Deriving Kepler's Laws as Kepler Did -- From (simulated) Noisy Data

Traditional curricula are imbued with assessment methods that emphasize answers. Students do problem sets, engage (or not) in labs, and take exams with the goal of getting the right answers. What we actually desire is for students to understand and incorporate into their mental tool kits the processes by which answers can be derived. What is needed, then, is a process-based, rather than an answer-based curriculum.

I will demonstrate this approach with the common first-year physics problem of Kepler’s Laws of Planetary Motion. Rather than lecture on ellipses and semi-major axes, and writing down the three laws, I provide the students with a computer simulation (by Dr. Kevin Lee, Univ. of Nebraska) that illustrates the transit method for detecting extrasolar planets. The simulation has many adjustable parameters (the noise level and integration time of the observations, the star, planet, and orbital parameters, etc.). I don’t mention Kepler, or say there are three laws. I give them a list of suggestions for things to try — first to understand what each of the parameters means, then to vary the parameters looking for patterns in the noisy data the simulation produces, to try and express those patterns in a mathematical form, and finally, to test their predictions with new simulations.

It takes 20 minutes to describe Kepler’s Laws in a lecture. It took my Quest University Canada students 3.5 hours with the simulation but, in the end, they got up and wrote Kepler’s three laws on the board, deriving them, as Kepler did, from “observations”. These students may not remember a year from now where the “G” goes in Kepler’s Third Law any better than students who “absorbed” this from a lecture. However, they know they can find patterns in noisy data, cast those patterns in a mathematical form, and use the result to predict the behavior of a physical system. They have constructed a bit of knowledge for themselves and understand a bit more fully the process of doing science.