Orbital Accessibility Problem for Spacecraft with a Single Impulse

The orbital accessibility problem for spacecraft is to determine whether a transfer to a given target is accomplishable with limited fuel consumption. In this study, limited fuel consumption is conveniently expressed in terms of a single available impulse. By using the terminal velocity hyperbola of the orbital two-oint boundary value problem, a geometrical description of the accessibility condition is attained and then further converted to an algebraic description through the analytic geometry for the convenience of numerical computation. Three typical applications are suggested: 1) solving the orbital accessibility problem when the available impulse magnitude and the target position are both given, 2) searching for the minimum impulse required when the target position is given, and 3) calculating the reachable domain when the available impulse magnitude is given. Numerical examples are presented to validate the proposed method and to demonstrate its three typical applications.