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K. Moriwaki, Y. Nakagawa (Kobe University)
We estimate upper limits of binary and planetary eccentricities in the extrasolar planetary system, MACHO-97-BLG-41 lens system. This planet was detected by gravitational microlensing, and is considered to be the first observed one orbiting both components of the binary star system. This observational technique cannot determine binary and planetary eccentricities. However, these orbital elements may be estimated by long-term numerical integrations of binary and planetary orbital motions. We performed such long-term numerical integrations with various initial conditions in order to see what initial configuration produces the stable planetary orbits during the integration (106 binary periods or approximately 2.8Myr). The numerical results show that the upper limit of binary eccentricity for stable planetary orbit in this system is about 0.5 under the assumption of the initial circular orbit of the planet. In the case of initial elliptic orbit of planet, we have found a tendency that planetary orbital motion become unstable in shorter time-scale and the upper limit of binary eccentricity decreases with increasing initial planetary eccentricity. The numerical results show that the upper limit of the initial planetary eccentricity is about 0.3 for stable planetary orbits. More over, we tried numerical integrations in the case of retrograde orbit, and found that the planetary retrograde orbit is more stable than the prograde case.
The author(s) of this abstract have provided an email address for comments about the abstract: moriwaki@jet.planet.sci.kobe-u.ac.jp