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 Sun-Jupiter 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