Analytical Approximations to the Solutions of the Equations of Motion in the Earth-Moon Space

Citation

Zukerman, Abraham (1962) Analytical Approximations to the Solutions of the Equations of Motion in the Earth-Moon Space. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZFV9-4018. https://resolver.caltech.edu/CaltechETD:etd-03302009-091409

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Two methods of obtaining approximate solutions of the equations of motion in the Earth-Moon space are derived. The first method - asymptotic expansions of the solutions of the equations of motion - is a power series expansion of the solutions in powers of the inverse maximum velocity [...]. A comparison of the results of numerical integration with the asymptotic expansions is presented, which shows the range of applicability of this method. The second method is similar to the small perturbation approach. In this method the zeroth order solution is a Keplerian orbit about the Earth (the Moon's effect being neglected). The first order solution corrects for the lunar gravity effects on the zeroth order trajectory. To demonstrate the computational difficulties involved in the application of this method, a straight line Keplerian trajectory was used as the zeroth order solution. Several applications of the solutions are discussed.

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