Can someone please explain why the moon and earths rotation are synchronized? Is it possible that it could become out of sync over time? I’m also confused at how it seems impossible that they would match up forever or even in the first place?
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What you are referring to is called “tidal locking” and the name hints at the reason it occurs.
When the moon was first formed it is theorized it started out as formed mostly from material from Earth blasted free by some immense impact. This glob of molten material would have been spinning wildly but being deformed by Earth’s gravity, stretching it out of a perfect sphere by the pull of gravity. This bulging would have shifted across the surface as the moon spun, but somewhat lagging behind as such shifts took time. Since this would lead to the bulge being unbalanced the pull of gravity would cause the spin to gradually slow, and the orbit of the moon to slow and become more distant from Earth.
Even today the moon is dragging our oceans around the world in a tidal bulge which saps energy from the moon’s orbit causing it to slowly move away from Earth. The moon becomes about 3.78 centimeters more distant from Earth every year.
So to answer your questions more succinctly, the rotation of Earth and the Moon are synchronized due to them pulling on each other via gravity. This tidal locking happens in other cases across our solar system and presumably the universe as well. They will not become out of sync unless there is some outside interference such as a massive body impacting their surface to impart a spin, but even if that occurred the process of tidal locking would just begin again.
The moon causes most of the changing tides on earth, due to gravity. In the same way, the earth causes tides on the moon. As the moon rotated, historically much faster than it does today, the tides moved and the earth pulled back on the tides, gradually slowing the moon’s rotation. Eventually the moon slowed to be in sync with its orbit around the earth so these tides no longer move and there’s no slowing effect from the earth.
The sun also causes tides on the moon and these are still trying to slow the moon further, to sync its spin with the year. The tides due to the earth are much stronger so the moon will remain locked to its earth orbit.
The moon is also trying to slow the earth’s spin in the same way, but the earth is much more massive so the process is much slower. The transfer of momentum from the earth’s spin to the moon’s orbit is pushing the moon slowly away from the earth. The greater the distance, the weaker the tides (by a cube law) so projections suggest that the moon will never escape, at least until the sun expands and consumes both the earth and the moon, billions of years from now.
Tides obey a cube law because they work due to differences in gravity, which follows a square law. The moon is pulling harder on the near side of the earth than on the far side, causing tides to be raised. The land experiences tides almost as big as the ocean tides but the ocean tides are much more noticeable because of the way the oceans slop around and so their tides are focused and exaggerated in many coastal locations.
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