Estimates for the Set-theoretic Distance between Orbits of Celestial Bodies
K. V. Kholshevnikov1,2
1Sobolev Astronomical Institute of St. Petersburg State University,
St. Petersburg, Russia
2Institute of Applied Astronomy of RAS, St. Petersburg, Russia
Abstract:
Prediction of close encounters of celestial bodies with the Earth or other
planets requires enormous calculations. It is reasonable to use preliminary
simple criteria for the proximity to intersection based on estimates of
set-theoretic distance ρ(Ε, Ε0) between orbits
Ε, Ε0 of celestial bodies
Ρ, Ρ0. As a first step it is sufficient to consider orbits as unperturbed.
We describe here two simple criteria and one more complicated one.
The first one uses the most unfavorable orientation of orbits with
given semi-major axes and eccentricities. The second one uses the
topological notion of linkage. Both give us lower and upper bounds
of the distance. The third one requires calculation of the distance
itself and it amounts to solving a trigonometric equation of the 8-th degree.
Key words:
Very Long Baseline Interferometry (VLBI), Small Solar System Body (SSSB), set-theoretic distance between orbits of celestial bodies, close encounters of celestial bodies with the Earth, criteria for the proximity to intersection, unperturbed orbits, semi-major axes and eccentricities, topological notion of linkage, lower bound of the distance, upper bound of the distance, a trigonometric equation of the 8-th degree.