Semi-analytical estimation of the probability of capture into 1:1 ground-track resonance of a low-thrust spacecraft around an asteroid

This paper presents a semi-analytical methodology to estimate the probability of capture into 1:1 ground-track resonance of a low-thrust spacecraft around an asteroid. The system dynamics are described by a Hamiltonian model that considers the perturbations from the irregular gravitational feld up to the second order and degree, and the continuous low thrust that remains constant in magnitude and is always in the direction opposite to the spacecraft’s velocity. The model focuses on the equatorial case of the 1:1 ground-track resonance. When a trajectory is close to the resonance location, its behavior becomes non-deterministic, making it necessary to estimate the probability of capture into resonance. A fourth-order polynomial is used to numerically approximate the separatrices of the resonance region, while the change of the system’s energy balance when the trajectory crosses the separatrices is determined with a global adaptive quadrature method. Subsequently, the probability of capture into resonance is estimated, and the accuracy of the results is verifed by comparing them to numerical simulations based on the perturbed Hamilton’s equations of motion. This research makes a signifcant contribution to the feld of astrodynamics by systematically and effciently analyzing the probability of low-thrust spacecraft capture into ground-track resonance around asteroids.