Obliquity Variations of Terrestrial Planets in Habitable Zones

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We have investigated obliquity variations of possible terrestrial planets in habitable zones (HZs) in extrasolar planetary systems.
All the extrasolar planets so far discovered are inferred to be Jovian-type gas giants, however, terrestrial planets could also exist in the extrasolar planetary systems. In order for life, in particular for land-based life, to evolve and survive on terrestrial planets, small obliquity variations of the planet is required in addition to its orbital stability, because large obliquity variations may cause significant climate change.
Large obliquity variations are caused by spin-orbit resonances where the precession frequency of a planet's spin nearly coincides with one of the precession frequencies of the planet's orbit. We derived the analytical formulae of obliquity variation amplitude of terrestrial planets in the spin-orbit resonant region. Using the analytical expressions, we evaluated the obliquity variations of terrestrial planets with prograde spins in HZs. Largest obliquity variations are produced by giant planets as far from the HZ as the orbits of the terrestrial planets are hardly perturbed. Stability of the obliquity variations of a terrestrial planet is not associated with its orbital stability.
We found the systems that have terrestrial planets both small obliquity variations and stable orbits in HZs are only 1/5 of the known extrasolar planetary systems. If additional planets are found in the known systems, they generally tend to enhance obliquity variations. On the other hand, a large and/or close satellite that significantly enhances precession rate of the spin axis of the terrestrial planet is likely to reduce obliquity variations of the planet on a stable orbit near 1AU. Moreover, if a terrestrial planet is in retrograde spin state, the spin-orbit resonance does not occur. Retrograde spin, or a large and/or close satellite might be essential for land-based life to survive on a terrestrial planet in a HZ.

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