PTIMAL time-fixed impulsive intercept trajectories from a point at rest on the surface of a planet or moon to a target in circular orbit are obtained. Some of the results in this study are in Heckathorn1 and form a companion analysis to the related problem of optimal direct-ascent rendezvous treated previously by Gross and Prussing.2 Previous optimal intercept studies in the literature deal primarily with time-open disorbit problems.3 Applications of the results obtained include interception or reconnaissance of orbiting satellites and deployment of satellites at specified locations that are intercepted by the deploying vehicle. The idealized results obtained assuming impulsive thrust and absence of atmospheric effects can be applied to more realistic cases by adding gravity and drag losses to the velocity requirements obtained to account for finite burn times and atmospheric drag. In addition, the case of airborne launch rather than launch from the surface can be obtained by interpreting the launch conditions differently, e.g., the contact force of the planet prior to launch becomes the lift on the aircraft. The optimal time-fixed results obtained can be used to perform time vs fuel trade-offs for missions that have operational time constraints.
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