The Influence of Giant Planets Near a Mean Motion Resonance on Earth-like Planets in the Habitable Zone of Sun-like Stars

We present a numerical study of several two-planet systems based on the motions of Jupiter and Saturn, in which the two giant planets move in low eccentric orbits close to a mean motion resonance. It is more likely to find two planets with similar characteristics in a system than a clone of the Jupiter-Saturn pair of our solar system. Therefore, we vary the distance between the two planets and their mass ratio by changing Saturn's semimajor axis from 8 to 11 AU and increasing its mass by factors of 2-40. The different two-planets were analyzed for the interacting perturbations due to the mean motion resonances of the giant planets. We select several mass ratios for the gas giants, for which we study their influence on test bodies (with negligible mass) moving in the habitable zone (HZ) of a Sun-like star. The orbits are calculated for 2×107 yr. In all cases the HZ is dominated by a significant curved band, indicating higher eccentricity, which corresponds to a secular resonance with Jupiter. Interesting results of this study are finding (1) an increase of Venus's eccentricity for the real Jupiter and Saturn masses and the actual semimajor axis of Saturn; (2) an increase of the eccentricity of a test planet at Earth's position when Saturn's mass was increased by a factor of 3 or more; and (3) if the two giant planets are in 2:1 resonance, we observe a strong influence on the outer region of the HZ