  Kepler's 2nd law, the law of the areas, is usually taught in passing, between
the 1st and the 3rd laws, to be explained "later on" as a consequence of
angular momentum conservation. The 1st and 3rd laws receive the bulk of
attention; the 1st law because of the paradigm shift significance in
overhauling the previous circular models with epicycles of both Ptolemy and
Copernicus, the 3rd because of its convenience to the standard curriculum in
having a simple mathematical statement that allows for quantitative homework
assignments and exams. In this work I advance a method for teaching the 2nd law
that combines the paradigm-shift significance of the 1st and the mathematical
proclivity of the 3rd. The approach is rooted in the historical method, indeed,
placed in its historical context, Kepler's 2nd is as revolutionary as the 1st:
as the 1st law does away with the epicycle, the 2nd law does away with the
equant. This way of teaching the 2nd law also formulates the "time=area"
statement quantitatively, in the way of Kepler's equation, M = E - e sin E
(relating mean anomaly M, eccentric anomaly E, and eccentricity e), where the
left-hand side is time and the right-hand side is area. In doing so, it
naturally paves the way to finishing the module with an active learning
computational exercise, for instance, to calculate the timing and location of
Mars' next opposition. This method is partially based on Kepler's original
thought, and should thus best be applied to research-oriented students, such as
junior and senior physics/astronomy undergraduates, or graduate students.
