Why is the Moon considered the major cause of tides, even though it is weaker than the Sun?

Question

You have likely read in books that tides are mainly caused by the Moon. When the Moon is high in the sky, it *pulls* the water on the Earth upward and a high-tide happens. There is some similar effect causing low-tides. They also say that the Sun does the same as well, but has smaller effect compared to the Moon. Here's my question: Why is the Moon the major cause of tides? Why not the Sun? The Sun is extremely massive compared to the Moon. One might say, well, the Sun is much farther than the Moon. But I've got a simple answer: Just substitute those numbers in $a=\\frac{GM}{d^2}$ and find gravitational acceleration for the Moon and then for the Sun (on Earth, by the way). You'll find something around $3.38$ $10^{-6}$ $g$ for the Moon and $6.05$ $10^{-4}$ $g$ for the Sun - I double checked it to make sure. As you can see, the sun *pulls* about $180$ times *stronger* on the Earth. Can anyone explain this? Thanks is advance.

Answer 1

Tides are due to the difference in force across an object: the side of Earth closest to the Moon is accelerated towards the Moon faster than the center of Earth (because 1/r² is larger in the first case), but the solid part of Earth doesn't move much. Water being free to move demonstrates this differential force. With our Sun being much farther away than the Moon, the percentage change in acceleration across Earth due to the Sun is smaller.