Frozen Orbits at high eccentricity and inclination: Application to Mercury orbiter

TL;DR

This paper analyzes the stability of high-eccentricity, high-inclination frozen orbits around oblate bodies under third-body perturbations, with applications to Mercury orbiters and the BepiColombo mission.

Contribution

It develops a general Hamiltonian framework to identify and characterize frozen orbits, including stability analysis and numerical validation for planetary missions.

Findings

Frozen orbits can be located and stabilized using the proposed Hamiltonian method.

The J_2 coefficient can mitigate eccentricity growth from Kozai-Lidov effects.

Application to Mercury orbiters demonstrates practical relevance.

Abstract

We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient J_2 is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect.