The stability of the terrestrial planets with a more massive "Earth"

Abstract

Although the long-term numerical integrations of planetary orbits indicate that our planetary system is dynamically stable at least +/- Gyr, the dynamics of our Solar System includes both chaotic and stable motions: the large planets exhibit remarkable stability on gigayear timescales, while the subsystem of the terrestrial planets is weekly chaotic with a maximum Lyapunov exponent reaching the value of 1/5 Myr. In this paper the dynamics of the Sun--Venus--Earth--Mars-Jupiter--Saturn model is studied, where the mass of Earth was magnified via a mass factor $\kappa_E$. The resulting systems dominated by a massive Earth may serve also as models for exoplanetary systems that are similar to our one. This work is a continuation of our previous study, where the same model was used and the masses of the inner planets were uniformly magnified. That model was found to be substantially stable against the mass growth. Our simulations were undertaken for more then 100 different values of K for a time of 20, in some cases for 100 Myrs. A major result was the appearance of an instability window at K = 5, where Mars escaped. This new result has important implications for the theories of the planetary system formation process and mechanism. It is shown that with increasing K the system splits into two, well separated subsystems: one consists of the inner, the other one consists of the outer planets. According to the results the model became more stable as K increases and only when K >= 540 Mars escaped, on a Myr timescale. We found an interesting protection mechanism for Venus. These results give insights also to the stability of the habitable zone of exoplanetary systems, which harbour planets with relatively small eccentricities and inclinations.