Preliminary assessment of the next generation equations of relative motion

Julio C. Benavides, David Bradley Spencer

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

2 Citations (Scopus)

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

Fingerprint

four body problem
Spacecraft
Satellites
Asteroids
Initial value problems
Moon
boundary value problems
Sun
Boundary value problems
spacecraft
Differential equations
Earth (planet)
formulations
moon
asteroids
numerical integration
sun
differential equations
asteroid

All Science Journal Classification (ASJC) codes

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

Cite this

Benavides, J. C., & Spencer, D. B. (2008). Preliminary assessment of the next generation equations of relative motion. In International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008 (pp. 4690-4699). (International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008; Vol. 7).
Benavides, Julio C. ; Spencer, David Bradley. / Preliminary assessment of the next generation equations of relative motion. International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008. 2008. pp. 4690-4699 (International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008).
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Benavides, JC & Spencer, DB 2008, Preliminary assessment of the next generation equations of relative motion. in International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008. International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008, vol. 7, pp. 4690-4699, 59th International Astronautical Congress 2008, IAC 2008, Glasgow, United Kingdom, 9/29/08.

Preliminary assessment of the next generation equations of relative motion. / Benavides, Julio C.; Spencer, David Bradley.

International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008. 2008. p. 4690-4699 (International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008; Vol. 7).

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

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Benavides JC, Spencer DB. Preliminary assessment of the next generation equations of relative motion. In International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008. 2008. p. 4690-4699. (International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008).