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


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Aeronautics and Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Stewart, Homer Joseph
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1962
Record Number:CaltechETD:etd-03302009-091409
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1218
Deposited By: Imported from ETD-db
Deposited On:31 Mar 2009
Last Modified:21 Dec 2023 22:41

Thesis Files

PDF (Zukerman_a_1962.pdf) - Final Version
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