*Astron. Astrophys. 354, 328-333 (2000)*
## Numerical integration of satellite orbits around an oblate planet
**
K.G. Hadjifotinou
**
Department of Mathematics, University of Thessaloniki, 540 06 Greece (khad@math.auth.gr)
*Received 22 September 1999 / Accepted 23 November 1999*
**Abstract**
A recurrent power series (RPS) method is constructed for the
numerical integration of the equations of motion of a planet and its
*N* satellites. The planet is considered as an oblate spheroid
with the oblateness potential calculated up to the factor
. The efficiency of the RPS method in
terms of accuracy and speed is compared to that of the commonly used
-order Gauss-Jackson backward
difference method (GJ). All tests are applied to the Saturnian
satellite system and cover the cases of one up to four satellites. For
each test problem we find the optimal values for the user-specified
tolerance and step-size of both methods and use these values for a
12000 days integration. The comparison of the results obtained by both
methods shows that the RPS method is up to 30 times more accurate than
the GJ. Furthermore, the good properties of the RPS method discussed
in Hadjifotinou & Gousidou-Koutita (1998) (such as the use of very
large step-sizes) are still preserved, although the system of
equations and the auxiliary variables needed for the construction of
the RPS method are now much more complicated.
**Key words:** methods:
numerical
celestial mechanics, stellar
dynamics
ephemerides
planets and satellites: general
This article contains no SIMBAD objects.
### Contents
© European Southern Observatory (ESO) 2000
Online publication: January 31, 2000
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