The capture probability of Dawn into ground-track resonances with Vesta

Abstract

The Dawn spacecraft approached the asteroid Vesta and descended from a high-altitude mission orbit to a low-altitude mission orbit using low-thrust propulsion. During this descent, the spacecraft crossed the 2:3 and 1:1 ground-track resonances with Vesta, which posed a risk of capture that might strongly perturb the spacecraft’s orbit. This study analyzes the effects of these resonances on the spacecraft’s orbital elements and estimates the probability of capture into it through Monte Carlo simulations. Specifically, a comprehensive investigation is performed to assess the effects of 1:1 and 2:3 ground-track resonances on the semimajor axis, eccentricity, and inclination. The dynamical model includes the gravitational field of Vesta using a spherical harmonics approximation up to the fourth degree and order and the low-thrust acceleration that is assumed to be opposite to the spacecraft’s velocity vector direction. It is observed that the eccentricity evolution is mostly influenced by the 2:3 ground-track resonance which results in a large variation when the spacecraft crosses that ground-track resonance, while the semimajor axis and inclination are mostly influenced by the 1:1 ground-track resonance. Then, the probability of capture into 1:1 ground-track resonance is found to have a negative correlation with the spacecraft’s thrust magnitude and the probability of capture into 2:3 ground-track resonance is found to arise as the spacecraft’s mass increases. It is found that for circular orbits below a certain inclination value the spacecraft’s trajectory is subject to the “automatic entry into libration” phenomenon, due to the singularity in the Hamiltonian function. This research contributes to the design of successful transfer strategies when crossing resonance for future missions.