The Earth-Moon Interaction

Earlier in class we talked about gravitational forces and how they make the tides.

So clearly the Moon influences the Earth in more than just an aesthetic way.

Think about this for class:

In what other ways does the moon affect the Earth and its inhabitants?

Tidal Evolution of Orbits

As the Moon's tidal forces raise  bulges on the Earth, the Earth's rotation moves these bulges forward to lead the Moon:

Since the tidal bulge has a little extra mass associated with it, the moon feels a little extra pull forward in its orbit. (Note that this is the opposite of what is happening to Mars' moon Phobos, who leads the bulges on Mars and thus feels a backwards drag.)

So the moon is being accelerated forwards, as if it had a little rocket on its back firing away.

Think about what happens in an orbit if you accelerate forwards. You are adding energy and angular momentum to your orbit, so you move outwards into a larger orbit with a longer orbital period.

The Moon is slowly moving away from the Earth!

How fast? About 3-4 cm/yr. (How do we measure this?)

So the moon is moving away, gaining energy and angular momentum from the Earth. But a basic law of physics says that energy and angular momentum are conserved (if there are no external torques).

So if the Moon gains angular momentum, the Earth must lose angular momentum.

The Earth's rotation rate is gradually slowing!

How fast? About 0.0016 seconds/century, or roughly 1 second every 50,000 years.
So a "dinosaur day" was about 23.5 hours long, not 24 hours long.
(Extrapolation doesn't work too far back, but best current models suggest that when the Earth and Moon were closest several billion years ago, one day was about 4-5 hours long!)

Can this go on forever? When does this all end?


Eventually the Earth's rotation period will be identical to the Moon's orbital period. This situation is called synchronous (1:1) rotation. In the distant future (many billions of years from now), the Earth will have a day which is 47 current days long, and the Moon will only be visible from one side of the Earth.

(What other familiar object is in a 1:1 synchronous rotation?)

At this point, with the bulges aligned with the Moon, no further orbit evolution will occur.