Approximate time-dependent solutions of the two-body problem

Julio César Benavides, David B. Spencer

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

1 Scopus citations


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
Number of pages18
StatePublished - 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
ISSN (Print)0065-3438


OtherAAS/AIAA Space Flight Mechanics Meeting
Country/TerritoryUnited States
CitySan Diego, CA

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science


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