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On the 3/1 planar and circular resonant problem. (English) Zbl 0635.70010
Among several asteroids near to 3/1 resonance with Jupiter, several are librating with respect to the critical angle (3\(\lambda\) ’-\(\lambda\)- 2\({\tilde \omega}\)) where \({\tilde \omega}\) is the longitude of the perihelion of the asteroid and \(\lambda\), \(\lambda\) ’ are the mean longitudes of the asteroid and Jupiter, respectively. Hori’s perturbation method [. G. Hori, Publ. Astron. Soc. Japan, 18, 287 ff. (1966)] is applied to the planar and circular case of 3/1 resonance for asteroids. Explicit solutions of the intermediate orbit are obtained. All types of motion are described in terms of two parameters. The model is tested against numerical results for a number of asteroids.
Reviewer: P.Smith

MSC:
70F15 Celestial mechanics
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