Is the Moon slowly moving away from the Earth?
Our Moon is drifting away from the Earth at approximately 3.8cm per year. Scientists know exactly how fast because of the Lunar Laser Ranging Experiment. This effect is due to tidal interactions between the Earth and the Moon. The ocean closer to the Moon actually bulges toward it. Because of the planetary rotation of the Earth and the gravitational interplay between the Earth and the Moon, the Moon is pulled faster along its orbital path. This boost in speed slowly pushes the Moon into a larger orbit. It also means that the Earth’s rotation is ever so slightly slowing down.
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If you're wondering if the moon will eventually escape Earth orbit and go spiraling away, it won't. One reasson is that it won't have time, because the sun will go nova and destroy the solar system in about 5 billion years. But if that didn't happen, the moon would keep moving away for about 50 billion years, when it would stabilize and the moon and Earth would tecome tidally locked - meaning one side of the Earth would always face the moon. At that point the moon would slowly begin moving back toward Earth. Then somehow it would eventually get torn apart by gravitational effects - I don't understand that part, it's just what I've read.
I've talked to fundamentalist Christians (I had a weird childhood) who would say that the universe couldn't be as old as 14 billion years old because extrapolating backwards in time the distance from the moon to the earth, the moon would be intersecting the earth much more recently than scientists have estimated the age of the moon to be. And this was advanced as "proof" not just that the universe was far younger than "evolutionists" thought it was, but also that in fact the universe was created in 7 literal days by God about 6,000 years ago.
The flaw in these "creationists'" thinking is that the moon is receding, but it's only been receding since the moon became "tidally locked" (meaning the same side of the moon always faces us) which is a very short time ago compared to the age of the moon, so the rate at which the moon is receding is no proof of a "young universe".