Stability and Instability of the Terrestrial Protoplanet System and Their Possible Roles in the Final Stage of Planet Formation

Abstract Recent studies indicate that the formation of jovian giant planets (probably Jupiter and possibly Saturn) may have preceded the formation of terrestrial planets because of the rapidity of the gas-capture process of jovian planets and the stability of the terrestrial protoplanet system. In this paper, we investigate the stability and orbital evolution of medium-sized protoplanets in the terrestrial region under the perturbation by jovian giant planets, Jupiter and Saturn. In our numerical models of the terrestrial protoplanet system, typical masses of the protoplanets are about 0.1 to 0.2 Earth mass, and their spacings are varied from 4 to 20 mutual Hill radii. In initially low-eccentricity and low-inclination orbits, secular perturbation by jovian planets can enhance the eccentricities of terrestrial protoplanets and increase the probability of close encounters when the separation of the protoplanets is large. Due to the effect of the secular perturbation, the instability time scale of the terrestrial protoplanet system is limited to 10 6 years, at most 10 7 years, The time scale of instability also depends much on initial random velocity. Initially high random velocity of protoplanets also reduces the instability time scale two orders of magnitude or so compared with low random velocity and can accelerate the dynamical evolution of the systems.