On the stability of Earth-like planets in multi-planet systems

We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g5 are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (aS ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4.