Differential forces at play

Clive Trotman, of Waititi, asked:

The gravitational force of the sun on Earth is 200 times greater than that of the moon. So why are ocean tides due to the moon?

John Campbell, a retired physicist at the University of Canterbury, who used to pose this question to his senior classes, responded:

Because it is not the gravitational force that matters, but the difference between the gravitational forces on the water either side of the earth (the differential force).

The sun is about 30 million times larger than the moon, but is only 434 times further away from Earth. The gravitational force (proportional to mass divided by the square of the distance away) at Earth due to the sun is about 200 times more than that of the moon on Earth.

Hence Earth rotates about the sun.

However, the differential force due to the moon is 20 times (depends on the cube of the distance) larger than that due to the sun, because the moon is much closer. Hence the tides are caused by the moon rather than the sun.

But for tides, we must consider water flow. The water at the surface of the earth can flow, so on the side facing the moon, it is attracted towards the moon, giving a high tide to the side facing the moon.

Earth is also attracted to the moon, and can be regarded as solid, so it moves towards the moon, with a slightly lesser force acting on the centre of Earth. The water on the far side of Earth has a slightly lesser gravitational force so is left behind. Thus there is a bulge of water on opposite sides of Earth and hence there are two tides every day.

In midocean, the tidal range (the difference between consecutive high and low tides) is about 0.6m.

Tides are a little more complicated. It depends on air pressure, whether or not the wind is piling the water against a coastline and, as the orbit of the moon around the earth is not circular but elliptical, there are times when the moon is closer to, or further from, Earth.

Land masses (e.g., a long northsouth mass such as New Zealand’s) complicate the water flowing freely to reach the region under the moon. At the New Zealand coastline, the tidal swing is about 2.4m. Likewise, large bays with the right shapes can cause the water flow to resonate, i.e., be much higher than the midocean average. In Canada’s Bay of Fundy the tides can be as high as 15m.

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