### Abstract

The restricted three-body problem, which treats the motion of an infinitesimal particle due to the gravitational attraction of two massive primaries moving on circular orbits about one another, provides an example of motion which is stable at potential maxima. In a reference frame rotating with the two primaries’ orbital angular velocity, the potential felt by a test particle in the plane of the primaries’ orbit has maxima at the two points which form equilateral triangles with the primaries. This potential is the sum of the gravitational potential and a term representing the position-dependent centrifugal force. The maxima, called L4 and L5, are stable locations for the test particle thanks to the velocity-dependent Coriolis force, which is not incorporated in the potential function. Any energy-dissipating process would tend to drive the test particle away from one of these stable points. These phenomena may run counter to common experience and physical intuition.

Original language | English (US) |
---|---|

Pages (from-to) | 1068-1070 |

Number of pages | 3 |

Journal | American Journal of Physics |

Volume | 46 |

Issue number | 10 |

DOIs | |

State | Published - 1978 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*American Journal of Physics*,

*46*(10), 1068-1070. https://doi.org/10.1119/1.11492

**Stability at potential maxima : The L4 and L5 points of the restricted three-body problem.** / Greenberg, Richard J.; Davis, Donald R.

Research output: Contribution to journal › Article

*American Journal of Physics*, vol. 46, no. 10, pp. 1068-1070. https://doi.org/10.1119/1.11492

}

TY - JOUR

T1 - Stability at potential maxima

T2 - The L4 and L5 points of the restricted three-body problem

AU - Greenberg, Richard J.

AU - Davis, Donald R.

PY - 1978

Y1 - 1978

N2 - The restricted three-body problem, which treats the motion of an infinitesimal particle due to the gravitational attraction of two massive primaries moving on circular orbits about one another, provides an example of motion which is stable at potential maxima. In a reference frame rotating with the two primaries’ orbital angular velocity, the potential felt by a test particle in the plane of the primaries’ orbit has maxima at the two points which form equilateral triangles with the primaries. This potential is the sum of the gravitational potential and a term representing the position-dependent centrifugal force. The maxima, called L4 and L5, are stable locations for the test particle thanks to the velocity-dependent Coriolis force, which is not incorporated in the potential function. Any energy-dissipating process would tend to drive the test particle away from one of these stable points. These phenomena may run counter to common experience and physical intuition.

AB - The restricted three-body problem, which treats the motion of an infinitesimal particle due to the gravitational attraction of two massive primaries moving on circular orbits about one another, provides an example of motion which is stable at potential maxima. In a reference frame rotating with the two primaries’ orbital angular velocity, the potential felt by a test particle in the plane of the primaries’ orbit has maxima at the two points which form equilateral triangles with the primaries. This potential is the sum of the gravitational potential and a term representing the position-dependent centrifugal force. The maxima, called L4 and L5, are stable locations for the test particle thanks to the velocity-dependent Coriolis force, which is not incorporated in the potential function. Any energy-dissipating process would tend to drive the test particle away from one of these stable points. These phenomena may run counter to common experience and physical intuition.

UR - http://www.scopus.com/inward/record.url?scp=0002290860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002290860&partnerID=8YFLogxK

U2 - 10.1119/1.11492

DO - 10.1119/1.11492

M3 - Article

AN - SCOPUS:0002290860

VL - 46

SP - 1068

EP - 1070

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 10

ER -