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TwiddleLab / Physics / Gravity and Orbits

Tides: Gravity Stretches

Lesson 9 of 10 · 7 min · Free, no account needed

What you will learn

  • The Moon pulls the near side of Earth more than the centre, and the centre more than the far side. The differences stretch Earth's ocean into two bulges.
  • Earth turns under both bulges, so most coasts get two high tides a day, about 12 h 25 min apart.
  • Sun and Moon in line give big spring tides; at right angles, small neap tides. The stretch falls as 1 / r³.

Start the lesson

How the lesson goes

  1. The Moon is on one side of Earth. Why are there high tides on both sides?

    First, your guess: draw the shape of the ocean.

  2. Drag the Moon round. Compare its pull on the near side, the centre and the far side.

  3. Now turn the Earth through a day. What does the harbour's tide gauge show?

  4. Tidal force, spring and neap tides

    The tidal force is the difference between the pull on one part of a body and the pull on its centre. It stretches along the line to the Moon.

    The Sun raises tides too, about half as strong. In line with the Moon (new and full Moon) they add: spring tides. At right angles (quarter Moons) they partly cancel: neap tides.

    Simplified model: a planet covered by ocean, no continents.

  5. Try the Moon in line with the Sun, then at right angles. Which gives bigger tides?

    The Sun's stretch is about 0.46 of the Moon's. In line: 1 + 0.46 = 1.46. At right angles the Sun's stretch squeezes the Moon's bulges: 1 - 0.46 = 0.54.

  6. Game: Harbor pilot. Get three ships through a shallow channel today.

    Each needs 1.5 h of water deeper than its draught. One ship in the channel at a time.

  7. Math: the stretch falls as 1 / r³. Move the Moon twice as far. Which bar is right?

    The stretch is the difference of two 1 / r² pulls across Earth's size, which goes as 1 / r³. Doubling r divides it by 8.

  8. The Sun pulls on Earth about 180 times harder than the Moon does. Why are its tides weaker?

    The Sun's mass is 27 million Moons, but it is about 390 times farther. The stretch goes as M / r³: 27,000,000 / 390³ is about 0.46.

  9. Speed round: spring tide or neap tide?

    At new and full Moon the Sun, Earth and Moon line up and the stretches add. At the quarters they are at right angles and partly cancel.

Previous lesson: Orbital Maneuvers: Slow Down to Catch Up · Next lesson: Project: Mission to Mars · Part of the course: Gravity and Orbits

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