Stationary Solutions in Simplified Resonance Cases of the Restricted Three-Body Problem
Abstract
In the planar elliptic problem Sun-Jupiter-massless body we consider the resonances of mean motion 3/2, 2/1, 3/1, 7/3 and 1/3. Short-period effects are eliminated by Schubart's averaging method. Applying a minimization technique, stationary solutions can be found in the given resonance cases. Some of these solutions are well-known as periodic solutions in the rigorous (i.e., unaveraged) restricted problem. It is illustrated how one can construct in a numerical way a linearized theory of motion around a stationary solution and results are presented.
- Publication:
-
Celestial Mechanics
- Pub Date:
- February 1980
- DOI:
- 10.1007/BF01230892
- Bibcode:
- 1980CeMec..21..157B
- Keywords:
-
- Asteroids;
- Jupiter (Planet);
- Resonance;
- Solar System;
- Three Body Problem;
- Astrodynamics;
- Motion Stability;
- Orbital Mechanics;
- Periodic Functions;
- Astronomy