Abstract
It is shown that a simple and rigorous theory of the perturbations of the orbits of close earth satellites can be constructed which is valid for all values of orbital eccentricity less than unity. A vector treatment is used which leads naturally to a description of the orbital geometry in terms of the angular momentum, the direction of perigee, and the eccentricity, from which other elements may be obtained without difficulty. The method is applied briefly to the first-order effects of the earth’s oblateness, and in more detail to the effects of atmospheric resistance. Certain integrals occurring in the theory of atmospheric resistance are evaluated as asymptotic series whose first two terms are sufficient for determining the perturbations to high accuracy.
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