Will the moon ever finally fall to Earth without some outside force acting upon it?
If the moon's orbit were decaying -- many satellite orbits do in
fact decay -- it would indeed crash into Earth one day. But the
average orbital distance from Earth is increasing, not decreasing,
for reasons that have nothing to do with the relative masses of the
Earth and moon. Because the Earth rotates a bit faster than the
moon orbits Earth, the so-called "tidal bulge" is always slightly
ahead of the moon. This actually exerts a force on the moon that
increases its total kinetic energy that, in turn, increases its
the earths gravitational pull isn't that strong, the moon just orbits.
(Another reply) It certainly does fall! It is constantly accelerating towards Earth (note 1). If there were no Earth gravity, the Moon would go in a straight line. As it is, the Earth's gravity is strong enough to force the Moon to move approximately in a circle - really in an elipse, around the Earth.
Note 1: Acceleration means a change in velocity; to specify velocity, you need the speed (magnitude), and the direction. Thus, if the direction of the speed changes, there is acceleration.