Subject: How do moons maintain their orbit, given gravity and other forces

I have never really understood how the moon orbits the Earth, for milllions
of years, without either shooting into outer space or falling to earth.  How
is the exact delecate balance not interrupted by the moon's moving closer or
farther from the Earth, or by the Earth's moving closer or farther from the
sun.   How do all the moons of various sizes, densities, etc., around a
planet like Jupiter, remain in orbit without affecting each other's orbit or 
running into each other.  
   I am asking just because I have been curious about this and have not found 
an answer.  

Re: How do moons maintain their orbit, given gravity and other forces