### Abstract

The following theorem is proved. THEOREM. For any n≥2, the set of collinear relative equilibria classes of the n-body problem generates by analytical continuation a total of n!(n+3)/2 relative equilibria classes of the n+1 body problem. Together with Arenstorf's results we state a general theorem for the 4 body problem with 3 arbitrary masses and 1 inferior mass.

Original language | English (US) |
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Pages (from-to) | 17-24 |

Number of pages | 8 |

Journal | Celestial Mechanics |

Volume | 28 |

Issue number | 1-2 |

DOIs | |

State | Published - Sep 1 1982 |

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

Palmore, J. I. (1982). Collinear relative equilibria of the planar N-body problem.

*Celestial Mechanics*,*28*(1-2), 17-24. https://doi.org/10.1007/BF01230656