### 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 language | English (US) |
---|---|

Pages (from-to) | 569-595 |

Number of pages | 27 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 10 |

Issue number | 2-3 |

State | Published - Dec 1 2008 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete and Continuous Dynamical Systems - Series B*,

*10*(2-3), 569-595.

}

*Discrete and Continuous Dynamical Systems - Series B*, vol. 10, no. 2-3, pp. 569-595.

**Making the moon reverse its orbit, or, stuttering in the planar three-body problem.** / Kaplan, Samuel R.; Levi, Mark; Montgomery, Richard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Making the moon reverse its orbit, or, stuttering in the planar three-body problem

AU - Kaplan, Samuel R.

AU - Levi, Mark

AU - Montgomery, Richard

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=73149104609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73149104609&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:73149104609

VL - 10

SP - 569

EP - 595

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 2-3

ER -