Precise determination of reachable domain for spacecraft with single impulse

Reachable domain refers to the collection of all positions accessible for a spacecraft under a given initial orbit and fuel constraint with free time of flight. In this study, the fuel constraint is conveniently expressed by a single available velocity impulse. To solve the envelope of the reachable domain, the radius of an accessible target position in a given direction is formulated. By evaluating the extreme values of the accessible radius in the given direction, two reachable boundaries and a reachable line segment are solved. The reachable domain in three-dimensional space is determined by rotating the direction and tracing all the reachable boundaries. The proposed method successfully solves the envelope of the reachable domain for the remaining two unresolved scenarios: the reachable domain with an arbitrary maneuver point and arbitrary impulse direction and the reachable domain with an arbitrary maneuver point and fixed impulse direction. This is the first time the accurate envelope of the reachable domain has been described in three-dimensional space.Acomparison of the results of the proposed numerical simulations with those of the existing method demonstrates the accuracy of the proposed method.