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Obliquity variations of terrestrial planets in habitable zones
We have investigated obliquity variations of possible terrestrialplanets in habitable zones (HZs) perturbed by a giant planet(s) inextrasolar planetary systems. All the extrasolar planets so fardiscovered are inferred to be jovian-type gas giants. However,terrestrial planets could also exist in extrasolar planetary systems. Inorder for life, in particular for land-based life, to evolve and surviveon a possible terrestrial planet in an HZ, small obliquity variations ofthe planet may be required in addition to its orbital stability, becauselarge obliquity variations would cause significant climate change. It isknown that large obliquity variations are caused by spin-orbitresonances where the precession frequency of the planet's spin nearlycoincides with one of the precession frequencies of the ascending nodeof the planet's orbit. Using analytical expressions, we evaluated theobliquity variations of terrestrial planets with prograde spins in HZs.We found that the obliquity of terrestrial planets suffers largevariations when the giant planet's orbit is separated by several Hillradii from an edge of the HZ, in which the orbits of the terrestrialplanets in the HZ are marginally stable. Applying these results to theknown extrasolar planetary systems, we found that about half of thesesystems can have terrestrial planets with small obliquity variations(smaller than 10°) over their entire HZs. However, the systems withboth small obliquity variations and stable orbits in their HZs are only1/5 of known systems. Most such systems are comprised of short-periodgiant planets. If additional planets are found in the known planetarysystems, they generally tend to enhance the obliquity variations. On theother hand, if a large/close satellite exists, it significantly enhancesthe precession rate of the spin axis of a terrestrial planet and islikely to reduce the obliquity variations of the planet. Moreover, if aterrestrial planet is in a retrograde spin state, the spin-orbitresonance does not occur. Retrograde spin, or a large/close satellitemight be essential for land-based life to survive on a terrestrialplanet in an HZ.
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