Reachable domain of spacecraft with a single normal impulse

The reachable domain for spacecraft with a single normal impulse is studied. In this paper, the problem is addressed in an analytical approach by analyzing for either the initial maneuver point or the impulse magnitude being arbitrary. The trajectories are considered lying in the intersection of a plane and an ellipsoid of revolution, whose family can be determined in an analytical way. In addition, the related orbital parameters such as angular momentum and eccentricity are also derived in a closed form for each case. The impulse constraints and time constraints are also considered while formulating the problem. Several numerical analyses are performed in MATLAB to show the geometry of the reachable domain.