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Now, this is a huge claim for Newton to be making--
that there is some mysterious entity pulling apples to the ground,
which he calls some force--iin fact, it calls it "gravity"--and that that same force somehow
causes the moon to go in a circular orbit around the earth.
Now, Newton calls this force gravity, and there's a few properties he claims it has.
He calls it a mutually attractive force, which means that all objects,
anything with mass, attracts every other object with mass.
So, right now my hand is attracted to this pen with some gravitational force,
just as he claims the earth is attracted to the moon.
Next, he claims this force is proportional to 1/r².
When I say "r", I mean the separation distance between the center
of the two things we're talking about.
We talked about this idea of proportionality last time,
and we know that 1/r² means that if we were to, say, double this distance
what would happen to the force?
Use your knowledge of proportionality to answer this question as best you can.