A Statistical Examination of the Short Term Stability of the Upsilon Andromedae System

Abstract

Because of the high eccentricities (~0.3) of two of the possible planets about the star Upsilon Andromeda, the stability of the system requires careful study. We present results of 1000 numerical simulations which explore the orbital parameter space as constrained by the observations. The orbital parameters of each planet are chosen from a Gaussian error distribution, and the resulting configuration is integrated for 1,000,000 years. We find that 84% of these integrations are stable. Configurations in which the eccentricity of the third planet is <0.3 are always stable, but when the eccentricity is >0.45 the system is always unstable, typically producing a close encounter between the second and third planets. A similar exercise with the gas giants in our own Solar System sampled with the same error distribution was performed. Approximately 81% of these simulations were stable for 10^6 years.