Preliminary assessment of the next generation equations of relative motion

Julio C. Benavides, David B. Spencer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

The restricted four-body problem is used to derive linearized equations of relative motion that take into account the perturbing effects of a larger, secondary gravitational source. The result is a system of coupled, first-order, linear differential equations that has a complete analytical solution. In this paper, we numerically integrate these linearized equations and compare the results to the outcomes of the restricted four-body problem and the well known Hill-Clohessy-Wiltshire equations. Various cases pertaining to two scenarios are analyzed: the relative motion of a chase spacecraft with respect to a target satellite orbiting an asteroid while both are perturbed by the Sun, and the relative motion of a chase spacecraft with respect to a target satellite orbiting the Moon while both are perturbed by the Earth. The results demonstrate that the Benavides-Spencer formulation is far more accurate than the results given by the Hill-Clohessy-Wiltshire equations when compared to the real-life outcomes returned by the numerical integration of the restricted four-body problem. Future work will unveil the complete analytical solution of the Benavides-Spencer formulation both as an initial value problem and a boundary value problem.

Original languageEnglish (US)
Title of host publicationInternational Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008
Pages4690-4699
Number of pages10
StatePublished - Dec 1 2008
Event59th International Astronautical Congress 2008, IAC 2008 - Glasgow, United Kingdom
Duration: Sep 29 2008Oct 3 2008

Publication series

NameInternational Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008
Volume7

Other

Other59th International Astronautical Congress 2008, IAC 2008
CountryUnited Kingdom
CityGlasgow
Period9/29/0810/3/08

All Science Journal Classification (ASJC) codes

  • Space and Planetary Science
  • Aerospace Engineering
  • Astronomy and Astrophysics

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