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