Hamiltonian model of a low-thrust spacecraft's capture into 1:1 resonance around Vesta

Boumchita, Wail and Feng, Jinglang (2021) Hamiltonian model of a low-thrust spacecraft's capture into 1:1 resonance around Vesta. In: 72nd International Astronautical Congress, 2021-10-25 - 2021-10-29, Dubai World Trade Centre.

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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 resonance, putting the spacecraft at risk of being permanently trapped at this altitude. The objective of this paper is to develop a hamiltonian model that represents the phenomenon, which is used as a bases for estimating the probability of capture using the adiabatic invariant theory. Firstly, we define the hamiltonian considering the irregular gravitational field up to the second order and degree and the thrust constant in magnitude and opposite to the velocity direction of the spacecraft. Then, we expand the model around the resonance which results the hamiltonian to be reduced in a pendulum-like expression. The reduced model is validated against numerical simulations and is proven to be a good approximation of the dynamics