What is the Sun and the Moon's relationship to the Earth tides?

(by Amara Graps)

Tides are produced by a difference between the gravitational force acting on different parts of an object. Tidal forces vary as the inverse cube of the distances between the masses.

Consider the distances between: the moon (side facing the Earth) and the nearest Earth's surface, and the moon (side facing the Earth) and the center of the Earth.

```         Earth
__
Moon    /  \
x   >| ^  |<
\__/
near    far
side    side
center
```
The difference between the two distances (center of the Earth and the side of the Earth facing the moon) is 6400 km. The moon's gravity tugs 3% more strongly, on the oceans on the near side of the Earth. The ocean waters flow into a bulge on the side of the earth facing the moon.

On the other side of the Earth, there is a gravitational difference between the distance to the moon, and the Earth's center. There, too, is a bulge due to differences in gravitational forces, and that small force causes the ocean waters on the Earth's far side to flow away from the moon

So, we have two bulges, i.e. "tides" on opposites sides of the Earth. The tides rise and fall twice a day, due to the moon.

The Sun, also produces tides on the Earth. It is 27 million times more massive than the moon, but it is at the same time 400 times further away. So the tidal force caused by the Sun is about 50% less than the tidal force caused by the moon.

At new moon and full moon, the moon and Sun are aligned with the Earth, and the tides are about 20% bigger. During the first and third-quarter moon, when the moon and the Sun pull at right angles to each other, the tides are about 20% smaller.

You can find more details of the tidal interaction in oceanography textbooks. One book that I've heard is quite good is: Pond, S. and Pickard, G. L., Introductory Dynamical Oceanography, Second Edition, Pergamon Press, pp. 329, 1989.

### Other areas of interest:

You may have heard that Nova Scotia's Bay of Fundy has the highest and lowest tides.

A 'harmonic analysis' method is often used for tide prediction.

You can read a similar description of tides at Phil Plait's tides WWW page.

#### References:

Michael Seeds, Foundations of Astronomy, 1997 p. 36-37.

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Special Thanks to A. Graps.