Canonical elements for Öpik theory

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 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.