An approximate solution to the relative motion of two close satellites in the presence of drag and oblateness

by Hans B. Schechter, Julian D. Cole

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An examination of the relative motion of two satellites moving around an oblate spheroid and acted on by drag forces. It is assumed that one of the bodies has a small tangential velocity increment less than or equal to 10 ft per sec relative to the second body, which moves initially along a circular orbit at an altitude of 100 n mi. Simple analytic expressions have been obtained for the separation distance that results after n revolutions. Maximum permissible altitude differences constrain the number of orbits to n less than or equal to (10 pi times K sub D) to the -1 power, while linearization of the differential equations restricts the intrack separation distance to less than about 300 to 400 n mi. These expressions have been compared numerically with the results of an independent machine integration program and found to be in excellent agreement for the time span considered. For the altitude considered, any influence of oblateness is negligibly small, compared with the effect of the drag forces. The variety of possible relative orbital motions, which can arise from different choices of drag coefficient and initial velocity difference, indicate that satellite/decoy discrimination based solely on differences in the nature of orbital motions is not feasible. 65 pp.

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