The four-body linear equations of planar relative motion

The very restricted four-body problem is used to derive linear equations of relative motion that take into account the perturbing effects of a secondary gravitational source. The outcome is a system of linear differential equations that has an analytical solution. The results of this solution are co...

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Bibliographic Details
Published inActa astronautica Vol. 66; no. 1; pp. 285 - 300
Main Authors Benavides, Julio Cesar, Spencer, David B.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 2010
Subjects
Four-body problem
Hill–Clohessy–Wiltshire
Linearization
Relative motion
Relative motion
Hill–Clohessy–Wiltshire
Four-body problem
Linearization
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Summary:The very restricted four-body problem is used to derive linear equations of relative motion that take into account the perturbing effects of a secondary gravitational source. The outcome is a system of linear differential equations that has an analytical solution. The results of this solution are compared to the outcomes of the very restricted four-body problem and the well known Hill–Clohessy–Wiltshire equations for various cases in the Sun–Ceres system. The results demonstrate that the Benavides–Spencer formulation's accuracy exceeds that of the Hill–Clohessy–Wiltshire equations when compared to the real-life outcomes returned by the numerical integration of the very restricted four-body problem.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0094-5765
1879-2030
DOI:10.1016/j.actaastro.2009.06.001