Numerical integration of satellite orbits around an oblate planet

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 J4. The efficiency of the RPS method in terms of accuracy and speed is compared to that of the commonly used 10th-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.