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N. Haghighipour (Northwestern University)
The question of stability of a planetary system is a major concern to astrodynamicists. Discovery of extra-solar planetary systems has added even more to this concern so that during the past several months, dynamicists have taken deeper looks at the formation theories and stability criteria for planetary systems. The purpose of this article is to present analytical approaches to the stability of MACHO-97-BLG-41 planetary system. This planetary system that has been discovered by gravitational microlensing[1], has a unique feature that makes it different from other extra-solar planetary systems; it consists of a planet orbiting both components of a binary system.
Previous studies of such planetary systems consist, mainly, of computational simulations of their dynamical evolution [2]. Results of these computations indicate that the planetary system above is stable. In this article, I present an analytical approach to the results of these computations. The method of partial averaging near a resonance is utilized to verify that the instability regions correspond to (m:1) resonances and the relation between the eccentricity of the planet and the semimajor axis of the binary system reported by Holman and Wiegert[2], will also be verified.
[1] Bennett et al., 1999, Nature, 402, 57.
[2] Holman M. J. and Wiegert P. A., 1999, AJ, 117, 621.