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We investigate the obliquity and spin period of Earth-Moon like systems after4.5 Gyr of tidal evolution with various satellite masses and initial planetaryobliquity and discuss their relations to the habitability of the planet. Wefind three possible outcomes: either i) the system is still evolving, ii) thesystem is double synchronous or iii) the satellite has collided with theplanet. The transition between case i) and ii) is abrupt and occurs at slightlylarger satellite mass ($m_s \sim 0.02m_p$) than the lunar mass. We suggest thatcases ii) and iii) are less habitable than case i). Using results from modelsof giant impacts and satellite accretion, we found that the systems that mimicour 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% ofthe possible outcomes. Elser et al. (2011) conclude that the probability of aterrestrial planet having a heavy satellite is 13%. Combining these resultssuggests that the probability of ending up with a system such as our own is ofthe order of 2%.

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