Well, if we double the distance, we can use this ratio to figure out
what's going on with f₂.
Here I've called the radius for f₂ twice the initial radius r₁.
I've made the exponent -2, because it's proportional to 1/r²,
so the 2 comes from it being r² and the negative comes from this being in the denominator.
When we work this out  we find that f₂ is only 1/4 of f₁.
But I'm still confused. How could a force be mutually attractive?
That means that this apple will be drawn to the center of the earth, which is exactly below it--
so the force will go that way--and the force on the moon will also be
towards the center of the earth.
How could a force pointing inward causing an object to move in a circle?
Seems like maybe you'd want a force that pointed that way or that way.
Let's do a little thought experiment with this apple,
and maybe that will help us see how an attractive force could actually cause
and object to perhaps move in a circular path.
