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

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.