Another interesting consequence of the long-term evolution in the Earth-Moon system is the mutual tidal lock: transfer of the angular momentum from the Earth spin to the Moon spin will be nearly complete, locking system in the doubly synchronous state, with the length of day on Earth circa 47 modern days.

It should take about 50 billion years to develop fully, like in the modern Pluto-Charon or Eris-Dysnomia pairs. Of course, it's highly likely that humankind of the far future will have made alterations to orbital parameters of Earth & Moon both, as well as to the Solar life cycle, long before said mutual locking may naturally materialize. Our survival by then, of course, will have already required cross-arm, if not cross-galactic, travel.