Making the moon reverse its orbit, or, stuttering in the planar three-body problem

Samuel R. Kaplan, Mark Levi, Richard Montgomery

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We investigate the planar three-body problem in the range where one mass, say the 'sun' is very far from the other two, call them 'earth' and 'moon'. We show that "stutters" : two consecutive eclipses in which the moon lies on the line between the earth and sun, occur for an open set of initial conditions. In these motions the moon reverses its sense of rotation about the earth. The mechanism is a kind of tidal torque (see the 'key equation'). The motivation is to better understand the limits of variational methods. The methods of proof are classical estimates and bounds in this asymptotic regime.

Original languageEnglish (US)
Pages (from-to)569-595
Number of pages27
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume10
Issue number2-3
StatePublished - Dec 1 2008

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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