A Solution of the Boundary Value Problem for Space Trajectories

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Abstract
This paper discusses a solution to the boundary value problem for space trajectories which has been found to be easily mechanized. Specifically, when the initial time, initial position, terminal time, and terminal position have been prescribed for a space flight, a method for finding the initial velocity that satisfies these constraints is presented. Three examples are given. They are the boundary value problems associated with an artificial satellite, a lunar impact trajectory, and an interplanetary trajectory. For purposes of illustrating the method and to assess the quality of the results, the lunar impact trajectory investigated was a 1963 Ranger trajectory and the interplanetary orbit selected was a 1969 Mars fly-by trajectory of the Mariner type. Each of the orbits was obtained through the courtesy of the Jet Propulsion Laboratory; however, it is to be emphasized that the ground rules adopted only permitted that the launch date, launch position, arrival date, and arrival position be known. The launch velocity was determined independently.