A dynamical study on the habitability of terrestrial exoplanets I: Tidally evolved planet-satellite pairs

We investigate the obliquity and spin period of Earth-Moon like systems after 4.5 Gyr of tidal evolution with various satellite masses and initial planetary obliquity and discuss their relations to the habitability of the planet. We find three possible outcomes: either i) the system is still evolving, ii) the system is double synchronous or iii) the satellite has collided with the planet. The transition between case i) and ii) is abrupt and occurs at slightly larger satellite mass ($m_s \sim 0.02m_p$) than the lunar mass. We suggest that cases ii) and iii) are less habitable than case i). Using results from models of giant impacts and satellite accretion, we found that the systems that mimic our own with rotation period $12 < P_p < 48$ h and current planetary obliquity $\varepsilon_p < 40^\circ$ or $\varepsilon_p > 140^\circ$ only represent 14% of the possible outcomes. Elser et al. (2011) conclude that the probability of a terrestrial planet having a heavy satellite is 13%. Combining these results suggests that the probability of ending up with a system such as our own is of the order of 2%.