The Earth-Moon system

Tidal locking

Goal: explain why we always see the same face of the Moon, and why that is not because the Moon does not rotate.

Predict

Does the Moon rotate on its axis? Commit to yes or no before reading on.

Run the experiment

Put a coin on the table. Walk around it, keeping your face towards it the whole time.

By the time you get back, have you turned around? Yes, once. Someone watching from the ceiling saw you face north, then east, then south, then west.

The Moon rotates exactly once per orbit. That is why we see one face. If it did not rotate, we would see every side of it over a month.

Why it ended up that way

Earth raises a tidal bulge on the solid Moon, just as the Moon raises one on our oceans. When the Moon spun faster, that bulge was dragged slightly out of line, and Earth's pull on the offset bulge acted as a brake.

The braking continued until the rotation matched the orbit and the bulge sat still. Then there was nothing left to brake. Tidal locking is the equilibrium state, and it is why most large moons in the solar system are locked.

The same process is happening to Earth, far more slowly: our day is lengthening by about 1.8 milliseconds per century, and the Moon is receding to conserve angular momentum.

Libration

We actually see about 59% of the Moon's surface, not 50%, and it takes two separate effects to get there.

East to west, the rotation is uniform while the orbital speed is not, because the orbit is an ellipse. The Moon runs ahead of its own rotation near perigee and lags near apogee, so it appears to rock about 7.9° either way.

North to south, the Moon's rotation axis is tilted about 6.7° to its orbital plane, so we look slightly over its north pole for half the month and slightly under its south pole for the other half.

Longitude libration alone would not get you to 59%. It is the two rocking motions together, at right angles, that expose the extra sliver all the way round the limb. Photograph the Moon monthly and you can watch craters near the edge appear and disappear.

Checkpoint

• I know the Moon rotates once per orbit
• I can explain locking as a braking process reaching equilibrium
• I know Earth's day is lengthening for the same reason
• I know what libration is

Questions to think about

• How long is a solar day on the Moon, 27.3 or 29.5 days? (Same question as

the end of synodic and sidereal.)

• If Earth eventually locks to the Moon, what happens to tides?

Next: The orbit is not a circle.