Reachable domain with a single coplanar impulse considering the target-visit constraint

This paper proposes a simple numerical method to solve the spacecraft reachable domain problem with a single coplanar impulse considering the target-visit constraint and the impulse-magnitude constraint. The target-visit constraint here is considered as the same position vector for the chaser and the target. Three cases are analyzed for either impulse time or visit time being free, or both being free. Firstly, for the impulse-magnitude constraint, the feasible ranges of impulse time and visit time are obtained based on Kepler's equation. Then, by using the Lambert solution, the extreme-value problems of all three cases are transformed into solving the roots of a single- or two-variable function, which are obtained by numerical methods. Finally, the envelopes of reachable domain are obtained by comparing the extreme values and the boundary values in the feasible ranges. Numerical examples verify the correctness and the effectiveness of the proposed methods by comparing with the traditional Lambert traversal method.