I felt kind of funny doing it this way. I had no problem with a vs. r but the a vs. Mo. I would hope my students would say, "how do we know these are the masses?"---uh yeah, about that . . . well you see . . .
It is one of those chicken and the egg things. If I could use the mathematical model for the universal law of gravitation then I could approximate the mass of the earth to get a round about number for G. But the only reason we want to get G is develop the mathematical model . . . now I really appreciate the genius of Newton. This feels very contrived.
Should I . . .
a) do this exact same lab and hope I don't get found out.
b) replicate the a vs. r part and lead students through a discussion that it is logical to think that a is also related to the mass of the central body (different masses on a trampoline and the effects on a ball bearing's acceleration).
I feel less guilty with option b) using planetary data instead of satellite only because I have a simulation. Additionally I would have the students find the relationship between the period and the radius (Kepler's law) and have them compare this to the harmonic relationships we found at the beginning of the year for a pendulum and in energy for a spring.
So then the next question is should we replicate the Cavendish experiment using a modeling approach somehow or should I have the students approximate the value for G by solving for the mass of the earth (radius known, assume volume of a sphere and the density of sand) and using g = GM/r^2?????
Really where am I going with this? I feel like this isn't really modeling anymore and that I'm back to quasi-lecturing and lobotomizing their creativity. Hmmmmmmm. Maybe I should just stop with the inverse square nature and have students investigate in real labs somehow other inverse square phenomena like light, sound, etc. I don't know. I'm just rambling now.