A model for close encounters in the planetary problem
Abstract
A model is proposed for single close encounters between two small masses, m_{1}and m_{2}, which orbit a much larger mass, M. The main new feature of the model is the assumption of conic motion of the center of mass of m_{1}and m_{2} in the gravitational field of M. Comparisons of the model with the threebody equations of motion indicate that the model is a useful approximation for m_{1}, m_{2} ≲ 10 ^{5}M. The model is therefore applicable for encounters between bodies of the order of an earth mass or smaller in the presence of the sun. Comparisons are also made of outcomes obtained by the model with outcomes of numerical integration for a large variety of close encounters. The above comparisons reveal that for many purposes the model is an adequate approximation for those encounters with ɛ ≥ 4, where ɛ is the eccentricity of the hyperbolic orbit of m_{1}about m_{2}.
 Publication:

Icarus
 Pub Date:
 May 1978
 DOI:
 10.1016/00191035(78)90177X
 Bibcode:
 1978Icar...34..415C
 Keywords:

 Astronomical Models;
 Celestial Mechanics;
 Encounters;
 Orbital Mechanics;
 Solar Orbits;
 Three Body Problem;
 Center Of Gravity;
 Mathematical Models;
 Orbital Elements;
 ORBITS;
 PLANETS;
 MOTION;
 TWO BODY PROBLEM;
 MODELS;
 Lunar and Planetary Exploration; Planets