Tides due to the Moon and the Sun

What causes the tides in the Earth's oceans? Gravitational forces are involved somehow -- but let's see exactly how.

First, please fill in the following table:

```

Body             Mass (kg)       Distance from Earth (m)
----------------------------------------------------------------

Sun

Moon

----------------------------------------------------------------
```

I'll remind you that the radius of the Earth is Re = 6.37 x 10^6 m.

• What is the Sun's gravitational force on a blob of water of mass 1 kg in the ocean at point A? Please compute the answer to 8 places after the decimal point.
• What is the Moon's gravitational force on a blob of water of water of mass 1 kg in the ocean at point A? Please compute the answer to 8 places after the decimal point.
• Which body exerts a stronger force on the water?
```

```

So, why do people seem to give the Moon more of an influence on the tides than the Sun? The answer is the same as it was for poor Joe, hanging from the chin-up bar. Sometimes, the important item is the difference between the forces on the ends of an extended object.

In this case, the object is the Earth's oceans, which stretch out across the planet from point A to point B.

```

Body            force on blob     force on blob       difference
at point A        at point B
--------------------------------------------------------------------
Sun

Moon

--------------------------------------------------------------------

```

It's this difference between the forces on the water at points A and B which leads to the oceans stre-e-etching out into an elongated shape. The two ends along the long axis are places where the water is farther from the center of the Earth -- in other words, "high tide". The ends along the short axis are places where the wather is closer to the center of the Earth -- in other words, "low tide".

• What happens to the bulge of water if the Sun and Moon are lined up together on opposite sides, or the same side, as the Earth?
• What happens to the bulge of water if the Sun and Moon are arranged so that they make a right triangle with the Earth?

Perhaps this record of the water height over time at several shorelines will be useful.

Image courtesy of Pacific ENSO