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Originally, we had a single, long Maple
worksheet that first showed the effective potential, and then showed the orbit for any
set of physical parameters. Unfortunately, without intervention, many students did
not immediately see how these two different graphical representations were related
to each other. We now address this issue by interposing the following kinesthetic
activity. A single student, carefully chosen to be someone who will be comfortable
with being put on the spot, is asked to come to the front of the room to act out the
part of the orbiting planet while the teacher plays the part of the sun. Most students,
on their first attempt, will walk around the teacher - after all, this is what planets do.
When directed to refer to the effective potential diagram, with its apparent classical
turning points, most students, on their second attempt, will move towards and away
from the teacher in a straight line, with an embarrassed laugh for the obvious
absurdity of their motion - this is not what planets do! It takes a significant class
discussion to bring out the role of the angular momentum in resolving the paradox.
After this classroom experience, most students are more effective at using the
computational simulation to explore the shape of the orbits in depth. For example, a
common question that now arises is how one knows where in the orbit the minimum
and maximum radii occur.

==== Comments by Mary Bridget Kustusch (post-doc and co-instructor, Winter 2012) ====
This year this activity was used more as a wrap-up than as a transition point. We had already talked about most of these issues in class already. Asking two students to act out the motion still allowed us to hit the main idea - that this is a 2D situation even though it looks 1D - but it didn't have the same kind of power that I think it would have if we hadn't already "given the game away."