Precise determination of the reachable domain for a spacecraft with a single impulse

Reachable Domain (RD) refers to the collection of all accessible positions for spacecraft given an initial orbit and a fuel constraint. In this paper, the fuel constraint is conveniently expressed by a single available velocity impulse. To solve the RD, the radius of an accessible target position in a given direction is formulated. Then, by evaluating the extreme values of the accessible radius in the given direction, two reachable boundaries and a reachable line segment can be solved. The RD in the three-dimensional space can be determined by rotating the direction and tracing all the reachable boundaries. The proposed method successfully gives the accurate solutions of the RD for the remaining two unresolved scenarios, namely, RD with arbitrary maneuver point and arbitrary impulse direction and RD with arbitrary maneuver point and fixed impulse direction. Numerical simulations, upon comparison with the results of the existing method, demonstrate the proposed method and its accuracy.