J/A+AS/110/411 Orbit determination f & g power series (Bem+, 1995)
High order f and g power series for orbit determination.
BEM J., SZCZODROWSKA-KOZAR B.
<Astron. Astrophys. Suppl. Ser. 110, 411 (1995)>
=1995A&AS..110..411B 1995A&AS..110..411B (SIMBAD/NED Reference)
Keywords: celestial mechanics - numerical methods - solar system
Description:
The table of coefficients and exponents of the power series f and g up
to derivatives of the 20-th order is the main achievement of this paper.
The accuracy of the calculation of orbits has been tested by tracing the
motion of all planets of the solar system.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table2 41 715 Coefficients and exponents
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Byte-by-byte Description of file: table2
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Bytes Format Units Label Explanations
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1- 3 I3 -- n Order of derivative
5- 7 I3 --- L+L' Number of terms belonging to the derivative
10- 31 E22.2 --- R" Coefficient R" in next L+L' lines (1)
33- 34 I2 --- i Exponent i of each term (1)
36- 37 I2 --- j Exponent j of each term (1)
39 I1 --- k Exponent k of each term (1)
41 I1 --- fg [1-2] Term of the serie, 1 for f, 2 for g
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Note (1):
To solve the Newtonian equation, d2r/dt2=-ur, in Taylor's series
form r={sum(n≥0)}[d0r/dt0(taun/n!)], and after introducing
Lagrangian variables u, p and q; the successive terms of Taylor's series
of order n take the form:
taun[r0{sum(1,L)}(RL.ui.pj.qk)
+ dr0/dt{sum(1,L')}(RL'.ui.pj.qk)]/n! (5)
R are integers numbers, R'=R/n! and R"=R'/(n+1)
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(End) Patricia Bauer [CDS] 12-Dec-1994