Optimization of Impulsive Trajectories from Circular Orbit to an Excess Velocity Vector

Feasible transfer trajectories are constructed to serve as initial guesses for determining constrained optimal impulsive escape trajectories, from a circular orbit to a target hyperbolic excess velocity vector. The proximity of these feasible solutions to their corresponding optima are quantified. The objective of this work is to improve the feasible solutions, thereby enabling general anytime escape trajectories to be targeted that result in substantially reduced fuel expenditure. The procedure is currently restricted to one- and three-impulse escape trajectories from a circular parking orbit. Two separate three-impulse methods are presented, each specific to whether the time of flight is free or fixed. Numerical results, obtained using nonlinear programming algorithms, are presented to validate the robustness of the method. Analysis and results are nondimensional, and therefore are applicable to departures from a circular orbit about any celestial body.