Conic Sections and Projectile Motion

A diagram that shows how a projectile around the earth would go from a semi-parabola to a circle around the earth to an ellipse, and so on. Beautiful. Because Newton’s Law of Universal Gravitation implied the conic sections as orbits.

This diagram is from “The Flight of Newton’s Cannonball” (May 2018, American Journal of Physics, 86(5):338-343, DOI:10.1119/1.5027489) by William Dean Pesnell.

Galileo had first analyzed projectile motion, but Newton went far beyond Galileo’s analysis. Here is Galileo’s diagram of projectile motion from the section The Fourth Day of his Two New Sciences. In the Fourth Day, at the beginning of the section, Galileo goes through the beautiful proof of Apollonius of what we know now as y = x^2 for a parabola.