On the predictability of unstable satellite motion around elongated celestial bodies

Abstract

Context. Close satellite orbits around small and elongated celestial bodies can experience massive aperiodic changes in shape. According to a number of published works, the changes are continuous functions of the orbit elements of the satellite's unperturbed trajectory. Aims. Later research, however, has revealed that the onset of instability is discrete, and highly correlated with the overlap of spin-orbit resonances. Since the interaction of resonances also can induce stochasticity in the orbiter's motion, we want to investigate more closely to what extent it is possible to predict the orbit evolution from the unperturbed elements. Methods. Numerical simulations of a natural or artificial satellite's motion in a rotating gravity field of second order and degree are conducted using different algorithms and software.Results. Consistent with the identification of resonance overlap as the responsible mechanism for the onset of orbit instability, we find that it is not always possible to predict qualitatively the outcome of a close encounter between satellite and the central body from the unperturbed orbit elements of the orbiter.Conclusions. The massive aperiodic changes in orbit energy experienced by natural and artificial satellites in orbit around small elongated bodies exhibit properties characteristic for stochasticity.