Cosmos: "tidal friction caused the Moon's orbit to rise"

I finally got a chance to watch some Cosmos episodes. Nice. Sure I miss Sagan, but the modern graphics are lovely.

One thing the narrator Tyson said was that the Moon’s orbit was originally very close to the Earth, but shifted higher due to tidal friction.

Can anyone please explain that? Thanks!

Here’s a good explanation from Cornell University. Basically: the Moon raises tidal bulges on the Earth. Since the Earth is rotating faster than the Moon is orbiting, this pushes the bulge “ahead” of the Moon in the rotation. The bulge then pulls the Moon ahead in its orbit (and slows down the rotation of the Earth.)

The net result is then that energy is transferred from the rotational energy of the Earth into the orbital energy of the Moon. This means that the Moon actually gets farther away from the Earth — the higher something is above the Earth’s surface, the more energy it has. This effect will continue until the Earth is rotating at the same rate as which the Moon rotates around it, a phenomenon called tidal locking. The Moon is already “locked” with the Earth — the near side always faces the Earth — and eventually the Earth will be locked with the Moon too.

Some of the stuff on the Earth’s surface is loose, mainly ocean water. The moon sits out there in space, going slowly around the Earth. The Moon’s gravity says “come to me, Earth oceans.” Friction between the firm Earth (the land, the seabed) and the loose Earth says “Nu uh, you’re coming with us, ocean.” So the ocean water is pulled in two different directions. Thus, the water’s gravity calls back to the moon, “Howzabout you come with me instead?” The moon’s all like “K.”

So the moon gets tugged along. But wait! At any given time, the Moon is being pulled along by this ocean bulge (the tide) in only one direction. It’s being pulled forward and down. Well, that little, extra “forward” velocity takes it further out into space before the rest of the Earth can rein it back in.

When you sum all these instantaneous nudges over a billion years, you get a higher (i.e. farther away) orbit.

So how long until the Earth is tidally locked to the moon? And how far away will the moon be then?

Wow. Thanks!

Piper, the Britannica article says “millions of years”.

Chessic, great anthropomorphizing. You should write an astronomy book for kids!

I still find it fascinating that speeding it up causes it to go higher which causes it to slow down even more than before, so while the Earth is speeding the moon up, the result is to slow it down.

I guess there’s a reason they call rocket scientists rocket scientists. :wink:

Actually IIRC the earth won’t make it to being tidally locked with the moon. It will be swallowed up by the sun when the latter expands into a red giant in 4 or so billion years first.

The bulge drags the Moon, which slows down the Earth’s rotation while speeding up the Moon’s velocity, causing the force vector to be ever so slightly away from the Earth. At least that’s how I’m understanding it. Someone feel free to correct me (there usually is someone like that around, lurking).

And how long will an Earth day be? It will necessarily be = one Earth month, right? But how long will that be?

Here I am! :smiley:
The moon’s velocity actually decreases as it moves into a higher orbit. The moon does gain energy, but it’s all transformed along with some of the moon’s own kinetic energy into increased potential energy at the higher altitude.

You can see the dynamic exchange of kinetic and potential energy in lower and higher orbits in a simulation of an eccentric orbit of a satellite around a large body like the earth. When an eccentrically orbiting satellite approaches the earth its speed increases (it’s literally falling toward the earth), and when it flies away its speed decreases. Its speed at any point in its orbit is inversely proportional to its altitude.

It’s “trying” to speed it up, but in the end it’s just giving it more energy. Same reason that it takes more fuel for a space shuttle to reach the ISS or the Hubble than to enter a lower orbit, but it’s actually moving more slowly at that higher orbit. I’ve played with orbital simulations and it’s very non-intuitive – my space ships always end up going where I don’t want them or crashing into the earth! :smiley:

I think I read somewhere that if the earth were ever to become tidally locked with the moon, the day would be about 40 present earth days long. (The earth’s rotation is slowing but so is the moon’s orbital period.) But there probably isn’t enough time for that to happen as the increasingly luminous sun is due to boil off the oceans sometime within the next billion years, and then as mentioned it’s going to do its red giant thing in about 4 billion or so years.