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The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar TrajectoriesThe restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.
Document ID
19620004477
Document Type
Conference Paper
Authors
Richard Schulz-Arenstorff (Marshall Space Flight Center Redstone Arsenal, Alabama, United States)
Mirt C Davidson, Jr (Marshall Space Flight Center Redstone Arsenal, Alabama, United States)
Hans J Sperling (Marshall Space Flight Center Redstone Arsenal, Alabama, United States)
Date Acquired
August 1, 2013
Publication Date
January 1, 1962
Publication Information
Publication: Proceedings of the National Meeting on Manned Space Flight (Unclassified Portion)
Subject Category
Numerical Analysis
Meeting Information
National Meeting on Manned Space Flight(St. Louis, MO)
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
Keywords
Euler equation
Three-body problem
Perturbation
Lunar trajectory

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IDRelationTitle19620004468Analytic PrimaryProceedings of the National Meeting on Manned Space Flight (Unclassified Portion)
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