Rotation of a Moonless Earth - Who needs a Moon?

We have numerically explored the obliquity variations of a hypothetical moonless Earth using a range of initial conditions and extending our calculations for up to 4 billion years. We find that while obliquity varies significantly more than that of the actual Earth over 100,000 year timescales, the obliquity remains within a constrained range, typically 20-25 degrees in extent, for timescales of hundreds of millions of years. Retrograde planets' obliqities are more stable than that of the real Earth. So having a large moon may not be needed for a planet to be habitable.