Originally posted by lausey
Thinking about it, the Earth-moon system will certainly become geosynchronous, but is the conclusion correct that by that time there would be not be enough energy in the moon's orbit for them to come together?
It all depends how far apart and how fast they are going at the time that they become geosynchronous. Anyone done any calculations on this?
It seems there are some serious misconceptions about gravity and orbits going on in this thread.
1. Everything else being equal, the moon would continue to orbit the earth at a fixed distance forever. That is a basic law of conservation of momentum.
2. The moon is pulled away from the earth due to angular momentum and pulled towards the earth by gravity. These two forces are in balance and are stable ie if the moon gets closer to the earth the force pulling it away becomes significantly stronger, and if it gets further away the same force becomes significantly weaker. This variation is greater than the variation in gravity, thus the moon will always stick to its orbit.
3. Tidal forces result in geosynchronization. The moon has already been forced into synchronization causing it to always face the same side towards earth. The moon is going slower than earths rotation, so the tidal forces are causing the earth to slow down the earths rotation and speed up the moons orbit. The result is the moons orbit gets further away from the earth. Once they are synchronized, the moon will not magically fall to earth, it will continue to orbit at a given distance.
http://en.wikipedia.org/wiki/Orbit_of_the_Moon#Tidal_evolution
According to wikipedia, all things being equal we have another 50 Billion years to go, but since the oceans will have evaporated long before that, it might take much longer.