Orbital accessibility problem with a single impulse

The orbital accessibility problem (OAP) for spacecraft under a single impulsive maneuver is studied. A geometrical description of the accessible condition is attained by using the terminal velocity hyperbola of the orbital two point boundary value problem (TPBVP). This geometrical description is further converted to an algebraic one through analytic geometry for the convenience of numerical computation. The OAP to a special collinear target is also considered and can be determined through a collinear accessibility function. Three typical applications are suggested: (1) to solve the OAP when both the impulse magnitude and the target position are specified, (2) to search the minimum impulse required when only the target position is given, and (3) to calculate the reachable domain (RD) when only the impulse magnitude is given. The RD is the first accurate solution in the three-dimensional space. Numerical examples are presented to validate the proposition and demonstrate the three typical applications.