The four-body linear equations of planar relative motion

Julio Cesar Benavides; David B. Spencer

doi:10.1016/j.actaastro.2009.06.001

The four-body linear equations of planar relative motion

Julio Cesar Benavides, David B. Spencer

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	285-300
Number of pages	16
Journal	Acta Astronautica
Volume	66
Issue number	1-2
DOIs	https://doi.org/10.1016/j.actaastro.2009.06.001
State	Published - Jan 2010

All Science Journal Classification (ASJC) codes

Aerospace Engineering

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10.1016/j.actaastro.2009.06.001

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AB - 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.

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The four-body linear equations of planar relative motion

Abstract

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