Satellite is in low orbit around the Earth

[Mentallic]

I've read that if a satellite is in low orbit around the Earth, the increased friction due to the atmosphere causing the satellite to slow down and finally fall back to Earth. What if a large celestial body such as the moon is slowed down by some means? Will it eventually fall to Earth?
I suppose that if the moon is slowed down slightly, it will slowly, but surely, fall to Earth. While a larger deceleration will cause the moon to fall to Earth faster. Am I correct here?

 

[maverick_starstrider]

Well the moon doesn't encounter air resistance (being in space an all) however its orbit is slightly mucked about with (the physicsy word is perturbed) by other celestial bodies. And no, the moons orbit is not perfect and eventually (in billions of years) the moon will either collide with the Earth or be flung from its orbit (currently it looks like it's going to collide however a lot can happen, like a colliision with a stray comet or the like, in a billion years). However, I wouldn't lose sleep over it. It's very likely our sun might fizzle out before this ever happens ;)

 

[Mentallic]

And why will this collision eventually happen? (don't worry though, no sleep will be lost. I would merely become psychotic because of all the nightmares)

By an imperfect orbit do you mean it is elliptical? I never quite understood how this works either. While the moon is orbiting, when it gets closer to the Earth on the minor axis of its orbit, the centripetal force would need be greater here wouldn't it? because the gravitational force is greater since the moon is closer to the Earth and since the moon manages to orbit into the major axis, it must have been going faster during its path through the minor axis. I don't understand how the velocity of the moon would increased...

 

[nooma]

when in an eliptical orbit an objects velocity (lets discount direction and focus on speed for this) differs at different points due to the centripetal force. This is such that it is going the fastest when it is closest to the planet and slowest at the point farthest away.

 

[Mentallic]

The centripetal force is the dependant of the velocity the moon is travelling, and you're trying to tell me the force is the independant in this case? Yes I realize the moon would be going fastest when nearest to the Earth because in order to get further away again it must have a higher centripetal acceleration and this is directly proportional to v^2 if I remember correctly.

 

[A.T.]

the centripetal force would need be greater here wouldn't it? because the gravitational force is greater

The gravitational force is the centripetal force.

I don't understand how the velocity of the moon would increased...

This is conservation of angular momentum. Distance to the center of rotation times velocity (perpendicular component) must stay constant: http://en.wikipedia.org/wiki/Angular_momentum#Definition

 

[maverick_starstrider]

No, it's not because it has an elliptical orbit but because the passage of say Jupiter or saturn at certain times messes up the moons orbit the slightest bit (since the earth-moon orbit isn't REALLY a closed system) and eventually all these "perturbations" will cause the orbit to decay. There are also other, more subtle, factors that cause the decay as well.

 

[D H]

And no, the moons orbit is not perfect and eventually (in billions of years) the moon will either collide with the Earth or be flung from its orbit (currently it looks like it's going to collide however a lot can happen, like a colliision with a stray comet or the like, in a billion years).

Currently it looks like the Moon is retreating from the Earth at 3.82 centimeters per year due to tidal interactions. In the far, far future it looks like the Moon will stop this retreat when the Earth-Moon separation grows to about 135% of its present value. The Moon most likely won't crash into the Earth.