Minimum-Fuel Escape from Two-Body Sun-Earth System

Escaping from the solar system by receiving gravity assist from the Earth is considered in this paper. A simple procedure, which neglects the eccentricity of the Earth's orbit and uses the two-body problem equations and the patched-conic approximation, provides near-optimal trajectories using either a single or multiple Earth flybys. The analysis shows that the amount of propellant required to escape from the solar system decreases with the number of flybys, but the mission time increases. The same approach is also used to find near-optimal trajectories that use a single powered flyby. The eccentricity of the Earth's orbit can be exploited to reduce the characteristic velocity; an indirect optimization procedure provides the most favorable locations where the Earth should be intercepted.