If the Moon is gradually moving farther away from us, will it eventually go away?

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The Moon is receding from the Earth, but will not continue to do so forever. We have to consider why the Moon is moving away at around 1.5 inches (3.78 cm) per year - a force is necessary to cause that.

The Moon exerts a tidal force on the Earth, causing a bulge. But, because the Earth rotates, that bulge is not directly between the Earth and Moon. It is slightly in front. That bulge has a gravitational pull on the Moon, causing it to move forward, slightly faster.

Causing the moon to move slightly faster results in it climbing very slowly to a higher orbit. The Moon climbs higher by about 3.78 cm, per year. But, since we just said that the force is gravitational and we know that gravity decreases with distance, we know that the force will also decrease with distance.

That means the rate at which the Moon recedes will decrease with time. But there’s more to it than that. A force acts upon both bodies. While the impact on the Moon is causing it to recede, the impact on the Earth is that it is being caused to slow its rotation. The day is getting longer.

Eventually, the length of the day will match the orbital period of the Moon. That means both bodies will be tidally locked - meaning the same part of the Earth will always face the same part of the Moon. And if that happens, there is no longer a leading bulge and thus no longer a force causing the Moon to move away.

This would happen when the orbital period of the Moon is about 47 days. That would put the Moon at a distance of about 550,000 km; less than half as far again as it is today. In other words, not very far.

However, it will take a long time for that to happen. In the meantime, the Sun will turn into a red giant and its outer layers will extend to where Mars is, today, meaning Earth, the Moon, and every In-N-Out restaurant will have been swallowed up and turned into loose atoms.