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Astron. Astrophys. 322, 352-358 (1997)

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Theoretical study of the partial derivatives produced by numerical integration of satellite orbits

K.G. Hadjifotinou 1 and S. Ichtiaroglou 2

1 Department of Mathematics, University of Thessaloniki, GR-540 06 Thessaloniki, Greece
2 Department of Physics, University of Thessaloniki, GR-540 06 Thessaloniki, Greece

Received 5 August 1996 / Accepted 30 September 1996


For the two-body system Saturn-Mimas and the theoretical three-body non-resonant system Saturn-Mimas-Tethys we present a theoretical analysis of the behaviour of the partial derivatives of the satellites' coordinates with respect to the parameters of the system, namely the satellites' initial conditions and their mass-ratios over Saturn. With the use of Floquet theory for the stability of periodic orbits we prove that all the partial derivatives have amplitudes that increase linearly with time. Their motion is a combination of periodic motions the periods of which can also be accurately predicted by the theory. This theoretical model can be used for checking the accuracy of the results of the different numerical integration methods used on satellite systems with the purpose of fitting the results to observations or analytical theories. On this basis, in the last part of the paper we extend the investigation of Hadjifotinou & Harper (1995) on the stability and efficience of the [FORMULA] -order Gauss-Jackson backward difference and the Runge-Kutta-Nyström RKN12(10)17M methods by now applying them to the above mentioned three-body system.

Key words: methods: numerical – celestial mechanics – ephe-merides – planets and satellites

Send offprint requests to: K.G. Hadjifotinou

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998