|The earth-moon center of gravity
The statement "the tidal force is mainly due to the gravitational pull of the moon" is true, but it doesn't say how the pull causes the tides. For example, how does the pull of the moon cause two bulges of water, one on each side of the earth? The moon's pull is in one direction, shouldn't it just cause the water to bulge outward toward the moon?
To understand the generation of two bulges, we first have to realize that the moon doesn't exactly revolve around the earth. Instead, the moon and the earth rotate in opposite directions around the center of their masses (center of gravity). Imagine the earth and the moon are big rocks (they more or less are), placed on a long board on the surface of a giant planet. Suppose furthermore that this board is balanced on a pivot, creating a see-saw (the earth will be closer to the pivot point because it is heaver). The position of the pivot is the center of mass of the earth and moon, and they revolve around this point. The earth is much more massive than the moon and thus the center of mass is actually inside the earth, about 4600 km from the center while the radius of the earth is about 6400 km (thanks to Tim Dierks for corrrecting my earlier version of this essay where I had the center of mass outside the earth).
|Two kinds of forces , opposite in direction but equal in magnitude, are acting on earth and moon. Gravitational force pulls them together while centrifugal force pushes them apart (physicists don't like the term "centrifugal force", but they still know exactly what we are talking about). Since the two forces are balanced, the earth and moon just keep on trucking around stable orbits.
If we were going to calculate the position of the center of mass (we don't have to actually do it here) we would make the assumption that all the mass of the earth was concentrated at the center of the earth, and the same for the moon. It is at the center of earth and moon that the forces balance each other.
|However, the moon's gravity does not balance centrifugal force on the left side of the earth. The surface of the water is closer to the moon than the center of the earth is, so gravitation pull toward the moon is stronger. But, the surface of the water is also closer to the center of rotation, so centrifugal force pushing it away from the center is weaker. Both effects add to create a net force toward the moon, causing a bulge.
Gravity also does not balance centrifugal force on the right side of the earth. The surface of the water is more distant from the moon than the center of the earth is, so gravitation pull toward the moon is weaker. But, the surface of the water is also more distant from the center of rotation, so centrifugal force pushing it away from the center of mass is stronger. Both effects add to create a net force away from the moon, causing a bulge.
Thus, it is the non-uniform nature of gravitational and centrifugal forces across the earth that causes the tides. One of the reasons the moon has a larger effect on tides than the sun is that it is so much closer to the earth than the sun, 240 thousand versus 93 million miles. Since the moon is closer, the percent difference of the gravitational pull from one side of the earth to the other, 8,000 miles apart, is much more than the percent difference in the pull of the sun. The greater non-uniformity of the moon's gravitational pull more than compensates for the greater total gravitational pull of the sun.