On estimations of Dawn spacecraft's capture probability into 1:1 ground-track resonance around Vesta

This paper develops semi-analytical and analytical methodologies to estimate the probability of the Dawn spacecraft being captured into a 1:1 ground-track resonance around Vesta. The spacecraft, using low-thrust propulsion, approached the asteroid Vesta, and one significant challenge during this phase is crossing ground-track resonances with the asteroid. As the capture phenomenon is dependent on the initial condition of the trajectory, it is necessary to accurately estimate the probability of such a capture. Firstly, the system dynamics are described by a model incorporating Hamiltonian perturbations from the irregular gravitational field up to the second degree and order, and continuous low-thrust that is constant in magnitude and directed in the opposite direction of the spacecraft’s velocity. The resonance region is enclosed by separatrices which are approximated with a fourth-order polynomial for quantitative analysis. The Hamiltonian, serving as a proxy for the system’s energy, changes when the spacecraft crosses the separatrices, and these changes are quantified using a global adaptive quadrature method. Finally, the probability of capture into ground-track resonance is estimated based on the energy change across the separatrices, and the accuracy and efficiency of the developed semi-analytical and analytical methodologies are investigated by comparing them to numerical simulations based on the perturbed Hamilton’s equations of motion. This research makes a significant contribution to the field of astrodynamics by providing a systematic and efficient approach to estimating the probability of resonance capture.