Analysis of the orbits of Titan, Hyperion, and Iapetus by numerical integration and by analytical theories

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Celestial Mechanics, Hyperion, Iapetus, Orbital Mechanics, Planetary Orbits, Titan, Numerical Integration, Orbit Perturbation, Orbital Elements, Saturn, Satellites, Titan, Hyperion, Iapetus, Analysis, Techniques, Orbits, Celestial Mechanics, Astrometry, Observations, Mass, Dynamics, Comparisons, Theoretical Studies

Scientific paper

The orbits of Titan, Hyperion, and Iapetus have been generated by both numerical integration and analytical theories and fitted to astrometric observations made in the period 1967-1982. For Titan and Iapetus the two fits to the observations were of similar accuracy, but for Hyperion the numerical integration was significantly better. The numerical integration gave good determinations of the mass ratio Titan/Saturn of (2.36777 + or - 0.00055) x 10 to the -4th, the dynamical flattening J2 of Saturn (0.01675 + or - 0.00089) and the mass ratio Saturn/sun of (2.85877 + or - 0.00021) x 10 to the -4th. A direct comparison of the analytical theories with the numerical integrations has been made and reveals very clearly the inadequacies of the theories.

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