How much stronger is the Sun's gravitational pull on the Earth than the Moon's?

The rise and fall of the sea along a coast is caused by gravity: the pull of the Moon and the Sun on the Earth and its oceans. Tides are really very long waves that move through the ocean. When the crest of one of these waves reaches a coast, the water is at high tide; when the trough arrives, it is low tide. The difference in height between the two is called the tidal range.

You might expect the Sun to be the stronger of the two. It is about 27 million times more massive than the Moon, and its gravitational pull on the Earth is more than 177 times as strong. Yet it is the Moon that has the bigger effect on the tides.

The reason is distance. The pull of gravity weakens with the square of the distance, but the force that raises tides weakens faster still, with the cube of the distance. The Sun is about 390 times farther from us than the Moon, so its tide-raising force is cut by 390 × 390 × 390, or about 59 million times. Weighing its great mass against its great distance, the Sun's tide-raising force works out at only about half of the Moon's.