Probability of spacecraft's 1:1 ground-track resonance capture around an asteroid with the adiabatic invariant theory

Boumchita, Wail and Feng, Jinglang (2022) Probability of spacecraft's 1:1 ground-track resonance capture around an asteroid with the adiabatic invariant theory. In: 73rd International Astronautical Congress (IAC), 2022-09-18 - 2022-10-22, Paris Convention Centre.

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Abstract

Vesta is the second largest celestial object of the main asteroid belt and it was visited and investigated 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 ground-track resonance, putting the spacecraft at risk of being permanently trapped into it. The objective of this paper is to apply the adiabatic invariant theory to estimate the Dawn's probability of capture into 1:1 ground-track resonance with Vesta. Firstly, we define the averaged Hamiltonian considering the irregular gravitational field up to the second order and degree and the thrust constant in magnitude and opposite to the direction of the spacecraft. Then, we expand the model around the resonance which results the Hamiltonian to be reduced into the first fundamental resonance model, a time-dependent one-degree of freedom Hamiltonian. The phase-space topology changes due to the time-dependency causing the area enclosed by the separatrices to grow. This is the cause of trapping into resonance and, based on the dynamical system's energy change, an intuitive definition of probability of captured is presented. Finally, we adapt the probability definition to be used with the first fundamental model, estimate the Dawn's probability of capture into 1:1 ground-track resonance around Vesta and validate it with Monte Carlo simulations.

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