The Effect of a Planet in the Asteroid Belt on the Orbital Stability of the Terrestrial Planets

If a planetary-mass body were present in the asteroid belt, the orbits of the terrestrial planets and those of the giant planets would be more closely coupled. A greater exchange of angular momentum could affect the stability of the terrestrial planets. Moreover, the planet in the asteroid belt could itself excite terrestrial planet eccentricities. To study these effects, we have simulated several systems consisting of the Solar System planets and a 0.1-10 Earth mass (M _⊕) object on the orbit of a main belt asteroid or on an initially circular orbit at Ceres's semimajor axis. An integration with Ceres at 5 M _⊕ remained stable for a billion years. Ceres at 10 M _⊕, however, caused the system to become unstable at ∼25-50 myr. When additional mass was given to both Ceres (bringing it up to 2 M _⊕) and Mars (1 M _⊕), the systems self-destructed in <100 myr. However, if these bodies were grown at an epoch when Mars' eccentricity was small, the resulting system was stable for the entire 500 myr simulated. Analogous results were found when other asteroids were grown to planetary masses. Thus, an "asteroid gap" is not required for a planetary system similar to our own to be stable on geological timescales.