NUMERICAL-INTEGRATION OF ORBITS OF PLANETARY SATELLITES

The 10(th)-order Gauss-Jackson backward difference numerical integration method and the Runge-Kutta-Nystrom RKN12(10)17M method were applied to the equations of motion and variational equations of the Saturnian satellite system. We investigated the effect of step-size on the stability of the Gauss-Jackson method in the two distinct cases arising from the inclusion or exclusion of the corrector cycle in the integration of the variational equations. In the predictor-only case, we found that instability occurred when the step-size was greater than approximately 1/76 of the orbital period of the innermost satellite. In the predictor-corrector case, no such instability was observed, but larger step-sizes yield significant loss in accuracy. By contrast, the investigation of the Runge-Kutta-Nystrom method showed that it allows the use of much larger step-sizes and can still obtain high-accuracy results, thus making evident the superiority of the method for the integration of planetary satellite systems.