On distances between orbits of planets and asteroids

Abstract

In various astronomical problems it is required to estimate a proximity of celestial bodies orbits. It can serve as a criterion of a common origin (usually of a parent body fragmentation). Several submetrics were proposed for this goal in the latter half of the 20th century. We call submetric a function defined for each pair of Keplerian orbits, and satisfying the first two axioms of metric space, but not obligatory the third, triangle axiom. It was shown during the last decade that for each of the proposed submetrics one can indicate an open set of orbital pairs for which this key axiom violates. Recently new metrics were constructed satisfying all axiom of mertric space, as well as induced by them metrics in widespread in celestial mechanics factor-spaces of the space of non-rectilinear Keplerian orbits. In the present paper we extended to examine properties of considered submetrics and metrics; calculated corresponding subdistances and distances between planetary orbits in the Solar System; calculated distances between all pairs of orbits of numbered asteroids (in the space of orbits, as well as in its three subspaces); calculated distances between the orbit of the Chelyabinsk body and orbits of all numbered asteroids.