Obliquity Variations of Extrasolar Terrestrial Planets

A planet's obliquity, which is the angle between its orbital angular momentum and its rotational angular momentum, is an important factor in determining its climate and habitability. For small obliquities, as well as obliquities close to 180 degrees, the planet receives more radiant energy from its star at equatorial latitudes than near its poles, whereas the poles are heated the most for obliquities near 90 degrees. Jacques Laskar has analyzed possible obliquity variations of the planets in our Solar System. His study also considers the same planets with different rotational periods, and the Earth without the Moon. He finds, using frequency map analysis, that the obliquity of the Earth is stabilized by the Moon, and can vary by at most a few degrees. In contrast, the obliquity of Mars can range from 0 to 60 degrees, and a hypothetical moonless Earth's axial tilt could be close to 0 degrees or as large as 85 degrees. Numerical integrations by Laskar and others have shown that Mars' obliquity indeed varies over most of its permitted range on time scales of tens of millions of years. In contrast, our analysis shows that the obliquity of a moonless Earth appears to be confined to the range of approximately 12 - 38 degrees over time scales of 100 million years. Results of ongoing longer integrations will be presented, and their implications discussed.