Stability Analysis of the Planetary System Orbiting υ Andromedae

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Abstract

We present numerical orbital integrations designed to test the stability of the three planets detected in orbit around υ Andromedae and possible smaller bodies orbiting in the system which have not yet been discovered. We find that some configurations are stable for at least 109 yr, whereas in other configurations planets can be ejected into interstellar space or crash into the star in less than 105 yr. The typical path to instability involves the outer planet exciting the eccentricity of the middle planet's orbit to such high values that it ventures close to the inner planet. In some stable systems, a secular resonance between the outer two planets prevents close approaches between them by aligning their longitudes of periastron. In relatively stable systems, test particles can survive for long times between the inner and middle planets as well as several AU exterior to the outer planet, but we could find no stable orbits between the middle and outer planets.

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