Studying the lifetime of orbits around Moons in elliptic motion

Abstract

The main goal of the present paper is to study the lifetime of orbits around moons that are in elliptic motion around their parent planet. The lifetime of the orbits is defined as the time the orbit stays in orbit around the moon without colliding with its surface. The mathematical model used to solve this problem is the second order expansion of the potential of the disturbing planet, assumed to be in an elliptical orbit. The results are presented in maps showing the lifetime of the orbit as a function of its initial inclination and eccentricity. The only perturbation acting on the orbit of the spacecraft is assumed to be the gravity of the planet, so the problem is solved by studying the orbital evolution of the spacecraft perturbed by a third body in an elliptical orbit. The region of inclination above the critical value of the third-body perturbation (around 63 $$^\circ $$ ) is studied, since below that value the orbits survive for a long time. The influence of the eccentricity of the primaries is also investigated, assuming a hypothetical system that has the same mass parameter and sizes of the Earth–Moon system, but the eccentricity can be in the range 0.0–0.2.