Abstract
Abstract A closed-form solution is obtained for the orbit of an Earth satellite which is influenced by the third harmonic in the potential in addition to the two dominant oblateness terms. The results are carried to the “second order” in the rates of the secular variations and in the periodic fluctuations. The secular equations are solved in closed form in two cases: when the inclination is close to 63.4° and when it is not. In the former case, the stability and period of the slow oscillation of the perigee are discussed.
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