On Brown's Conjecture
Abstract
We examine the conjecture made by Brown (1911) that in the restricted three body problem, the long period family of periodic orbits aroundL _{4}, ends on a homoclinic orbit toL _{3}. By numerical integration we establish that for the mass ratio SunJupiter such a homoclinic orbit toL _{3} does not exist but that there exists a family of homoclinic orbits to periodic orbits aroundL _{3}.
 Publication:

Celestial Mechanics
 Pub Date:
 October 1983
 DOI:
 10.1007/BF01686813
 Bibcode:
 1983CeMec..31..115H
 Keywords:

 Celestial Mechanics;
 Jupiter (Planet);
 Orbital Mechanics;
 Solar Orbits;
 Three Body Problem;
 Asymptotes;
 Jacobi Integral;
 Manifolds (Mathematics);
 Mass Ratios;
 Orbit Perturbation;
 Systems Stability;
 Astronomy