Optimizing the maneuvers of an observation satellite for rapid overflight of a precise point on Earth

For the purpose of heightened surveillance, it may be necessary to modify the quasipolar circular orbit of an Earth observation satellite and place it in a geosynchronous circular orbit in order to observe repeatedly a precise point on Earth once a day over a given time period. This maneuver should be effected as rapidly as possible, in less than two days. Because the altitudes of the orbits are close, it is possible to get rid of the constraints of heliosynchronism and solve the problem by considering the two orbits to have the same inclination. The difficulty of the problem lies in the fact that the maneuver must be accomplished in a short time period, with limited reserve capacity, and with an engine with a low power level. The maneuver must proceed by stages. Three studies are described in an effort to solve the generalized problem. One uses simplified hypotheses on the physical constraints and mathematical equations. The second, with more realistic hypotheses, accounts for the low thrust level and establishes the propulsive arc. The third study addresses the problem without simplification. It is a functional optimization in which the controls to be determined are the power module and its orientation in the local orbital reference.