Canonical Elements for Öpik Theory |
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| Authors: | Giacomo Tommei |
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| Institution: | (1) Department of Mathematics, University of Pisa, via Buonarroti 2, 56127 Pisa, Italy |
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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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| Keywords: | canonical elements hyperbolic collision orbits ?pik theory |
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