Stationary solutions in simplified resonance cases of the restricted three-body problem

Astronomy and Astrophysics – Astronomy

Scientific paper

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Asteroids, Jupiter (Planet), Resonance, Solar System, Three Body Problem, Astrodynamics, Motion Stability, Orbital Mechanics, Periodic Functions

Scientific paper

In the planar elliptic problem sun-Jupiter-massless body the resonances of mean motion 3/2, 2/1, 7/3, and 1/3 are considered. 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. The construction in a numerical way of a linearized theory of motion around a stationary solution is illustrated, and results are presented.

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