Near Minimum Energy Trajectories in the Two Fixed Force-Center Problem

Author: Philippou, Demetrius

Year: 1964

Degree: Engineer's thesis

Advisor: Kevorkian, Jirair

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/ZXGH-NV43

Abstract

The class of symmetric orbits with near minimum energy which originate very close to the earth and pass very close to a fixed moon of small mass are studied using asymptotic methods. An exact solution for the orbit is found using Bonnet's Theorem. This is an ellipse with the force centers as foci. Results obtained from the approximate solution are seen to agree exactly with the predictions of Bonnet's Theorem. The solutions thus obtained are the periodic solutions. A one dimensional study is undertaken as a guide to the planar problem.

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