Gravity, Calculus & Planetary Motion

My view is that youngsters with well above average aptitude and inquisitive minds should be exposed to applied mathematics, including the calculus and differential equations, at an early age. Not that they should be expected to master these subjects, but they should acquire an appreciation for the role that applied mathematics plays in explaining the physical world. This requires an ability to follow the mathematical arguments and proofs — a lesser standard than being able to furnish the proofs. It’s somewhat analogous to being able to read a novel, rather than write one. But even to read one must know the language, and calculus is the language of physics. How best to motivate a youngster to study this material is the question.

My approach is to focus on the particular of problems that spurred the development of applied mathematics in the first place: namely, the motions of the Solar system. Isaac Newton developed the calculus primarily to explain these motions and in the process formulated his three laws of motion, which form the basis for the branch of physics known as classical mechanics (or dynamics). An example of the adage: “Necessity breeds invention”.