Will the moon ever fall to Earth?
Of course not. But consider this.
As the moon continues along its orbit around the Earth, its gravity influences things on Earth. The most prevalent phenomenon associated with this is the cyclic changes in the water level of the oceans. Scientists refer to this as “the tide.” The difference in water level between high tide, when the moon is overhead, and low tide, when the moon is on the other side of the Earth, can be as much as 25 feet. Think of that. All that water being pulled up and moved around by the gravity of the moon.
So what? Consider this:
Keeping all of these millions of gallons of water flowing in and out obviously requires a lot of energy. Because of friction, the water must be continually supplied with energy to keep moving as it does. Since the water is being pulled around by the moon, we can conclude that the energy which keeps the tides flowing in and out is the kinetic energy of the moon moving through space with respect to the Earth.
Pulling all of this water around creates a drag on the moon. This means, unless something else is pulling on the moon to speed it up, that the moon is slowing down with respect to the Earth. When an object in orbit slows down, it moves closer to the body which it orbits. This is because objects stay in orbit because of their their mutual gravitational attraction, balanced against the centripetal acceleration from them trying to continue in a straight line. When the object slows down, the object has to travel in a tighter circle to generate the centripetal force to counteract the gravitational forces.
Ultimately, the moon will continue slowing until moving at the same speed as the Earth. At this point, the slowing will stop and the moon will be in a geosynchronous orbit. The moon will stop slowing because it will will no longer be pulling water around if it is in the same place relative to the Earth. The area beneath the moon’s stationary orbit will experience daily eclipses and would most likely be continually submerged.
This will not happen for probably billions of years. The moon has a great deal of kinetic energy. Moving the tides around takes a comparitively insignificant amount of energy. However, since nothing is speeding the moon up, this eventuality is inevitable.
On the plus side, traveling to the moon would be relatively minor ordeal since it would be much closer, and may pull up some of our atmosphere. We would still have to pressurize it to use it, much like in an airplane, since the moon lacks the gravity to keep up the necessary atmospheric pressure to prevent our blood from exploding.