Tides

What causes tides

Goal: understand why there are two bulges, and why the Sun loses to the Moon despite being far more massive.

Predict

Before reading:

1. The Moon pulls on the ocean. Why is there a high tide on the side of Earth

facing away from the Moon?

1. The Sun is 27 million times more massive than the Moon. Which produces the

bigger tide?

Learn

It is the difference, not the pull

Gravity weakens with distance. The near side of Earth is about 12,700 km closer to the Moon than the far side, so it is pulled slightly harder. Earth's centre is pulled a medium amount. The far side is pulled least.

Now work in the frame of Earth's centre, subtract the centre's acceleration from everything. Relative to the centre:

• Near-side water is pulled towards the Moon
• Far-side water is left behind, so it moves away from the Moon

Both lift water away from the centre. Two bulges, on opposite sides.

The tide is caused by the difference in pull across Earth, not by the pull itself. That single sentence resolves almost every tide misconception.

Why the Sun loses

Gravitational force falls off as 1/r². But the difference across a body falls off as 1/r³, differentiate and see.

The Sun pulls on Earth about 175 times harder than the Moon does. But it is so far away that the difference across Earth's width is small, and the tidal effect ends up at about 46% of the Moon's.

This is why the Moon rules the tides despite being a small rock.

The 1/r³ law is why tidal forces matter enormously close in; it is what tears comets apart near Jupiter and what would stretch you unpleasantly near a black hole.

Two highs a day

Earth rotates through both bulges every day, so most coasts see two highs and two lows. Not all, see Why local tides are hard.

Run

moonfield tide explain

Checkpoint

• I can explain why there are two bulges, not one
• I know the tide comes from the difference in pull
• I know tidal effect falls off as 1/r³, not 1/r²
• I can explain why the Sun's tide is smaller despite its mass

Questions to think about

• If Earth had no rotation, would there still be tides?
• The Moon is slowly moving away from Earth. What happens to tides over

millions of years?

• Does the solid Earth have tides too? (Yes, about 30 cm. You are rising and

falling twice a day.)

Next: The lunar day.