### Abstract

The dynamical interactions of planetary systems may be a clue to their formation histories. Therefore, the distribution of these interactions provides important constraints on models of planet formation. We focus on each system's apsidal motion and proximity to dynamical instability. Although only 25 multiple planet systems have been discovered to date, our analyses in these terms have revealed several important features of planetary interactions. 1) Many systems interact such that they are near the boundary between stability and instability. 2) Planets tend to form such that at least one planet's eccentricity periodically drops to near zero. 3) Mean-motion resonant pairs would be unstable if not for the resonance. 4) Scattering of approximately equal mass planets is unlikely to produce the observed distribution of apsidal behavior. 5) Resonant interactions may be identified through calculating a system's proximity to instability, regardless of knowledge of angles such as mean longitude and longitude of periastron (e.g. GJ 317 b and c are probably in a 4:1 resonance). These properties of planetary systems have been identified through calculation of two parameters that describe the interaction. The apsidal interaction can be quantified by determining how close a planet is to an apsidal separatrix (a boundary between qualitatively different types of apsidal oscillations, e.g. libration or circulation of the major axes). This value can be calculated through short numerical integrations. The proximity to instability can be measured by comparing the observed orbital elements to an analytic boundary that describes a type of stability known as Hill stability. We have set up a website dedicated to presenting the most up-to-date information on dynamical interactions: http://www.lpl.arizona.edu/~rory/research/xsp/dynamics.

Original language | English (US) |
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Pages (from-to) | 469-478 |

Number of pages | 10 |

Journal | Proceedings of the International Astronomical Union |

Volume | 3 |

Issue number | S249 |

DOIs | |

State | Published - Oct 1 2007 |

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### ASJC Scopus subject areas

- Medicine (miscellaneous)
- Astronomy and Astrophysics
- Nutrition and Dietetics
- Public Health, Environmental and Occupational Health
- Space and Planetary Science

### Cite this

*Proceedings of the International Astronomical Union*,

*3*(S249), 469-478. https://doi.org/10.1017/S1743921308016980