NOTES
This chart shows the total energy for the Earth moon system. The orbital frequency of the Moon, the distance from the Earth to the Moon and the rotation rate of the Earth are all allowed to change in such a way that the total angular momentum in the system remains constant (I've assumed that the Moon's rotational rate will always match its orbital rate). The minimum energy is reached when both the Earth and Moon are rotating with a period of about a month and a half, and the Moon is about 40% further from the Earth than it is currently; this process would take tens of billions of years however, and would not be complete until after the Sun became a red giant.