Originally Posted by

**uptonryan**
Janus do you have some mathematical modelling to support that theory? My model says that it will escape earth orbit but only way after the sun has become a super red giant.

First, let's consider your 6 billion year prediction for Moon escape.

For the Moon to escape, it would have to get beyond the Earth's Hill sphere. This has a radius of 1.5 million km. If you take the difference between this and the Moon's present distance and then divide that by 4cm/yr you find that even if the moon constantly receded at the same rate it does now, it would take ~28 billion years to reach the edge of the Hill sphere.

Now let's consider as to whether the Earth even can transfer enough energy to the Moon in order to lift it to the edge of the Hill sphere.

The total rotational energy of the Earth works out to ~2.6 x 10^29 joules. This is the maximum energy it could possibly transfer to the Moon in lifting its orbit. (and it would have to come to a dead stop to do so. )

The orbital energy of the Moon can be found by

Where M is the mass of the Earth, m the mass of the Moon and a the Earth-Moon distance.

If you take the difference between the Moon's orbital energy now, and its energy at the edge of the Hill sphere, you get an answer of

2.8 x 10^28

Now this is ~1/10 what the Earth has to give up, so, at first glance, it looks possible. However, we must go back to something that I mentioned earlier, not all of the energy the Earth loses is given to the Moon. To find out how much, we compare the energy given up by the Earth compared to the energy gained by the Moon.

The Earth presently slows at a rate of 17 milliseconds/century.

This works out to an energy loss of:

~10^23 joules.

In that same century, the Moon recedes by 4 meters, and gains:

4 x10^20 joules.

or 1/250 as much energy as the Earth loses. This means the transfer of energy from Earth to Moon is not very efficient. The rest is given up as waste heat.

It also means that even though the Earth has almost 10 times the energy stored in its rotation needed to cause the Moon's escape, it actually can only transfer 1/250 of that energy to the Moon.

The Earth can't transfer enough energy to the Moon to get it outside of the Hill sphere.

That only leaves the possibility of the Earth tidal locking to the Moon.

Now, as far as the Moon spiraling back in, that is due to tidal deceleration:

Tidal acceleration - Wikipedia, the free encyclopedia
Of course, all of this is a mute point considering the life-cycle of the Sun, and the time scales needed for the scenario to play out.