The Laws of Planetary Motion (A Teaching Method Inspired by the History of Physics)

Abstract

In high school, and also in introductory physics courses in higher levels of schooling, the law of universal gravitation of planets is introduced by postulating Johannes Kepler’s three laws, and later Isaac Newton’s law of the inverse of the square of the distance to the Sun. The justification of the laws is only achieved in advanced courses in mechanics. We present material to teach the law of areas and the law of attraction, which is inspired by Newton’s analysis of motions under central forces, as done in Mathematical Principles of Natural Philosophy. The method is geometric, so that the dynamics behind the laws can be discussed with a ruler, triangles, and compass, or some software, without appeal to equations, and can be used on levels of instruction that dispense with analytic treatment.

Isaac Newton’s early documents on circular motion: can the dynamic reasoning in the “Principia” be found in them?

“…A signature of the mature dynamics described from De Motu on is that the geometric segments are "animated" in the sense that they are associated with a dynamic motion described by a moving point mass. It means that an orbit can actually be drawn by a graphic program, such as GeoGebra [23], or by numerical computation [14], or by hand (as certainly did Newton). The treat De Motu contains this structure, but not yet in the sophisticated form it attains in the Principia.…”