A virtual-time method for modeling relative motion of noncircular satellites

Ryan E. Sherrill, Andrew J. Sinclair, T. Alan Lovell, Richard Linares

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

3 Scopus citations


The Hill-Clohessy-Wiltshire equations describe the motion of a deputy satellite in close proximity to a circular chief. This paper presents an extension of the Hill-Clohessy-Wiltshire equations to elliptic chiefs by a virtual-time approach. The relative position at each instant is approximated by evaluating the Hill-Clohessy-Wiltshire solution at a virtual time. Therefore, the shape of the trajectory is approximated using an Hill-Clohessy-Wiltshire trajectory, but the progress along the trajectory is modified to account for the chief's eccentricity. Example solutions for the virtual time are calculated, and the errors of the Hill-Clohessy-Wiltshire and virtual-time solutions are compared.

Original languageEnglish (US)
Title of host publicationSpaceflight Mechanics 2011 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the 21st AAS/AIAA Space Flight Mechanics Meeting
Number of pages10
StatePublished - 2011
Event21st AAS/AIAA Space Flight Mechanics Meeting - New Orleans, LA, United States
Duration: Feb 13 2011Feb 17 2011

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Other21st AAS/AIAA Space Flight Mechanics Meeting
Country/TerritoryUnited States
CityNew Orleans, LA


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