------------------- PLUTO TABLES (1995) ------------------- J. Chapront, G. Francou Bureau des Longitudes - France Group : Dynamics of Solar System December 1996 Authors' Address : Bureau des Longitudes 77, avenue Denfert Rochereau F75014 Paris France Tel : (33) (1) 40.51.22.60 Fax : (33) (1) 46.33.28.34 E-mail : francou@bdl.fr Summary : 1. PRESENTATION 2. FORMULAE 3. SERIES TABLES 4. PRECISION AND TEST-VALUES --------------- 1. PRESENTATION --------------- The tables of Pluto have been constructed by J. Chapront (BDL) with a new method of approximation using frequency analysis as described in the paper : Representation of planetary ephemerides by frequency analysis. Application to the five outer planets. Astron. & Astrophys.Suppl. Ser., 109, 191 (1995). This representation uses the result of numerical integration DE200 of Jet Propulsion Laboratory as a source : Standish E. M., 1990, The observational basis for JPL'DE200, the planetary ephemerides of the Astronomical Almanac. Astron. Astrophys., 233, 252. The interval of validity is 146120 days. Start : Jan 01 1700 0h JD2341972.5 End : Jan 24 2100 0h JD2488092.5 The tables contain series which represent the heliocentric rectangular coordinates of Pluto as functions of time. The reference frame is defined with dynamical equinox and equator J2000 (DE200). The time scale is Barycentric Dynamical Time (TDB). ----------- 2. FORMULAE ----------- The heliocentric rectangular coordinates X, Y, Z of Pluto (mean equinox and equator J2000) for a julian date JD are computed by the formulae : X, Y, Z = A(0) + A(1)*x + A(2)*x**2 + A(3)*x**3 (1) + SUM(n=1,82) C(n)*cos(FQ(n)*Fx) + S(n)*sin(FQ(n)*Fx) (2) + x * ( SUM(n=83,101) C(n)*cos(FQ(n)*Fx) + S(n)*sin(FQ(n)*Fx) ) (3) + x**2 * ( SUM(n=102,106) C(n)*cos(FQ(n)*Fx) + S(n)*sin(FQ(n)*Fx) ) (4) with the variables : x = 2*(DJ-2341972.5)/146120 - 1 Fx = x*73060 In these formulae, the multiplication is denoted by an asterisk (*) and the power function by two asterisks (**). Line (1) refers to secular terms. Line (2) refers to periodic terms. Line (3) refers to Poisson terms (order 1). Line (4) refers to Poisson terms (ordre 2). Frequencies FQ are expressed in radian per day. Coefficients A, C et S are expressed in 1.E10 au. The frequencies FQ(n=1,106) are the same for the 3 rectangular coordinates. The coefficients of secular series A(i=0,3) are given in the tables AX, AY, AZ. The coefficients of Cosine and Sine of periodic series and Poisson series C(n=1,106) et S(n=1,106) are given in the tables CX, SX, CY, SY, CZ, SZ. Warning ! in the tables given hereunder the coefficients of Cosine and Sine are reversed for the Poisson series of order 1. The Fortran subroutine PLUTO (in file pluto.sub) uses this formulae for computing the positions of Pluto. By derivation one can also compute the velocities (au/day). --------- 3. TABLES --------- TABLE FQ : Frequencies. Coordinates X, Y, Z (radian/day) -------------------------------------------------------- Periodic Terms. n FQ 001 0.0000645003954767 002 0.0001083248054773 003 0.0001302772403167 004 0.0001647868659960 005 0.0001935009111902 006 0.0002223740247147 007 0.0003032575201026 008 0.0003259246239385 009 0.0003564763034914 010 0.0004265811293132 011 0.0004503959517513 012 0.0004638675148284 013 0.0005009272733421 014 0.0005163593863414 015 0.0005578826828210 016 0.0005882795362847 017 0.0006450023602974 018 0.0007097635821639 019 0.0007630643253588 020 0.0007740033551209 021 0.0008385031396726 022 0.0008950591609720 023 0.0009545118163938 024 0.0010255417569600 025 0.0010826728325744 026 0.0011680358909203 027 0.0012405125052369 028 0.0012931805883876 029 0.0013460706181008 030 0.0014190059530383 031 0.0014394705053002 032 0.0014502634075377 033 0.0014992014575181 034 0.0015434430430867 035 0.0016000710611098 036 0.0016562809940875 037 0.0017275924266291 038 0.0017454042542465 039 0.0018215079641428 040 0.0018694826929211 041 0.0019274630193251 042 0.0020276790928706 043 0.0021822818660433 044 0.0022885289854970 045 0.0023167646379420 046 0.0023445464874575 047 0.0024069306189938 048 0.0024473146628449 049 0.0024778027974419 050 0.0025244208011161 051 0.0025682157855485 052 0.0026028617439482 053 0.0026544444009919 054 0.0026987455959123 055 0.0027308225916697 056 0.0027735113723168 057 0.0028728385464030 058 0.0029001725379479 059 0.0029379670182566 060 0.0029750359447782 061 0.0031326820696785 062 0.0031822107498712 063 0.0031931048857857 064 0.0032268922327691 065 0.0034657232066225 066 0.0037838581645670 067 0.0038055149432355 068 0.0038631344783149 069 0.0039129259467328 070 0.0040311445462510 071 0.0040607542008930 072 0.0041490103414206 073 0.0043500678052272 074 0.0046321937641054 075 0.0058000376725240 076 0.0091460971544658 077 0.0091560629947357 078 0.0172021239411871 079 0.0182919855069063 080 0.0279624510118796 081 0.0344040996177640 082 0.0714245719830324 Poisson Terms Order 1 n FQ 083 0.0001083248054773 084 0.0001647868659960 085 0.0003032575201026 086 0.0003259246239385 087 0.0003564763034914 088 0.0005009272733421 089 0.0005882795362847 090 0.0007097635821639 091 0.0007630643253588 092 0.0008950591609720 093 0.0011680358909203 094 0.0014502634075377 095 0.0017454042542465 096 0.0029001725379479 097 0.0031822107498712 098 0.0040607542008930 099 0.0043500678052272 100 0.0091460971544658 101 0.0279624510118796 Poisson Terms Order 2 n FQ 102 0.0001083248054773 103 0.0003032575201026 104 0.0011680358909203 105 0.0043500678052272 106 0.0279624510118796 TABLE AX : Secular Terms. Coordinate X (1.E10 au) ------------------------------------------------- i AX 0 98083308510. 1 -1465718392. 2 11528487809. 3 55397965917. TABLE AY : Secular Terms. Coordinate Y (1.E10 au) ------------------------------------------------- i AY 0 101846243715. 1 57789. 2 -5487929294. 3 8520205290. TABLE AZ : Secular Terms. Coordinate Z (1.E10 au) ------------------------------------------------- i AZ 0 2183700004. 1 433209785. 2 -4911803413. 3 -14029741184. TABLES CX ET SX : Periodic and Poisson Terms. Coordinate X (1.E10 ua) --------------------------------------------------------------------- Periodic Terms n CX SX 001 -16338582222. -308294137468. 002 -5995086437. -68820910480. 003 23663880362. 28346466257. 004 10304632056. -1755658975. 005 -3996936944. 7818660837. 006 -4136465568. -1098895702. 007 1188702881. -1192462299. 008 -621434363. -772129982. 009 566898160. 1061702581. 010 -75880391. -639572722. 011 576146406. 1128327488. 012 -659684298. -423570428. 013 451962774. -175317704. 014 -153724334. 251601606. 015 -603163280. -869448807. 016 364764379. 551228298. 017 193062130. 87807522. 018 161493959. -11540541. 019 1167349082. -103236703. 020 -1417467887. 92638954. 021 15325240. -3624991. 022 -3624391. 1004975. 023 -587306. 304396. 024 132022. -56532. 025 -106501. 55554. 026 228373. -799096. 027 -95106. 56947. 028 56299. -48016. 029 -48339. 50599. 030 803937. -680660. 031 -6172744. 5858452. 032 -18962749. 38125648. 033 133022. -109460. 034 -25964. 18684. 035 7111. -5269. 036 -4998. 2771. 037 32034. -6814. 038 -29666. 47130. 039 -1983. 1192. 040 114. -1387. 041 191. 379. 042 -1063. -612. 043 419. -52. 044 346. 813. 045 5059. -4354. 046 -81. -2275. 047 1408. 685. 048 2964. -1352. 049 -5364. 4681. 050 1509. -1908. 051 -4924. -6530. 052 2954. 8667. 053 2034. 1675. 054 -5199. 874. 055 604. 898. 056 -1247. 965. 057 4576. -7124. 058 -350741. -1145389. 059 -4023. 2931. 060 1147. -618. 061 -38. -34. 062 -99. -6562. 063 -11686. 8038. 064 1129. -697. 065 582. -8. 066 -83. 12. 067 -97. -267. 068 431. -131. 069 -134. 304. 070 -323. -756. 071 -292. -103. 072 195. -250. 073 39068. 19816. 074 523. -596. 075 -1747. 576. 076 3135. 4122. 077 -619. 65. 078 -12095. -27900. 079 6. 217. 080 18476. -137. 081 -130. -269. 082 -438. 531. Poisson Terms Order 1 n SX CX 083 -24338350765. 102345278799. 084 11210995713. -9329130892. 085 2793567155. 1484339404. 086 -776019789. 472660593. 087 1528323591. -581239444. 088 -249354416. 1016663241. 089 1127608109. -1054199614. 090 -667692329. 99039105. 091 -1570766679. -52190030. 092 -9724425. -3394173. 093 26552. -16529. 094 3332520. 3102430. 095 -27607. 2286. 096 -11696. -10955. 097 -7297. -5293. 098 -104. -654. 099 -184. 124. 100 -455. -85. 101 -16. 29. Poisson Terms Order 2 n CX SX 102 418209651. 39813894679. 103 -1191875710. 3633087275. 104 -823081. 522728. 105 -558. -320. 106 -1091. -1401. TABLES CY ET SY : Periodic and Poisson Terms. Coordinate Y (1.E10 ua) --------------------------------------------------------------------- Periodic Terms n CY SY 001 299584895562. -53545027809. 002 75951634908. -8838029861. 003 -36135662843. 23553788174. 004 18125610071. 13775798112. 005 -20398008415. -6068121593. 006 6125780503. -2853107588. 007 -162559485. 750355551. 008 4352425804. -82067770. 009 -3819676998. 230091832. 010 1168107376. -259838942. 011 -5041323701. 197944074. 012 4093828501. 27141006. 013 -1727274544. -105334544. 014 134214260. 95175918. 015 5033950069. -139461973. 016 -3071449401. 80593104. 017 -1190419055. -5126842. 018 -775881742. -21953793. 019 -5524713888. -163767784. 020 6803228005. 192436228. 021 -65675611. -2479113. 022 15155413. 561687. 023 2009509. 121909. 024 -389682. -30275. 025 275571. 16333. 026 474366. 68105. 027 132163. 24081. 028 -81550. -11228. 029 69996. 667. 030 -706470. -73047. 031 4777898. 1007089. 032 -44002785. -22814549. 033 -58735. 434. 034 7624. 1013. 035 -1922. 710. 036 -729. 1100. 037 -1733. -4598. 038 -35642. 1990. 039 -586. 564. 040 -258. 828. 041 -368. -1119. 042 1286. -1249. 043 -136. -597. 044 883. 227. 045 2673. 5467. 046 331. 801. 047 50. -2029. 048 178. -1892. 049 2901. 4713. 050 -654. -459. 051 -8972. 1757. 052 3034. -9303. 053 1113. -2357. 054 570. 7679. 055 -72. -2953. 056 1950. 629. 057 8550. 5011. 058 1047593. -333905. 059 -2348. -2388. 060 313. 415. 061 432. 139. 062 6765. -5726. 063 -8240. -4583. 064 335. 310. 065 140. 681. 066 -833. -107. 067 252. 301. 068 -210. -525. 069 366. 198. 070 -920. -379. 071 1215. -230. 072 -217. -64. 073 -17780. 36069. 074 581. 459. 075 -560. -1596. 076 -4131. 2509. 077 390. -146. 078 25613. -11081. 079 -206. 4. 080 1850. 15764. 081 171. -147. 082 -471. -362. Poisson Terms Order 1 n SY CY 083 117449924600. 26437625772. 084 -7691661502. -12674907683. 085 -4771148239. -1067899665. 086 3733883366. -2082744. 087 -7081845126. -43195632. 088 3502526523. 211912497. 089 -8115570206. -108307161. 090 3607883959. -63033809. 091 7690328772. -203850703. 092 37384011. -1672332. 093 -164319. 7136. 094 -2859257. 803655. 095 1593. -10985. 096 -11997. 9126. 097 -6476. 3317. 098 1419. -151. 099 34. 160. 100 232. 138. 101 32. -27. Poisson Terms Order 2 n CY SY 102 -36463065062. 2752753498. 103 -5816560445. -672124207. 104 1576292. 154239. 105 -21. -400. 106 -295. 372. TABLES CZ ET SZ : Periodic and Poisson Terms. Coordinate Z (1.E10 ua) --------------------------------------------------------------------- Periodic Terms n CZ SZ 001 98425296138. 76159403805. 002 25475793908. 17987340882. 003 -18424386574. -1193982379. 004 2645968636. 4828308190. 005 -5282207967. -4248985438. 006 3278235471. -559147671. 007 -425422632. 593594960. 008 1526641086. 208799497. 009 -1323182752. -249913200. 010 235873266. 115051024. 011 -1617466723. -282588988. 012 1557465867. 135883560. 013 -848586296. 23091693. 014 218182986. -49187976. 015 1636044515. 223956575. 016 -1001334243. -137344299. 017 -455739370. -28188872. 018 -348173978. -2636274. 019 -2511254281. -14202661. 020 3062521470. 25488216. 021 -32079379. 419837. 022 7597939. -150966. 023 1138566. -64906. 024 -238849. 3719. 025 192377. -2226. 026 83169. 86321. 027 148694. -15970. 028 -92489. 16609. 029 87116. -15782. 030 -1281070. 200300. 031 9950106. -1500491. 032 -25105642. -9161491. 033 -171749. 37481. 034 31035. -4616. 035 -8648. 224. 036 5360. -1027. 037 -30345. 5220. 038 11482. -6976. 039 1322. -267. 040 -467. 556. 041 96. -23. 042 894. -711. 043 -381. -122. 045 -583. -97. 046 2525. 2440. 047 -569. 786. 048 226. -806. 049 -2039. -167. 050 3728. -156. 051 -1540. 572. 052 42. 2532. 053 -3144. -4582. 054 658. -1178. 055 220. 875. 056 1848. -558. 057 678. 781. 058 -7289. 3230. 059 463291. -116132. 060 3945. -1440. 061 -1141. 438. 062 -26. 176. 063 -10607. 1072. 064 11458. -5850. 064 -1005. 418. 065 120. 267. 066 -301. 60. 067 135. 134. 068 -186. -85. 069 118. -59. 070 30. 112. 071 197. -168. 072 -182. -89. 073 -8585. 14986. 074 240. 190. 075 -226. -685. 076 -2049. 1018. 077 283. -48. 078 11109. -4807. 079 -100. 0. 080 -842. 7066. 081 71. -54. 082 -181. -229. Poisson Terms Order 1 n SZ CZ 083 44126663549. -22591501373. 084 -5626220823. -1138977908. 085 -2536450838. -782718600. 086 1536292657. -141483824. 087 -2916144530. 159033355. 088 949074586. -246222739. 089 -2842935040. 287284767. 090 1500396857. -48002332. 091 3415136438. -41114335. 092 19702076. 578004. 093 -46995. -8420. 094 -5801645. -766779. 095 33470. 957. 096 17674. 5780. 097 7355. 4141. 098 199. 417. 099 11. -8. 100 205. 65. 101 33. -22. Poisson Terms Order 2 n CZ SZ 102 -11656050047. -11127973411. 103 -1186276469. -1310869292. 104 1388681. -164753. 105 201. -107. 106 561. 284. ---------------------------- 4. PRECISION AND TEST-VALUES ---------------------------- Hereunder, we give 5 test-values computed with the subroutine pluto.sub. In this output the number of decimals is intentionally superabundant for checking the use of this subroutine. The numerical accuracy can be evaluated with the largest discrepancy obtained in a comparison with the ephemerides DE200 on the period 1700-2100 : for the positions : 5 E-7 au (0.003"), for the velocities : 6 E-9 au/d. PLUTO Heliocentric Rectangular Coordinates (mean equinox and equator J2000) Date: Jan 01 1700 H : 00h 00m 00s (TDB) JD: 2341972.5000000 X :-25.48366603086599 Y : 22.25190224179014 Z : 14.61666566142614 au X': -0.00140296544832 Y': -0.00253543942176 Z': -0.00036577359317 au/d Date: Jan 02 1800 H : 06h 00m 00s (TDB) JD: 2378497.7500000 X : 36.33316699469712 Y :-11.84871881208418 Z :-14.64079073464049 au X': 0.00151098228705 Y': 0.00214812030172 Z': 0.00021249511616 au/d Date: Jan 03 1900 H : 12h 00m 00s (TDB) JD: 2415023.0000000 X : 10.29158303131287 Y : 44.52906466047693 Z : 10.79081191605171 au X': -0.00216104614307 Y': -0.00004877516272 Z': 0.00063748726618 au/d Date: Jan 04 2000 H : 18h 00m 00s (TDB) JD: 2451548.2500000 X : -9.86615874601937 Y :-27.98285304568784 Z : -5.75779357947923 au X': 0.00302900782509 Y': -0.00112671144850 Z': -0.00126494662037 au/d Date: Jan 05 2100 H : 00h 00m 00s (TDB) JD: 2488073.5000000 X : 39.67448463874504 Y : 28.47968765660414 Z : -3.06796133066342 au X': -0.00097971861494 Y': 0.00171018575529 Z': 0.00082844820875 au/d