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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)