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Canonical Elements for Öpik Theory

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Abstract

The purpose of this paper is to find a set of canonical elements to use within the framework of Öpik theory of close encounters of a small body with a planet (Öpik, Interplanetary Encounters, 1976). Since the small body travels along a planetocentric hyperbola during the close approach and Öpik 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Pisa, via Buonarroti 2, 56127, Pisa, Italy

    Giacomo Tommei

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  1. Giacomo Tommei
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Correspondence to Giacomo Tommei.

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Tommei, G. Canonical Elements for Öpik Theory. Celestial Mech Dyn Astr 94, 173–195 (2006). https://doi.org/10.1007/s10569-005-4820-3

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  • DOI: https://doi.org/10.1007/s10569-005-4820-3

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