It DOES continue to accelerate, however due to it's angular motion, the direction that the moon accelerates is constantly changing so it's not a linear acceleration.
Grossly simplified, it's the same thing as putting a weight on the end of a string and whirling it around your head. The force you feel on your hand (the tension in the string) is the force of gravity. If you whirl the weight around harder (increasing your simulated gravitational pull), the weight goes faster. Let go of the string (simulating setting earth's gravity to zero), the weight flings itself off on a direction almost exactly 90 degrees away from the angle the string was originally stretched out, because that's the weight's actual motion is always 90 degrees away from the direction it's being accelerated.
Think about it this way - At one point of an orbit, the moon is being accelerated towards the earth, and let's call that direction "left". Imagine the moon at the 3-oclock position on a clock. For the next 90 degrees of orbit, there will be some acceleration "left". The exact amount is the sin of the angle away from the original position. In any case, the moon has had 90 degrees of orbit with a "left" acceleration. After that 90 deg is completed (moon at the 12-oclock position), the moon can be considered to be on the other side of the earth, and is now being accelerated back to the "right". By the time the moon is exactly 180 degrees on the other side of the earth (at the 9-oclock position), it's had exactly the same amount of acceleration both left and right, and this is the inherent property of an orbit, namely that in a perfect situation (no tidal forces, no drag, no third object interference, etc), the orbit will continue indefinately at the exact same energy level. In a perfectly circular orbit, this would mean that at any point in time, the moon would always have the same velocity and height above the earth. The only thing that changes is the direction of that velocity, because the earth is always pulling the moon in a direction 90 degrees away from it's motion.
If you still don't get it, you never will without a good textbook on basic orbital mechanics and someone to explain it with diagrams and strings with weights attached to them. I haven't gone into the mathematics involved because while simple, they require a good solid understanding of geometry, trigonometry and Newton's laws. Understanding vector mathematics helps too, because it's all easy to understand if you know that a vector is a speed plus a direction.
Sigh... Professor eagl now tries to describe vectors to his class without a blackboard.
Imagine an arrow. The length of the arrow is the speed, and where the arrow is pointing is the direction. Forces on a vector pull from the pointy end, and always result in acceleration of some type. If the force pulls along the shaft of the arrow, the arrow speeds up or slows down. If the arrow is pulled at an angle though, it turns too. Imagine then this arrow being pulled at the pointy end exactly 90 degrees off of the arrow's direction. Since there's no pull to "stretch" the arrow, it doesn't speed up or slow down, it simply turns. Now imagine the moon is this arrow zinging around the earth. There's no pull back or forth around the shaft, so the length (speed) of the arrow doesn't change. The pull is always 90 degrees off, so the arrow just turns. The speed of the moon simply determines it's orbital height. Elliptical orbits are slightly more complicated, but mathematically a circular orbit is merely a special type of elliptical orbit anyhow.
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eagl <squealing Pigs> BYA
Oink Oink To War!!!
