CalG
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The "cause and effect" in the above statement is flawed.Actually, the Moon is moving farther away from the Earth, as the tidal drag on the Earth is slowing it down in it's orbit, stealing energy from it, and that makes it move away from the Earth. Billions of years ago, the Moon was much closer to the Earth, but the tidal drag has caused it to recede to it's present orbit. So at some point, the Sun's gravity will be strong enough disturb it's orbit sufficiently to break free of the Earth's gravitational influence and flung somewhere else in the solar system.
If the moon STOPPED it's motion, it would fall to the earth. Just as if the EARTH stopped it's orbiting motion, it would fall to the sun.
Gravity is an attraction, an orbit is continually missing the target!
If this were not the case, "abandoned" satellites etc. would "fall" away from the earth. and they do not.
The earth moon system as it relates to tidal induced velocities is that the earth is SLOWING it's rotation speed, and the MOON is gaining speed. That velocity increase to the moon, expands it's orbital radius. (pushes the moon out and away from the earth and increasing it's orbit path distance).
It is predicted that eventually, the earth rotation speed and the moons orbit around the earth will coincide.
But don't hold your breath waiting for the day. The aliens will have returned by then.