The Moon spins away from the Earth at the rate of about 3.78 centimeters per year and has been moving away for almost 4.5 billion years. Will this rate drift our moon sufficiently away that it escapes the Earth’s influence after some time?

Well, simply, no, the moon will never leave us. When considering all that takes to keep the moon in orbit around the Earth, things get complex.

The moon moves about 3.78 centimeters away from Earth every year due to tidal synergies between the Earth and the moon. The moon’s gravitational attraction exerts a drag on the Earth, which slows its rotation and the gravity of Earth pulls on the Moon, which expands its orbit. These two great effects cancel each other out while conserving angular momentum. However, this four cm/year rate is the current rate of motion. The tidal interactions vary greatly depending on continents’ and water bodies’ arrangements and even the Earth’s internal structure. To study this movement of the moon, scientists must look back into the history of the change in the orbit over the past four billion years.

Looking forward, after about fifty billion years, the Moon’s orbit would reach its maximum extent. Then, one lunar month would be about forty-seven days, and The Earth’s rotation period would also have increased to forty-seven days. Thus, one side of the Earth would always be facing the moon. At that time, since all the motions are synchronous, the resulting tidal synergies between Earth and Moon would cease, causing the moon to stop drifting away. However, Sun’s tidal forces still continue to act on the Earth, slowing its rotation even more. This results in the Earth exerting a drag on the moon, drawing it steadily closer. After perhaps a few hundred billion years, the moon would spiral in so close that it would get ripped apart by the Earth’s gravitational pull, settling into a ring.

Only, this would be the situation if the Earth is not destroyed by then. In about 4.5 – 5.5 billion years from now, the Sun will swell into a Red Giant, expanding until its radius is about a hundred times it is now. The Sun at this time would have swallowed up the Earth and the moon, thus making the above discussion irrelevant. Even so, there is still a minuscule possibility that the Sun would have shed its outer layers, giving the Earth and moon duo a chance to escape their obliterating fate. The Sun would have become a White Dwarf with about two-thirds of its current mass, and the Earth would be a scorched rocky ball with an assortment of rings around it.