ENVELOPE OF ELLIPTIC TRAJECTORIES,
TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF
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This report deals with some theoretical investigations on trajectories of the two-body problem in Celestial Mechanics. Specifically, consideration is given elliptic trajectories having the same attracting focus and corresponding to a fixed value of the total energy. The purpose of the report is twofold a to find the envelope curve for the planar system of elliptic trajectories passing through a fixed point, b to determine which one of the two trajectories passing through two fixed points yields a strong minimum for the action integral in the sense of the calculus of variations.