Orbital interactions  A new geometrical formalism
Abstract
The geometry of encounters between two bodies on independent Keplerian orbits around a third body is considered by a novel analysis, which avoids approximations made in previous studies. For the case of most of the applications considered, the formulas for collision frequencies and orbital element rates of change due to close approaches which comprise the method agree with past results. It is shown that the method can be extended to such other applications as the consideration of oscillations in orbital elements due to secular perturbations, and the computation of probabilities of escape from the system.
 Publication:

The Astronomical Journal
 Pub Date:
 January 1982
 DOI:
 10.1086/113095
 Bibcode:
 1982AJ.....87..184G
 Keywords:

 Celestial Mechanics;
 Collision Rates;
 Orbit Perturbation;
 Orbital Elements;
 Planetary Orbits;
 Two Body Problem;
 Encounters;
 Formalism;
 Geometry;
 Probability Theory;
 Protoplanets;
 Secular Variations;
 Statistical Analysis;
 Astrophysics