2005MNRAS.363..241S

Although the long-term numerical integrations of planetary orbits indicate that our planetary system is dynamically stable at least ±4 Gyr, the dynamics of our Solar system includes both chaotic and stable motions: the large planets exhibit remarkable stability on gigayear time-scales, while the subsystem of the terrestrial planets is weakly chaotic with a maximum Lyapunov exponent reaching the value of 1/5 M/yr. 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 κ_E. The resulting systems dominated by a massive Earth may serve also as models for exoplanetary systems that are similar to ours. 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 than 100 different values of κ_Efor a time of 20 Myr, and in some cases for 100 Myr. A major result was the appearance of an instability window at κ_E~ 5, where Mars escaped. This new result has important implications for theories of the planetary system formation process and mechanism. It is shown that with increasing κ_E the system splits into two, well-separated subsystems: one consists of the inner planets, and the other consists of the outer planets. According to the results, the model becomes more stable as κ_Eincreases and only when κ_E≥ 540 does Mars escape, on a Myr time-scale. We found an interesting protection mechanism for Venus. These results give insights also into the stability of the habitable zone of exoplanetary systems, which harbour planets with relatively small eccentricities and inclinations.