Studies on Planetary Sattelites. Satellite Capture in the ThreeBody Elliptical Problem
Abstract
Satellite capture is examined for planets in elliptical orbits. Expressions are developed for the Jacobian constant of a satellite in a coordinate system rotating with the primaries about the center of mass. These are transformed to a coordinate system centered upon and moving with the planet, and enable the orbital elements of a captured satellite to be derived in terms only of the mass ratio and the eccentricity of the planetary orbit. By adopting a reasonable criterion for the maximum value of the semimajor axis which gives a stable orbit, these expressions are applied to determine the possibility of satellite capture by each of the planets. Capture may only take place at perihelion or aphelion. Capture at perihelion usually leads to direct orbits and captures at aphelion, where these are possible, to retrograde orbits. It is shown that the masses of planets and the eccentricities of the orbits are such that all planets may effect the capture of satellites when at perihelion.
 Publication:

The Astronomical Journal
 Pub Date:
 March 1972
 DOI:
 10.1086/111263
 Bibcode:
 1972AJ.....77..177B