Deriving and applying Newton’s PQRST formula with pre-service phyiscs teachers

Abstract

One of Newton’s greatest scientific achievements was to show that Kepler’s first law follows from the assumption of an inverse-square central force. Despite its importance, this connection is rarely taught in physics courses at introductory level due to the mathematical complexities involved in the proof. A possible didactic solution to this problem is to focus on a conceptual understanding of Proposition VI of Newton’s Principia. In this paper, we report a study conducted with the goal of teaching pre-service physics teachers key aspects of Proporsition VI, as well as its application to determine the force law, given the orbit shape and the sun’s position. Our findings consist of students’ interpretations and difficulties when trying to understand Newton’s original reasoning.