1:1 resonance capture of a low-thrust spacecraft around Vesta

Vesta is the second largest celestial object in the main asteroid belt and it was visited and studied by the DAWN mission in 2011. The spacecraft used solar-electric propulsion that generates continuous low-thrust. As the spacecraft slowly descends from high altitude mission orbit (HAMO) to low altitude mission orbit (LAMO), it crosses the 1:1 resonance, putting the spacecraft at risk of being permanently trapped at this altitude. The objective of this paper is to analyze the probability that the spacecraft has to be captured into the 1:1 resonance with Vesta. Firstly, we model the dynamics considering the irregular gravitational field up to the fourth-order and degree and the thrust constant in magnitude and opposite to the velocity direction of the spacecraft. Then, we calculate the probability of capture for orbits with different combinations of the semi-major axis and true anomaly. In addition, we simplify the dynamical model by considering the harmonic terms related to the 1:1 resonance and the second-order degree harmonics, respectively. It is found that the simplified models are not capable of estimating this probability promisingly. Therefore, through pure numerical simulations of the complete model, we investigate the sensitivity of this capture to different orbital geometries and physical properties of the spacecraft. The results show that the probability of capture is more dependent on the value of the mass of the spacecraft and the magnitude of the thrust, and is less dependent on the value of the specific impulse. In addition, it is found that the spacecraft is more prone to be captured into the 2:3 resonance with Vesta if the descent starts from a non-polar orbit.