Shining a light on Harriot and Galileo: On the mechanics of reflection and projectile motion

Abstract

Decades before Newton’s Principia ushered in the age of modern science, Aristotelian physics faced a serious challenge against its weakest point, in the quest to construct a new theory of projectile motion. Yet how were such new principles of motion conceived, without reference to an established theory of mechanics? This paper explores the conceptual space between the rejection of Aristotle’s physics and the appearance of Newton’s physics in which people such as Harriot and Galileo sought new ways to understand mechanical phenomena. This paper seeks to show that both Harriot and Galileo looked to the (early seventeenth-century) zeitgeist of accepting the law of reflection as a law of oblique projection-rebound for all material bodies, for their foundational (non-Aristotelian) conceptual resource. The kinematics and dynamics of light’s compound, oblique motion had been developed over centuries within optics, and constituted the ‘ideal’ resource for novel analyses of oblique projectile motion. Whereas Harriot’s inclusion of air resistance restricted the generalizability of optical principles to his simplest case, the upright parabola, Galileo’s idealized analysis of projectile motion in a vacuum represented all cases of projectile motion as upright parabolas. He was thus able to generalize these optical principles to projectile motion per se.

The English Galileo and His Vision of Projectile Motion under Air Resistance

“…us, while Galileo occupies a central position in the history of scientific developments, the name and the accomplishments of Harriot are far less established, and a systematic investigation of his nachlass comprising thousands of folio sheets has come into focus only recently. In addition to the extensive account [1] of Harriot and his work on projectile motion, the articles [2,3] also fill this historical gap by shedding light on the discoveries of the English Galileo.…”

“…e curves shown in Figure 1 are based on the numerical solution of the differential equations resulting from Newton's law for projectile motion under air resistance quadratic in speed, as will be detailed in the last section. Although the modern approach is certainly far beyond the theoretical and computational tools available to preclassical mechanics, in his more advanced models, Harriot was able to construct ballistic trajectories that are astonishingly similar to those shown in Figure 1, see the folios shown in Figures 8 and 9 of [2], Figure 58 of [1], and Figures 4 and 5 of [3]. One of the specific aspects of the practitioners' knowledge that Harriot tried to address in his models was the asymmetry of the trajectory in the following form.…”