First of all, anybody who has said that the Sun's gravitational pull on the Moon is weaker than the Earth's is absolutely wrong. "Dump the liberals into Jupiter" has an awful sentiment as a username, but has done a fantastic job of showing why. Indeed, the Sun's gravitational pull on the Moon is more than twice as strong as the Earth's.

Why doesn't the Moon fly away? Several people have hinted at the right answer, but nobody has nailed it yet.

What's important here is not force but acceleration. The Sun's gravity causes a Sun-ward acceleration in both the Earth and the Moon. The Sun-Earth force is greater than the Sun-Moon force because of Earth's greater mass, but that greater mass also provides greater inertia and prevents the Earth from accelerating toward the Sun any faster than the Moon does. Let's slow down here and emphasize this point: an object's acceleration is DIRECTLY proportional to the magnitude of the net force (more force = more acceleration) but INVERSELY proportional to its mass (more mass = less acceleration) Put those competing factors together and here's what you get: The Earth and Moon are accelerating toward the Sun at roughly the same rate despite their vastly different masses. This has nothing to do with the Earth-Moon force...we'll get to that in a minute.

Now wait a minute, I hear you saying. If the Earth and Moon are accelerating toward the Sun, why haven't we crashed into it? Because we're also moving perpendicular to that acceleration, which means that instead of plummeting INTO the Sun we plummet...well, around it. In other words, we orbit the Sun. Our direction of travel is always approximately at right angles to the gravitational pull of the Sun, which keeps us orbiting around and around. This is true for both the Earth and the Moon.

Looking at it from that perspective, it's easy to see that the Earth and Moon are both in a state of constant freefall around the Sun. In that case, neither should be pulled more toward the Sun than the other as long as they are both about the same distance away.

The Moon also moves perpendicularly (more or less) to the gravitational pull of the Earth, so as well as being pulled around the Sun, it is also pulled around the Earth. Remember, as long as the Earth and Moon are ROUGHLY the same distance from the Sun and pretty close to each other, they will continue to be gravitationally bound to each other.

But what would happen if the Moon's orbit were much further away from the Earth. What if, when the Moon moved between the Earth and the Sun, it were close enough to the Sun that its acceleration Sunward were signifcantly greater than the Earth's Sunward acceleration? Wouldn't it then start to "fall" toward the Sun faster than the Earth does, effectively becoming its own planet?

In a word, yes. There is a critical radius, called the Hill radius, wherein any body orbiting the Earth (or any other planet) is dominated by the Earth's gravity and is not pulled out of orbit by the Sun. If any body ventures past the Hill radius, its Sunward acceleration will be significantly different from the Earth's and it will start to orbit the Sun rather than the Earth.

The Hill radius for the Earth is about 1.5 million kilometers. The Moon's orbit is only about 385,000 km in radius, so it is well within the limits where it could be pulled away from the Earth.

I hope that helps. Good luck!

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