Tommei, Giacomo (2006) *Canonical elements for Opik theory.* Celestial Mechanics and Dynamical Astronomy, 94 (2). pp. 173-195. ISSN 1572-9478

| PDF Download (200Kb) | Preview |

## Abstract

SUMMARY The purpose of this paper is to find a set of canonical elements to use within the framework of O¨ pik theory of close encounters of a small body with a planet (O¨ pik, Interplanetary Encounters, 1976). Since the small body travels along a planetocentric hyperbola during the close approach and O¨ pik formulas are valid, without approximations, only at collision, we derive a set of canonical elements for hyperbolic collision orbits (eccentricity e→1+, semi-major axis a fixed) and then we introduce the unperturbed velocity of the small body and the distance covered along the asymptote as a new canonically conjugate pair of orbital elements. An interesting result would be to get a canonical set containing the coordinates in the Target Plane (TP), useful for the analysis of the future encounters: in the last part we prove that this is not possible.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Opik theory, hyperbolic collision orbits, canonical elements |

Subjects: | Area01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica Area02 - Scienze fisiche > FIS/05 - Astronomia e astrofisica |

Divisions: | Dipartimenti (until 2012) > DIPARTIMENTO DI MATEMATICA "L. TONELLI" |

Depositing User: | Dr Giacomo Tommei |

Date Deposited: | 11 May 2010 |

Last Modified: | 21 Dec 2010 13:42 |

URI: | http://eprints.adm.unipi.it/id/eprint/713 |

### Repository staff only actions

View Item |