
0.000831e-6_wp, 951.718406251_wp, 2.471094709_wp, &
0.000767e-6_wp, 4694.002954708_wp, 5.363125422_wp, &
0.000756e-6_wp, 1349.867409659_wp, 1.046195744_wp, &
0.000775e-6_wp, -11.045700264_wp, 0.245548001_wp, &
0.000597e-6_wp, 2146.165416475_wp, 4.543268798_wp, &
0.000568e-6_wp, 5216.580372801_wp, 4.178853144_wp, &
0.000711e-6_wp, 1748.016413067_wp, 5.934271972_wp, &
0.000499e-6_wp, 12036.460734888_wp, 0.624434410_wp, &
0.000671e-6_wp, -1194.447010225_wp, 4.136047594_wp, &
0.000488e-6_wp, 5849.364112115_wp, 2.209679987_wp, &
0.000621e-6_wp, 6438.496249426_wp, 4.518860804_wp, &
0.000495e-6_wp, -6286.598968340_wp, 1.868201275_wp, &
0.000456e-6_wp, 5230.807466803_wp, 1.271231591_wp, &
0.000451e-6_wp, 5088.628839767_wp, 0.084060889_wp, &
0.000435e-6_wp, 5643.178563677_wp, 3.324456609_wp, &
0.000387e-6_wp, 10977.078804699_wp, 4.052488477_wp, &
0.000547e-6_wp, 161000.685737473_wp, 2.841633844_wp, &
0.000522e-6_wp, 3154.687084896_wp, 2.171979966_wp, &
0.000375e-6_wp, 5486.777843175_wp, 4.983027306_wp, &
0.000421e-6_wp, 5863.591206116_wp, 4.546432249_wp, &
0.000439e-6_wp, 7084.896781115_wp, 0.522967921_wp, &
0.000309e-6_wp, 2544.314419883_wp, 3.172606705_wp, &
0.000347e-6_wp, 4690.479836359_wp, 1.479586566_wp, &
0.000317e-6_wp, 801.820931124_wp, 3.553088096_wp, &
0.000262e-6_wp, 419.484643875_wp, 0.606635550_wp, &
0.000248e-6_wp, 6836.645252834_wp, 3.014082064_wp, &
0.000245e-6_wp, -1592.596013633_wp, 5.519526220_wp, &
0.000225e-6_wp, 4292.330832950_wp, 2.877956536_wp, &
0.000214e-6_wp, 7234.794256242_wp, 1.605227587_wp, &
0.000205e-6_wp, 5767.611978898_wp, 0.625804796_wp, &
0.000180e-6_wp, 10447.387839604_wp, 3.499954526_wp, &
0.000229e-6_wp, 199.072001436_wp, 5.632304604_wp, &
0.000214e-6_wp, 639.897286314_wp, 5.960227667_wp, &
0.000175e-6_wp, -433.711737877_wp, 2.162417992_wp, &
0.000209e-6_wp, 515.463871093_wp, 2.322150893_wp, &
0.000173e-6_wp, 6040.347246017_wp, 2.556183691_wp, &
0.000184e-6_wp, 6309.374169791_wp, 4.732296790_wp, &
0.000227e-6_wp, 149854.400134205_wp, 5.385812217_wp, &
0.000154e-6_wp, 8031.092263058_wp, 5.120720920_wp, &
0.000151e-6_wp, 5739.157790895_wp, 4.815000443_wp, &
0.000197e-6_wp, 7632.943259650_wp, 0.222827271_wp, &
0.000197e-6_wp, 74.781598567_wp, 3.910456770_wp, &
0.000138e-6_wp, 6055.549660552_wp, 1.397484253_wp, &
0.000149e-6_wp, -6127.655450557_wp, 5.333727496_wp, &
0.000137e-6_wp, 3894.181829542_wp, 4.281749907_wp, &
0.000135e-6_wp, 9437.762934887_wp, 5.979971885_wp, &
0.000139e-6_wp, -2352.866153772_wp, 4.715630782_wp, &
0.000142e-6_wp, 6812.766815086_wp, 0.513330157_wp, &
0.000120e-6_wp, -4705.732307544_wp, 0.194160689_wp, &
0.000131e-6_wp, -71430.695617928_wp, 0.000379226_wp, &
0.000124e-6_wp, 6279.552731642_wp, 2.122264908_wp, &
0.000108e-6_wp, -6256.777530192_wp, 0.883445696_wp, &
0.143388e-6_wp, 6283.075849991_wp, 1.131453581_wp, & ! T^3
0.006671e-6_wp, 12566.151699983_wp, 0.775148887_wp, &
0.001480e-6_wp, 155.420399434_wp, 0.480016880_wp, &
0.000934e-6_wp, 213.299095438_wp, 6.144453084_wp, &
0.000795e-6_wp, 529.690965095_wp, 2.941595619_wp, &
0.000673e-6_wp, 5746.271337896_wp, 0.120415406_wp, &
0.000672e-6_wp, 5760.498431898_wp, 5.317009738_wp, &
0.000389e-6_wp, -220.412642439_wp, 3.090323467_wp, &
0.000373e-6_wp, 6062.663207553_wp, 3.003551964_wp, &
0.000360e-6_wp, 6076.890301554_wp, 1.918913041_wp, &
0.000316e-6_wp, -21.340641002_wp, 5.545798121_wp, &
0.000315e-6_wp, -242.728603974_wp, 1.884932563_wp, &
0.000278e-6_wp, 206.185548437_wp, 1.266254859_wp, &
0.000238e-6_wp, -536.804512095_wp, 4.532664830_wp, &
0.000185e-6_wp, 522.577418094_wp, 4.578313856_wp, &
0.000245e-6_wp, 18849.227549974_wp, 0.587467082_wp, &
0.000180e-6_wp, 426.598190876_wp, 5.151178553_wp, &
0.000200e-6_wp, 553.569402842_wp, 5.355983739_wp, &
0.000141e-6_wp, 5223.693919802_wp, 1.336556009_wp, &
0.000104e-6_wp, 5856.477659115_wp, 4.239842759_wp, &
0.003826e-6_wp, 6283.075849991_wp, 5.705257275_wp, & ! T^4
0.000303e-6_wp, 12566.151699983_wp, 5.407132842_wp, &
0.000209e-6_wp, 155.420399434_wp, 1.989815753_wp ], [3,787])
! 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,1.0_wp) * d2pi + elong
! FUNDAMENTAL ARGUMENTS: Simon et al. 1994.
! Combine time argument (millennia) with deg/arcsec factor.
w = t / 3600.0_wp
! Sun Mean Longitude.
elsun = mod(280.46645683_wp + 1296027711.03429_wp * w, 360.0_wp) * dd2r
! Sun Mean Anomaly.
emsun = mod(357.52910918_wp + 1295965810.481_wp * w, 360.0_wp) * dd2r
! Mean Elongation of Moon from Sun.
d = mod(297.85019547_wp + 16029616012.090_wp * w, 360.0_wp) * dd2r
! Mean Longitude of Jupiter.
elj = mod(34.35151874_wp + 109306899.89453_wp * w, 360.0_wp) * dd2r
! Mean Longitude of Saturn.
els = mod(50.07744430_wp + 44046398.47038_wp * w, 360.0_wp) * dd2r
! TOPOCENTRIC TERMS: Moyer 1981 and Murray 1983.
wt = + 0.00029e-10_wp * u * sin(tsol + elsun - els) &
+ 0.00100e-10_wp * u * sin(tsol - 2.0_wp*emsun) &
+ 0.00133e-10_wp * u * sin(tsol - d) &
+ 0.00133e-10_wp * u * sin(tsol + elsun - elj) &
- 0.00229e-10_wp * u * sin(tsol + 2.0_wp*elsun + emsun) &
- 0.0220e-10_wp * v * cos(elsun + emsun) &
+ 0.05312e-10_wp * u * sin(tsol - emsun) &
- 0.13677e-10_wp * u * sin(tsol + 2.0_wp*elsun) &
- 1.3184e-10_wp * v * cos(elsun) &
+ 3.17679e-10_wp * u * sin(tsol)
! =====================
! Fairhead et al. model
! =====================
! T**0
w0 = 0.0_wp
do j=474,1,-1
w0 = w0 + fairhd(1,j) * sin(fairhd(2,j)*t + fairhd(3,j))
end do
! T**1
w1 = 0.0_wp
do j=679,475,-1
w1 = w1 + fairhd(1,j) * sin(fairhd(2,j)*t + fairhd(3,j))
end do
! T**2
w2 = 0.0_wp
do j=764,680,-1
w2 = w2 + fairhd(1,j) * sin(fairhd(2,j)*t + fairhd(3,j))
end do
! T**3
w3 = 0.0_wp
do j=784,765,-1
w3 = w3 + fairhd(1,j) * sin(fairhd(2,j)*t + fairhd(3,j))
end do
! T**4
w4 = 0.0_wp
do j=787,785,-1
w4 = w4 + fairhd(1,j) * sin(fairhd(2,j)*t + fairhd(3,j))
end do
! 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 = 0.00065e-6_wp * sin(6069.776754_wp*t + 4.021194_wp) + &
0.00033e-6_wp * sin( 213.299095_wp*t + 5.543132_wp) + &
( -0.00196e-6_wp * sin(6208.294251_wp*t + 5.696701_wp) ) + &
( -0.00173e-6_wp * sin( 74.781599_wp*t + 2.435900_wp) ) + &
0.03638e-6_wp * t * t
! ============
! Final result
! ============
! TDB-TT in seconds.
TDB_minus_TT = wt + wf + wj
end function DTDB