Spacecraft multi-impulse reachable domain

The concept of the spacecraft Reachable Domain (RD) has garnered significant scholarly attention due to its crucial role in space situational awareness and on-orbit service applications. While the existing research has largely focused on single-impulse RD analysis, the challenge of Multi-Impulse RD (MIRD) remains a key area of interest. This study introduces a methodology for the precise calculation of spacecraft MIRD. The reachability constraints specific to MIRD are first formulated through coordinate transformations. Two restricted maneuvering strategies are examined. The derivation of two extremum conditions allows for determining the accessible orientation range and the nodes encompassing the MIRD. Subsequently, four nonlinear programming models are developed to address two types of MIRD by skillfully relaxing constraints using scale factors. Numerical results validate the robustness and effectiveness of the proposed approach, showing substantial agreement with Monte Carlo simulations and confirming its applicability to spacecraft on various elliptical orbits.