Approximate time-dependent solutions of the two-body problem

Julio César Benavides, David Bradley Spencer

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

1 Scopus citations

Abstract

The N-body problem is defined and its equations of motion are introduced along with the equations of motion for the two-body problem. Time dependent series solutions of the two-body problem are discussed. A new time transformation based on these series solutions is introduced and used to develop a time-dependent, analytic, first-order solution of the two-body problem. A process of deriving higher-order, time-dependent, analytic solutions of the two-body problem is also introduced. These analytic solutions are shown to be capable of describing complete, two-body trajectories with good accuracy and with far fewer function evaluations than are required by numerical integration.

Original languageEnglish (US)
Title of host publicationSpaceflight Mechanics 2010 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the AAS/AIAA Space Flight Mechanics Meeting
Pages1239-1256
Number of pages18
StatePublished - Dec 1 2010
EventAAS/AIAA Space Flight Mechanics Meeting - San Diego, CA, United States
Duration: Feb 14 2010Feb 17 2010

Publication series

NameAdvances in the Astronautical Sciences
Volume136
ISSN (Print)0065-3438

Other

OtherAAS/AIAA Space Flight Mechanics Meeting
CountryUnited States
CitySan Diego, CA
Period2/14/102/17/10

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All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

Benavides, J. C., & Spencer, D. B. (2010). Approximate time-dependent solutions of the two-body problem. In Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting (pp. 1239-1256). (Advances in the Astronautical Sciences; Vol. 136).