JPL-HP41 Ephemerides
Overview
1°) Heliocentric Rectangular Equatorial
Coordinates ( Geocentric for the Moon )
2°) Geocentric Rectangular Equatorial
Coordinates
3°) Data Files
a) 2013/09/25 0h TDB - 2013/10/27
0h TDB ( 329 numbers )
b) 2013/10/27 0h TDB - 2013/11/28
0h TDB ( 350 numbers )
-The programs listed in "JPL Ephemerides for the HP-41" use a DATA file
of 1017 numbers.
-Even if we only store the coefficients enough large to get 10-digit
accuracy, it would require about 600 registers.
-In order to reduce the number of coefficients to be stored - and thanks
to my HP-48 - I've calculated Chebyshev coefficients that are valid
over time-spans
of 32 days to compute the rectangular equatorial coordinates
of the major planets & the Moon and the nutations ( the libration is
neglected here ).
-So, you will "only" have to store a little more than 300 numbers every
32 days. ( the exact number of coefficients may vary from month to month...
)
-Moreover, the coordinates are directly heliocentric for the
planets ( of course still geocentric for the Moon )
1°) Heliocentric Rectangular Equatorial
Coordinates ( Geocentric for the Moon )
-First create a DATA file named "DE430" ( or another name, cf line 09
below ) and save the 329 numbers given in paragraph 3°)a)
-Many decimals may be neglected, thus saving several keystrokes.
-These numbers are computed from the latest JPL ephemerides DE430/LE430
-They were recently released, in August 2013.
-I've used the method that is described in "Chebyshev Approximation
for the HP-41"
but with an HP-48 to get the coefficients with a better precision.
-All the coordinates are referred to the International Celestial Reference
Frame ( ICRF )
Data Registers: R00 & R33 .... : temp R35 = number of Chebyshev coefficients per coordinate
R01 = XMercury R04 = XVenus
R07 = XEarth R10 =
XMars R13 = XJupiter
R16 = XSaturn
R02 = YMercury R05 = YVenus
R08 = YEarth R11 =
YMars R14 = YJupiter
R17 = YSaturn
R03 = ZMercury R06 = ZVenus
R09 = ZEarth
R12 = ZMars R15 =
ZJupiter R18 = ZSaturn
R19 = XUranus R22 = XNeptune
R25 = XPluto R28 = XMoon
R31 = Delta Psi = nutation in longitude ( in degree )
R20 = YUranus R23 = YNeptune
R26 = YPluto R29 = YMoon
R32 = Delta Epsilon = nutation in obliquity ( in degree )
R21 = ZUranus R24 = ZNeptune
R27 = ZPluto R30 = ZMoon
Flags: /
Subroutines: "J0" or "J1" or J2" (
cf "Julian & Gregorian Calendars for the HP-41" )
"CdT" M-Code routine or focal program ( cf "Ephemerides & Chebyshev
Polynomials for the HP-41 )
| 01 LBL "JPL41"
02 HR 03 24 04 / 05 X<>Y 06 XEQ "J2" 07 2451544.5 08 + 09 "DE430" 10 0 11 SEEKPTA 12 CLX 13 GETX 14 - 15 + 16 16 17 ST- Y |
18 /
19 STO 00 20 ACOS 21 SIGN 22 STO 33 23 37.036 24 STO 34 25 3 E-3 26 STO 36 27 15 28 XEQ 01 29 8 30 XEQ 01 31 8 32 XEQ 01 33 7 34 XEQ 01 |
35 5
36 XEQ 01 37 4 38 XEQ 01 39 4 40 XEQ 01 41 4 42 XEQ 01 43 4 44 XEQ 01 45 33 46 XEQ 01 47 1.5 48 ST/ 36 49 26 50 XEQ 01 51 GTO 00 |
52 LBL 01
53 STO 35 54 RCL 36 55 ST+ 33 56 LBL 02 57 RCL 34 58 RCL 35 59 E3 60 / 61 + 62 GETRX 63 RCL 00 64 CdT 65 STO IND 33 66 ISG 33 67 GTO 02 68 RTN |
69 LBL 00
70 RCL 28 71 82.30055986 72 / 73 ST- 07 74 RCL 29 75 LASTX 76 / 77 ST- 08 78 RCL 30 79 LASTX 80 / 81 ST- 09 82 RCL 03 83 RCL 02 84 RCL 01 85 END |
( 183 bytes )
| STACK | INPUTS | OUTPUTS |
| Z | / | ZMer |
| Y | YYYY.MNDD | YMer |
| X | HH.MNSS | XMer |
where the time is expressed in TDB ---Execution time = 54s---
Example: 2013/10/16 21h41m37s TDB
2013.1016 ENTER^
21.4137
XEQ "JPL41" returns:
• Mercury
R01 = 0.324818828 AU = X
R02 = -0.195722676 AU = Y
R03 = -0.138227060 AU = Z
• Venus
R04 = 0.643218754 AU
R05 = -0.293687996 AU
R06 = -0.172841042 AU
• Earth
R07 = 0.914003038 AU
R08 = 0.364595061 AU
R09 = 0.158054913 AU
• Mars
R10 = -0.857640398 AU
R11 = 1.257829390 AU
R12 = 0.600085721 AU
• Jupiter
R13 = -0.761270280 AU
R14 = 4.687875714 AU
R15 = 2.027888733 AU
• Saturn
R16 = -7.159708625 AU
R17 = -6.373442832 AU
R18 = -2.324204656 AU
• Uranus
R19 = 19.70413786 AU
R20 = 3.438318953 AU
R21 = 1.227277984 AU
• Neptune
R22 = 26.96190158 AU
R23 = -11.88695432 AU
R24 = -5.536523471 AU
• Pluto
R25 = 6.018040628 AU
R26 = -29.95392978 AU
R27 = -11.16071273 AU
• Moon
R28 = 0.002523645817 AU
R29 = -0.000149978079 AU
R30 = 0.000097355611 AU
• Nutation
R31 = 0°002713386 = Delta Psi = nutation in longitude
R32 = -0°001880743 = Delta Epsilon = nutation in obliquity
Notes:
-The execution time depends on the M-Code version of CdT that you are
using.
-The M-Code CdT may of course be replaced by a focal program "CdT".
-Lines 70 to 81 replace the coordinates of the Earth-Moon-Barycenter by the coordinates of the Earth in registers R07-R08-R09.
-Since the number of coefficients / coordinate may vary, lines 27-29-31-33-35-37-39-41-43-45-49
must be modified if need be.
-Alternatively, these lines may be replaced by GETX if
you store the number of coefficients in the DATA file...
-The coefficients for the nutations give a precision of the order of
E-9 degree
-This is perhaps superfluous: store less constants if a lesser accuracy
is sufficient.
-If you don't want to calculate the nutations, delete lines 47 to 50.
-Other programs may be written that do not call "CdT". Cf "INPOP-HP41
Ephemerides"
2°) Geocentric Rectangular Equatorial Coordinates
-"GEO" replaces the heliocentric coordinates by the geocentric coordinates.
-The coordinates of the Moon and the nutations are unchanged.
-The coordinates of the Sun replace the coordinates of the Earth in
registers R07-R08-R09
Data Registers: R00 is unused R31 , R32 , ...... are undisturbed too.
R01 = XMercury R04 = XVenus
R07 = XSun
R10 = XMars R13 =
XJupiter R16 = XSaturn
R02 = YMercury R05 = YVenus
R08 = YSun
R11 = YMars R14 =
YJupiter R17 = YSaturn
R03 = ZMercury R06 = ZVenus
R09 = ZSun
R12 = ZMars R15 =
ZJupiter R18 = ZSaturn
R19 = XUranus R22 = XNeptune
R25 = XPluto R28 = XMoon
R31 = Delta Psi
R20 = YUranus R23 = YNeptune
R26 = YPluto R29 = YMoon
R32 = Delta Epsilon
R21 = ZUranus R24 = ZNeptune
R27 = ZPluto R30 = ZMoon
Flags: /
Subroutines: /
| 01 LBL "GEO"
02 RCL 09 03 CHS 04 RCL 08 05 CHS 06 RCL 07 07 CHS 08 27 09 SIGN 10 LBL 01 11 R^ 12 ST+ IND L 13 DSE L 14 R^ 15 ST+ IND L 16 DSE L 17 R^ 18 ST+ IND L 19 R^ 20 DSE L 21 GTO 01 22 R^ 23 STO 09 24 R^ 25 STO 08 26 R^ 27 STO 07 28 END |
( 44 bytes )
| STACK | INPUTS | OUTPUTS |
| Z | / | ZSun |
| Y | / | YSun |
| X | / | XSun |
Example: The same one
-After executing "JPL41"
XEQ "GEO" returns in 4 seconds
• Mercury
R01 = -0.914003038 AU
R02 = -0.560317736 AU
R03 = -0.296281973 AU
• Venus
R04 = -0.270784285 AU
R05 = -0.658283057 AU
R06 = -0.330895955 AU
• Sun
R07 = -0.914003038 AU
R08 = -0.364595061 AU
R09 = -0.158054913 AU
• Mars
R10 = -1.771643436 AU
R11 = 0.893234329 AU
R12 = 0.442030808 AU
• Jupiter
R13 = -1.675273318 AU
R14 = 4.323280653 AU
R15 = 1.869833820 AU
• Saturn
R16 = -8.073711663 AU
R17 = -6.738037893 AU
R18 = -2.482259569 AU
• Uranus
R19 = 18.79013482 AU
R20 = 3.073723892 AU
R21 = 1.069223071 AU
• Neptune
R22 = 26.04789854 AU
R23 = -12.25154938 AU
R24 = -5.694578384 AU
• Pluto
R25 = 5.104037590 AU
R26 = -30.31852484 AU
R27 = -11.31876764 AU
• Moon
R28 = 0.002523645817 AU
R29 = -0.000149978079 AU
Registers R28 thru R32 are unchanged.
R30 = 0.000097355611 AU
• Nutation
R31 = 0°002713386 = Delta Psi = nutation in longitude
R32 = -0°001880743 = Delta Epsilon = nutation in obliquity
3°) Data Files
a) 2013/09/25 0h TDB - 2013/10/27 0h TDB
( 329 numbers )
ITEM POINTER Nb of Coeff / coordinate
JDi 0 1 Initial julian day number
Mer 1
to 45
15
Ven 46 to
69
8
EMB 70 to 93
8
We could store directly the coefficients for the Earth, but it would require
about 48 coefficients instead of 24
Mar 94 to 114
7
Jup 115 to 129
5
Sat 130 to 141
4
Ura 142 to 153
4
Nep 154 to 165
4
Plu 166 to 177
4
Moon 178 to 276
33
Nut 277 to 328
26
TOTAL .............................. 329 coeff.
{ 2456560.5 JDi
{ .179751479548
X-Mercury
.238002495041
-5.94174899994E-2
-1.54343346002E-2
-7.523944287E-4
4.75709377188E-5
5.09733482188E-5
1.31645817188E-5
2.33086303125E-6
2.31609125E-7
-2.1983065625E-8
-1.7663459375E-8
-5.153965625E-9
-9.8403125E-10
-1.04028125E-10
} {
-.239877657003
Y-Mercury
.235533812089
6.53267651281E-2
-5.75018911253E-3
-1.78920628241E-3
-3.10478724156E-4
-4.1182526875E-5
-6.7617521875E-7
1.23477825E-6
4.5195521875E-7
9.80275E-8
1.379265625E-8
3.1490625E-10
-.000000000531
-2.033125E-10
} {
-.146774026921
Z-Mercury
.101143189281
4.10565478297E-2
-1.47149972653E-3
-8.77761503875E-4
-1.70784820906E-4
-2.72836111563E-5
-1.7259825625E-6
4.1795615625E-7
2.174120625E-7
5.464178125E-8
9.19878125E-9
7.0290625E-10
-1.8190625E-10
-9.765625E-11
} {
.551890253781
X-Venus
.188402990139
-2.80032593757E-2
-1.56871791206E-3
1.12389408844E-4
3.7168556875E-6
-1.54592875E-7
-3.40125E-9
} {
-.367803299742
Y-Venus
.232927266721
1.86571931099E-2
-1.92427228591E-3
-7.61460672813E-5
4.41157740625E-6
1.1296140625E-7
-3.35921875E-9
} {
-.200408421492
Z-Venus
9.28786064188E-2
1.01664358896E-2
-7.66517468125E-4
-4.1372163375E-5
1.7497083125E-6
6.06021875E-8
-1.298875E-9
} {
.933343467358
X-Earth-Moon-Barycenter
-8.72274025638E-2
-1.79881360741E-2
2.3708066225E-4
2.95727235625E-5
-6.990871875E-8
-2.071325E-8
-.000000000195
} {
.272460686567
Y-Earth-Moon-Barycenter
.237417373036
-5.26262036581E-3
-7.68628772997E-4
5.79256678125E-6
7.80250328125E-7
3.1308875E-9
-4.57846875E-10
} {
.11811510209
Z-Earth-Moon-Barycenter
.102924429084
-2.28140860717E-3
-3.33213569081E-4
2.51108352188E-6
3.382378875E-7
1.347709375E-9
-1.92359375E-10
} {
-.785994699761
X-Mars
-.187092030901
3.43347363122E-3
1.2285765875E-4
-1.70951040625E-6
4.89709375E-9
.000000000125
} {
1.28436521026
Y-Mars
-8.27889774397E-2
-5.61643843406E-3
8.196485375E-5
1.1533228125E-6
-2.08990625E-8
4.328125E-10
} {
.610322452608
Z-Mars
-3.29213474656E-2
-2.66882967363E-3
3.42786159375E-5
5.75157625E-7
-.000000009724
1.9446875E-10
} {
-.716500010856
X-Jupiter
-.121129472595
9.86440471875E-5
2.720666375E-6
-3.25490625E-9
} {
4.69154939158
Y-Jupiter
-1.12295918094E-2
-6.46612192188E-4
6.178809375E-7
6.660625E-9
} {
2.02837341592
Z-Jupiter
-.001864344855
-2.79554385313E-4
1.98759375E-7
2.894375E-9
} {
-7.18033747881
X-Saturn
5.61848654056E-2
1.41828729688E-4
-2.148565625E-7
9.0625E-11
} {
-6.35141336008
Y-Saturn
-5.94546550372E-2
1.24950784063E-4
1.64874375E-7
-6.915625E-10
} {
-2.3142164482
Z-Saturn
-2.69788551825E-2
4.54975784375E-5
7.7343125E-8
-3.325E-10
} {
19.7085035008
X-Uranus
-.011922744925
-4.6426484375E-5
4.09375E-10
} {
3.41841417173
Y-Uranus
5.39263979313E-2
-8.5884328125E-6
-2.87309375E-8
} {
1.21849805041
Z-Uranus
2.37881222331E-2
-3.0972046875E-6
-1.232875E-8
} {
26.9539324409
X-Neptune
2.15595445031E-2
-1.8959990625E-5
-5.715625E-9
} {
-11.9025392083
Y-Neptune
4.22515962656E-2
.00000783285
-1.2215625E-8
} {
-5.54270385205
Z-Neptune
1.67565080478E-2
3.670349375E-6
-4.8559375E-9
} {
5.99950255503
X-Pluto
5.02329867572E-2
-.000003307155
-7.2534375E-9
} {
-29.9557510877
Y-Pluto
4.96735674688E-3
1.596648125E-5
-1.011875E-8
} {
-11.1556846264
Z-Pluto
-1.36148406625E-2
5.918328125E-6
-2.53125E-9
} {
-1.3156465488E-4
X-Moon
3.33652655738E-4
-2.14603267447E-4
-2.03634942343E-3
1.1264699147E-4
5.29208254463E-4
-1.50009831553E-5
-7.69700348294E-5
1.21671845569E-6
1.07624971516E-5
-4.34407668656E-7
-1.14446519481E-6
2.1426405525E-7
-4.25944828125E-9
-7.76082614375E-8
4.44431629063E-8
2.23079301875E-8
-1.59326446563E-8
-5.125934625E-9
4.03072128125E-9
8.707951875E-10
-8.2481584375E-10
-6.36326875E-11
1.359770625E-10
-2.62295625E-11
-1.518390625E-11
1.546715625E-11
-4.0525E-13
-5.1728125E-12
9.124375E-13
1.31909375E-12
-3.5953125E-13
-2.570625E-13
} {
1.1131674568E-3
Y-Moon
2.12497261925E-5
2.08159935133E-3
-1.36638800441E-4
-1.13285932698E-3
3.16348180422E-5
1.96353394453E-4
-2.28175798281E-6
-2.74336803869E-5
3.587061775E-7
3.5697754825E-6
-2.79186710938E-7
-2.42751895E-7
1.2599241625E-7
-4.7987536875E-8
-4.12258753125E-8
2.6405418125E-8
1.071090875E-8
-7.7120678125E-9
-2.1714540625E-9
1.7500890625E-9
2.892575E-10
-3.254571875E-10
7.6103125E-12
4.6793125E-11
-2.12028125E-11
-3.305E-12
8.813125E-12
-9.246875E-13
-2.5540625E-12
5.521875E-13
5.76875E-13
-1.88125E-13
} {
3.81906578538E-4
Z-Moon
2.48646126099E-5
7.15360958653E-4
-1.68864944301E-4
-3.89574069084E-4
4.28636953184E-5
6.77467904631E-5
-5.43371326356E-6
-9.51637382141E-6
7.72988401438E-7
1.22220325669E-6
-1.66829910375E-7
-7.20809226875E-8
4.3939058625E-8
-2.14208934375E-8
-1.17779345625E-8
1.05686796875E-8
2.7946208125E-9
-3.004096125E-9
-5.1818821875E-10
6.6435275E-10
5.17014375E-11
-1.1769953125E-10
1.083521875E-11
1.481359375E-11
-8.333375E-12
-2.339375E-13
3.059E-12
-6.330625E-13
-8.39625E-13
2.7253125E-13
1.804375E-13
-8.090625E-14
} {
2.80239399488E-3
Delta Psi
-2.06921154065E-4
2.69483660997E-5
1.45704774128E-5
1.02400882469E-6
3.09099637547E-5
-1.20972671634E-5
-2.81386878256E-5
6.35544468188E-6
1.17316565831E-5
-1.97209069063E-6
-3.61248048906E-6
5.3252706875E-7
8.65516184375E-7
-1.45176074375E-7
-1.47775077188E-7
3.95914771875E-8
9.8647053125E-9
-9.7355134375E-9
6.021916875E-9
2.2123234375E-9
-4.0898915625E-9
-6.093096875E-10
1.7332734375E-9
2.3261E-10
-5.380234375E-10
} {
-1.88893737981E-3
Delta Epsilon
-7.23612696934E-5
-2.10407741734E-5
5.22656437469E-6
-2.26074837719E-6
4.29809041E-6
1.42157548706E-5
-4.25558851625E-6
-7.97854814E-6
1.61236965625E-6
2.7789035525E-6
-4.7024077875E-7
-7.5590999875E-7
1.26555708125E-7
1.59171094375E-7
-2.6821469375E-8
-2.407458125E-8
2.577239375E-9
1.771793125E-9
7.63733125E-10
2.961453125E-10
-4.51578125E-10
-1.235859375E-10
1.243771875E-10
2.3363125E-11
-2.9325E-11
} }
b) 2013/10/27 0h TDB - 2013/11/28 0h TDB
( 350 numbers )
ITEM POINTER Nb of Coeff / coordinate
JDi 0 1 Initial julian day number
Mer 1
to 60
20
Ven 61 to
87
9
EMB 88 to 111
8
Mar 112 to 129
6
Jup 130 to 144
5
Sat 145 to 159
5
Ura 160 to 174
5
Nep 175 to 186
4
Plu 187 to 198
4
Moon 199 to 297
33
Nut 298 to 349
26
TOTAL .............................. 350 coeff.
{ 2456592.5 JDi
{ -4.13719401071E-2
X-Mercury
-.402329510424
2.07502535124E-2
3.83626225508E-2
-3.69884366068E-3
-2.31375753334E-3
4.9731027088E-4
1.4713422986E-4
-6.040991576E-5
-7.98888004E-6
6.94669784E-6
9.080938E-8
-.000000756818
7.302814E-8
7.68581E-8
-1.690896E-8
-7.00132E-9
2.77392E-9
5.1534E-10
-3.9102E-10 }
{ .130144888616
Y-Mercury
-.051651679923
-.127572416169
1.00514876295E-2
8.19833955274E-3
-1.33679719851E-3
-4.97693564494E-4
1.62031436858E-4
2.915074994E-5
-1.8681067936E-5
-9.7383456E-7
2.056367012E-6
-1.18378088E-7
-2.13232904E-7
3.6871606E-8
2.0217964E-8
-6.538386E-9
-1.632108E-9
9.60632E-10
8.5786E-11 }
{ 7.38103719183E-2
Z-Mercury
1.41198059961E-2
-7.02982797546E-2
1.39211124605E-3
4.76288962434E-3
-4.74216972926E-4
-3.17417781828E-4
7.1300383677E-5
2.18347966658E-5
-9.150866448E-6
-1.2404005768E-6
1.0890617628E-6
1.52269502E-8
-1.214766078E-7
1.17279468E-8
1.25529582E-8
-2.7667766E-9
-1.1594338E-9
4.596964E-10
8.63544E-11 }
{ .669444399042
X-Venus
-7.61633922978E-2
-3.43213756646E-2
5.9257741988E-4
1.4261697266E-4
-9.8596938E-7
-2.275179E-7
-1.11824E-9
1.4504E-10 }
{ .164482789722
Y-Venus
.276595013176
-8.45281332962E-3
-2.3257528226E-3
3.02867528E-5
.000005729395
-1.660742E-8
-6.16738E-9
-9.586E-11 }
{ 3.16435646927E-2
Z-Venus
.129267590904
-1.63132638945E-3
-1.08392119414E-3
4.602219172E-6
2.64020446E-6
6.912326E-9
-2.702766E-9
-5.1658E-11 }
{ .629483393734
X-Earth-Moon-Barycenter
-.212001374082
-1.24435996282E-2
6.7004454182E-4
2.277212704E-5
-6.180918E-7
-2.235098E-8
2.3246E-10 }
{ .67788337174
Y-Earth-Moon-Barycenter
.161187498617
-1.34144906276E-2
-5.5167690516E-4
2.102046176E-5
6.8238478E-7
-1.219548E-8
-6.817E-10 }
{ .293872842531
Z-Earth-Moon-Barycenter
6.98776628024E-2
-.005815395266
-2.3916299276E-4
9.11286848E-6
2.9584502E-7
-5.29356E-9
-2.899E-10 }
{ -1.12836524699
X-Mars
-.154183913492
4.7472084398E-3
9.637136556E-5
-.00000160274
4.66942E-9 }
{ 1.07717317633
Y-Mars
-.123500637485
-4.5341451338E-3
.00009762259
8.337638E-7
-.000000011995 }
{ .524533419619
Z-Mars
-5.24833211144E-2
-2.20787746998E-3
4.217511284E-5
4.2584224E-7
-5.61548E-9 }
{ -.957866968785
X-Jupiter
-.120210499367
1.3102869086E-4
2.67770594E-6
-4.00716E-9 }
{ 4.66394205676
Y-Jupiter
-1.63710295734E-2
-.000638551032
7.317394E-7
8.3242E-9 }
{ 2.02241638628
Z-Jupiter
-4.0904686842E-3
-2.768925122E-4
2.479818E-7
.000000003843 }
{ -7.06684117538
X-Saturn
5.73093443456E-2
1.393185122E-4
-.000000201783
-3.502E-10 }
{ -6.4693169275
Y-Saturn
-.05844730913
1.268803356E-4
.000000163515
1.2684E-9 }
{ -2.36780730977
Z-Saturn
-2.66112593148E-2
4.63968338E-5
7.59328E-8
7.438E-10 }
{ 19.6842867524
X-Uranus
-.012293931528
-.000046338452
.00000001602
-2.08E-10 }
{ 3.5261970846
Y-Uranus
.053856200891
-8.9596098E-6
-2.63006E-8
1.5022E-9 }
{ 1.26604899517
Z-Uranus
.023762680122
-3.2653488E-6
-1.22894E-8
8.352E-10 }
{ 26.9968997657
X-Neptune
.021407790064
-.00001894678
.000000009668 }
{ -11.8179739017
Y-Neptune
.042313561118
.00000765954
-.000000009796 }
{ -5.50916171096
Z-Neptune
.016785565323
3.5919602E-6
-4.8152E-9 }
{ 6.0999419324
X-Pluto
5.02063851924E-2
-.000003311532
8.2442E-9 }
{ -29.9456891114
Y-Pluto
.005094490542
.0000158181
-.000000007846 }
{ -11.1828671109
Z-Pluto
-.013567688568
.000005867648
-.000000002536 }
{ -9.48576768669E-4
X-Moon
1.07583803649E-4
-2.02234139812E-3
-8.22355429964E-4
1.1022997711E-3
1.67783268831E-4
-1.91614176033E-4
2.891776958E-6
2.51486146716E-5
-6.0994068582E-6
-1.9889413738E-6
1.490577219E-6
-3.778901424E-7
-1.79002694E-7
1.991004288E-7
-2.45349144E-8
-4.51913654E-8
2.00932742E-8
4.6169848E-9
-5.9466838E-9
9.56019E-10
9.768674E-10
-6.029772E-10
5.9424E-12
1.543002E-10
-6.3641E-11
-1.70126E-11
2.32638E-11
-3.9948E-12
-4.5362E-12
2.6652E-12
1.624E-13
-7.37E-13 }
{ 5.98881701429E-4
Y-Moon
3.00504570512E-4
8.99589628104E-4
-1.76636500824E-3
-4.59274075958E-4
4.60781116328E-4
3.97582156076E-5
-6.66676397236E-5
7.6352158418E-6
7.8385524982E-6
-3.0392048334E-6
-5.9228828E-8
5.613868724E-7
-3.052082792E-7
-2.38862226E-8
9.68207798E-8
-2.57969784E-8
-1.6342546E-8
1.10110454E-8
2.651526E-10
-2.5073064E-9
8.460524E-10
2.522714E-10
-3.118014E-10
6.30794E-11
5.81856E-11
-3.94402E-11
-8.45E-13
1.0617E-11
-3.611E-12
-1.3798E-12
1.4282E-12
-1.874E-13 }
{ 1.53368421931E-4
Z-Moon
1.12844335069E-4
1.94311998352E-4
-6.65575225206E-4
-9.50059395288E-5
1.7060749348E-4
2.46493786172E-6
-2.30637054238E-5
4.16330557676E-6
2.36975989162E-6
-1.17853499034E-6
6.844244942E-8
1.7334732372E-7
-1.172003117E-7
3.51869022E-9
3.23264753E-8
-1.169086106E-8
-4.5062538E-9
4.1164673E-9
-2.6158826E-10
-8.1781562E-10
3.5339254E-10
5.209594E-11
-1.0844568E-10
3.120196E-11
1.651384E-11
-1.47757E-11
1.0899E-12
3.467E-12
-1.5301E-12
-3.2258E-13
5.0806E-13
-1.0928E-13 }
{ 2.55766377485E-3
Delta Psi
-2.41041206074E-5
3.68854541146E-5
-2.41199649716E-5
9.1848563876E-6
-2.26925180992E-5
-2.49820664336E-5
2.40466219986E-5
9.7749471116E-6
-1.10020933828E-5
-8.196098128E-7
3.4908785236E-6
-6.90548504E-7
-6.718978142E-7
4.083266948E-7
-8.9015186E-9
-1.21883766E-7
5.82161578E-8
1.4300885E-8
-2.0408362E-8
6.947568E-9
2.4656468E-9
-5.4095146E-9
7.64703E-10
2.1610434E-9
-4.413952E-10 }
{ -2.07105208935E-3
Delta Epsilon
-1.07070648075E-4
1.13904131638E-5
9.3462043886E-6
1.946283136E-6
8.6235780614E-6
-1.18489163356E-5
-7.301664342E-6
7.14228512E-6
1.5747263852E-6
-2.6615403474E-6
1.78513744E-7
6.657531816E-7
-2.391254166E-7
-8.0641669E-8
8.95339638E-8
-1.51577284E-8
-1.86545288E-8
1.25193608E-8
1.7008278E-9
-4.544187E-9
2.485128E-10
1.185694E-9
-9.68624E-11
-2.45732E-10
2.94978E-11
} }
Reference:
[1] ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii
-The JPL ephemerides DE430/LE430 are valid from 1550
Jan 01 to 2650 Jan 22
-Of course, you can also use DE431/LE431 which are valid from 13201
B.C. to 17191 A.D. (!)