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

Samuel R. Kaplan; Mark Levi; Richard Montgomery

doi:10.3934/dcdsb.2008.10.569

Article Contents

2008, Volume 10, Issue 2&3: 569-595. Doi: 10.3934/dcdsb.2008.10.569

This issue Previous Article A mechanism for the fractalization of invariant curves in quasi-periodically forced 1-D maps Next Article Entropy estimates for a family of expanding maps of the circle

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

1.
Department of Mathematics, University of North Carolina Asheville, CPO#2350 Asheville, NC 28804-8511
2.
Department of Mathematics, Penn State, State College, PA 16801
3.
Mathematics Department, University of California, Santa Cruz, CA 95064

Received: September 30, 2006

Revised: October 31, 2007

Published: August 2008

Abstract Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: Primary: 70F07, 37N05; Secondary: 70H33.

Citation:

Article Metrics

HTML views() PDF downloads(93) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content