The four-body linear equations of planar relative motion

Julio Cesar Benavides, David B. Spencer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Pages (from-to)285-300
Number of pages16
JournalActa Astronautica
Issue number1-2
StatePublished - Jan 2010

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering


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