### Abstract

Öpik's assumptions on the geometry of particle trajectories leading to and through planetary close encounters are used to compute the distribution of changes in heliocentric orbital elements that result from such encounters for a range of initial heliocentric orbits. Behaviour at encounter is assumed to follow two-body (particle-planet) gravitational scattering, while before and after encounter particle motion is only governed by the force of the Sun. Derivation of these distributions allows precise analysis of the probability of various outcomes in terms of the physical characteristics of the bodies involved. For example, they allow an explanation and prediction of the asymmetry of the extreme energy perturbations for different initial orbits. The formulae derived here may be applied to problems including the original accumulation of planets and satellites, and the continuing evolution of populations of small bodies, such as asteroids and comets.

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

Pages (from-to) | 111-131 |

Number of pages | 21 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1990 |

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### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Celestial Mechanics and Dynamical Astronomy*,

*49*(2), 111-131. https://doi.org/10.1007/BF00050709

**Planetary close encounters : geometry of approach and post-encounter orbital parameters.** / Carusi, A.; Valsechi, G. B.; Greenberg, Richard J.

Research output: Contribution to journal › Article

*Celestial Mechanics and Dynamical Astronomy*, vol. 49, no. 2, pp. 111-131. https://doi.org/10.1007/BF00050709

}

TY - JOUR

T1 - Planetary close encounters

T2 - geometry of approach and post-encounter orbital parameters

AU - Carusi, A.

AU - Valsechi, G. B.

AU - Greenberg, Richard J.

PY - 1990/6

Y1 - 1990/6

N2 - Öpik's assumptions on the geometry of particle trajectories leading to and through planetary close encounters are used to compute the distribution of changes in heliocentric orbital elements that result from such encounters for a range of initial heliocentric orbits. Behaviour at encounter is assumed to follow two-body (particle-planet) gravitational scattering, while before and after encounter particle motion is only governed by the force of the Sun. Derivation of these distributions allows precise analysis of the probability of various outcomes in terms of the physical characteristics of the bodies involved. For example, they allow an explanation and prediction of the asymmetry of the extreme energy perturbations for different initial orbits. The formulae derived here may be applied to problems including the original accumulation of planets and satellites, and the continuing evolution of populations of small bodies, such as asteroids and comets.

AB - Öpik's assumptions on the geometry of particle trajectories leading to and through planetary close encounters are used to compute the distribution of changes in heliocentric orbital elements that result from such encounters for a range of initial heliocentric orbits. Behaviour at encounter is assumed to follow two-body (particle-planet) gravitational scattering, while before and after encounter particle motion is only governed by the force of the Sun. Derivation of these distributions allows precise analysis of the probability of various outcomes in terms of the physical characteristics of the bodies involved. For example, they allow an explanation and prediction of the asymmetry of the extreme energy perturbations for different initial orbits. The formulae derived here may be applied to problems including the original accumulation of planets and satellites, and the continuing evolution of populations of small bodies, such as asteroids and comets.

UR - http://www.scopus.com/inward/record.url?scp=0002354409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002354409&partnerID=8YFLogxK

U2 - 10.1007/BF00050709

DO - 10.1007/BF00050709

M3 - Article

AN - SCOPUS:0002354409

VL - 49

SP - 111

EP - 131

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 2

ER -