Study of Kirkwood Gaps in a Planar Restricted Three-Body Formulation

It was discovered by Kirkwood [1] that the distribution of asteroid orbital frequencies contains gaps for orbits whose period is commensurate with that of Jupiter and a resonance phenomenon owing to the presence of that body has been invoked as a mechanism to account for the absence of asteroids in these gaps [2]. In an extension of previous work [3], we solve the coupled differential equations of motion of Jupiter and an asteroid test body under assumptions of a stationary Sun, circular orbits for Jupiter and a test body of negligible mass placed initially in a forbidden orbit. Deviations from the forbidden orbits were studied and in one case a periodic return to the starting orbit was observed. This periodicity suggests confirmation of the presence of a resonance mechanism.

* Now at Chalmers University of Technology, Gothenburg, Sweden.

1. Daniel Kirkwood, Proceedings of the American Association for the Advancement of Science,

pp.8-14 (1866).

2. See, for example, M. K. Ammar, Astrophys Space Sci 312, 17-22 (2007).

3. David W. Kraft, Bull. Am. Phys. Soc. 33, 64 (1988).