How can only one side of the moon be always visible to us?

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Is its rotation on its own axis so perfectly synchronized to how it rotates around the earth? I imagine even a fraction of a degree off will eventually cause a part of the other side to be revealed even if it takes a very long time.

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The moon is tidally locked with the earth. So think of it like the moon is kind of egg-shaped. The heavier side naturally stays to the outside of its orbit. As a result, we always see the skinny end (even though it does “wobble” a bit). Hope that helps.

It’s called tidal locking. The moon used to not be synchronised. But, just as we have tides on Earth, the Earth was causing a similar effect on the Moon with the moon rock itself, but much smaller of course since rock doesn’t flow very well.

This caused a bulge on the side of the moon facing Earth, and as it rotates further, that bulge is not quite aimed at Earth, but offset.

This in turn makes Earth’s gravity pull unevenly on the Moon, by pulling harder on that bulge because it’s closer. And because it’s not aimed straight at Earth, this causes torque which slowly but surely eventually synchronised the moon’s rotation with its orbit.

In addition to the explanations given already, I will also stress that it’s common and normal for tidal locking to occur; the majority of moons in our solar system are locked with their planets, Mercury has a different kind of synchronous rotation, and we can calculate some exoplanets are locked to their host stars.