Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978a%26a....68..295b&link_type=abstract
Astronomy and Astrophysics, vol. 68, no. 1-2, Aug. 1978, p. 295-301.
Astronomy and Astrophysics
Astrophysics
5
Asteroids, Jupiter (Planet), Orbital Mechanics, Three Body Problem, Trojan Orbits, Lagrangian Equilibrium Points, Optimization, Satellite Orbits, Stationary Orbits
Scientific paper
In the planar elliptic three-body problem, sun-Jupiter-asteroid, the 1/1 resonance with Jupiter is investigated. Important examples of objects in this resonance are the Trojan asteroids. The problem is simplified in so far as the short-period effects in the asteroidal motion are neglected by Schubart's averaging procedure. In order to draw a rough picture of the resonance, stationary solutions are constructed. Not only well-known Lagrangian solutions occur, but also solutions connected with fictitious satellites of Jupiter. For all stationary solutions a linear theory of motion in their immediate neighbourhood is presented and the stability is discussed. To complete the picture, general, i.e., nonlinear, orbits are studied. Most of them are Trojan-like or represent very remote satellites of Jupiter.
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