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Tides

Middle schoolGeographyEquilibrium tide: the Moon and the Sun each raise two bulges, h = A cos 2(φ - φ_body), with A_Sun ≈ 0.46 A_Moon

About this experiment

Twice a day the sea creeps up the beach and twice a day it goes back out. The Moon's gravity pulls a little harder on the side of the Earth facing it and a little less on the far side, stretching the oceans into two bulges. As the Earth turns, every coast passes through both bulges. The Sun does the same, but less strongly. Run the Earth through a month, watch the high tides arrive about 50 minutes later each day, and see how the Sun and Moon together make spring and neap tides.

Learning goals

  • Explain why there are usually two high tides and two low tides a day
  • Explain why high tide is about 50 minutes later each day
  • Describe how the Sun and Moon together cause spring tides and neap tides
  • Link spring and neap tides to the phases of the Moon
  • Explain why there is a bulge on the side of the Earth away from the Moon

How to use it

  1. 1Play at 1 h/s and watch the orange dot. How many high tides do you get in one day?
  2. 2Pause at a high tide and note the time. Find the next high tide one day later. How much later is it?
  3. 3Switch off the pull of the Sun. Then switch the Sun back on and the Moon off. Which body causes bigger tides?
  4. 4Play at 1 d/s for a month and watch the bars of daily range. When are the tides biggest? What is the Moon phase then?
  5. 5Switch on the tidal forces. Why do the arrows point outwards on both the near side and the far side?

The model

Gravity falls with the square of distance; the tidal stretch falls with the cube
The Sun is far more massive but so far away that its tides are less than half as big
Time for a place to come back under the Moon

Assumptions

  • Equilibrium tide: the ocean covers the whole Earth and takes up its balanced shape instantly. Real tides are waves that bounce around ocean basins, so coasts have bigger and later tides than this.
  • The Moon and Sun move in the plane of the equator and the observer stands on the equator, so the two daily high tides are equally high.
  • Amplitudes on the equator: 0.27 m for the Moon and 0.124 m for the Sun. The ocean bulges in the picture are hugely exaggerated.
  • Day 0 starts at midnight at a new moon. The Moon orbits in 27.3 days relative to the stars, giving a 29.5 day cycle of phases.

Try this in class

  1. Q1High tide at a harbour is at 06:10 today. At about what time will it be tomorrow?
  2. Q2Explain why spring tides happen at both new moon and full moon.
  3. Q3Neap tides happen at first and last quarter. Explain using the directions of the Sun and Moon.
  4. Q4Why is there a high tide on the side of the Earth facing away from the Moon?
  5. Q5Why are the tides in the Bay of Fundy over 15 m, when the equilibrium tide is less than 1 m?

Frequently asked questions

Do spring tides only happen in spring?

No. The name comes from the water springing up. Spring tides happen twice a month all year round, at new moon and full moon.

If the Moon pulls the water, why is there a bulge on the far side?

The Moon pulls the near side of the Earth more strongly than the centre, and the centre more strongly than the far side. Relative to the centre, the near ocean is pulled towards the Moon and the far ocean is left behind. Both bulge outwards.

Why does this model give only about 0.8 m of range?

That is the equilibrium tide for an ocean covering the whole Earth. Real tides depend on the shape of the coast and the depth of the sea. Bays and estuaries can make them much bigger, while some places, like much of the Mediterranean, have almost no tide.