I hope you understand that the force of gravity equation does not account for the acceleration of the moon as it rotates around the earth. The equation doesn't actually assume "that the earth travels in concentric spheres", it only explains what the force of attraction between two bodies of mass is. Any, and all, bodies of mass exert a gravitational attraction to one another regardless of whether it's "moving in concentric circles" or it's "at rest". Those people are attempting to disprove the existence of a moon by severely misrepresenting what the various equations of physics actually imply, which is stupid.
If you do a proper analysis of the forces acting on the moon, you'll find that the force of the moon spinning around the earth exceeds the gravitational force, and as such the moon is actually moving slightly further and further away with each passing year (i think about half an inch?).
So yeah, eventually, the moon will break free from the earth's gravitational pull, and we'll have no more moon.
With your argument, I could say that we're moving closer and closer to the sun, and eventually we'll be incinerated when we get too close. So yeah, we'd be dead by now. Unless you think the world was created last thursday, that is.
Also, that scam has already been tried. The cake is a lie, all the time.