## The Moon slows the Earth's rotation, but how fast was it spinning billions of years ago? (Intermediate)

When was the Moon formed and how fast was the Earth spinning then?

In a previous answer you said: "The Earth's rotation is slowing down because of this [the Moon pulling back on its tidal bulge]. One hundred years from now, the day will be 2 milliseconds longer than it is now."

I've seen numbers for the Moon's formation from 4 to 4.6 billion years ago. At the rate you gave above, the Earth would have been making a rotation every couple hours in the first case, or actually spinning BACKWARDS in the latter. I understand that the rate is definitely not constant, but wouldn't the Moon pull harder, and thus lengthen the day faster, when it was closer, making the problem even worse?

Everything you've said is quite right! The missing piece of the puzzle is in the details how the Moon interacts with the Earth via tides.

The Moon does cause a small distortion in the Earth's shape, but as everyone knows, the major effect is tides on the ocean. The Moon's gravity is actually dragging most strongly on the tidal bulge raised on the oceans.

And as it happens, it takes about 12 hours for a big wave to slosh across the Pacific Ocean and back--just in time for its height to be reinforced by the next high tide. So because of the size of the Pacific Basin, the Moon is very effective at slowing the Earth's rotation right now. However, the size of the ocean changes due to contiental drift, so in the past, even though the Moon was closer, tidal friction was a much weaker effect. Unfortunately, it's very difficult to measure or calculate exactly how the positions of the continents have changed over time to the degree of precision that is necessary to work out the effect on tides, and we have just a few ways to measure the rotation of the Earth at different times in its history, so we do not have a complete history of how the Earth and Moon have interacted, and we are not sure exactly how far from the Earth the Moon was when it first formed, or how fast the Earth was rotating at that time.

#### Britt Scharringhausen

Britt studies the rings of Saturn. She got her PhD from Cornell in 2006 and is now a Professor at Beloit College in Wisconson.

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