Earth Escape Trajectories Starting from L2 Point

Abstract

The L1 and L2 points of the Sun-Earth system, which are located about 1.5 million km away from the Earth in the sun and anti-sun direction, are widely used as suitable locations for space observatories to a great extent. These points are also thought as a gateway for the interplanetary transfer in the near future. This paper investigates the escape trajectories from the Earth's gravity leaving the Sun-Earth L2 point in the restricted three-body problem. Firstly, we discussed the one-impulse escape strategy assuming velocity correction only at L2 point, and the two-impulse escape strategy assuming the first velocity correction at L2 point and the second velocity correction at the subsequent perigee point. By keeping the hyperbolic excess velocity constant, the required total velocity correction amount and the flight path geometry are analyzed both analytically using Jacobi integral. Finally, optimal escape trajectories of these strategies are calculated by SQP (Sequential Quadratic Programming method), optimal multi-impulse escape strategy is also investigated.