(3) We do an end run. We do orbits using a spring force center:
Another option, if you're interested in models: You can build a
model of the general relativity version of gravitation:
geodesics.
Masking tape is the key ingredient.
-- If you just want to model "some" geodesic deviation, the
curvature of cups and saucers will suffice.
-- If you want to model the spacetime curvature associated
with planetary orbits, you need to make some darts, as
described at http://www.av8n.com/physics/geodesics.htm
Making the darts is too tricky for high-schoolers to do on
their own, but if you make the darts in advance the students
can arrange them to represent the gravitational field.
I realize that this is non-responsive to the letter of the
request concerning F= G (m1m2/d^2) ... but perhaps is makes
contact with some of the spirit.
It certainly makes contact with yesterday's discussion about
unforced acceleration; the geodesics in the model can (at
least in one school of thought) be thought of as free particles,
free of any forces, yet they accelerate relative to one another.
If you place the darts on transparent acetate you can put it on
an overhead projector and work with the model in real time in
front of a large audience.
The demo is really quite easy to do. It is also very informative.
There's probably not one physicist in 100 (except those who have
seen this demo) who have a good intuitive understanding about
the spacetime curvature near a gravitating planet. Just try
asking people "in what direction is the curvature?" For sure
some of them know, but not many of them.