Naturally Accelerated Motion

Abstract

The motion of falling bodies was explored by Salviati, Sagredo and Simplicio in the First Day of Galileo’s Dialogues Concerning Two New Sciences, but this first science was only pursued insofar as it elucidated the second science, the strength of materials. For example, they considered how falling objects are affected by the specific gravity and the cohesion of the material through which they fall. Now, in the Third Day, our friends address the science of falling bodies in earnest, with an eye toward eventually understanding the motion and force of artillery. Salviati begins by referring his listeners to a text in which the author (Galileo himself) defines uniform motion and naturally accelerated motion. These two classes of motion will eventually play a critical role in his subsequent treatment of projectiles. But before simply accepting Galileo’s theory of falling bodies, Sagredo and Simplicio offer a number of objections which Salviati must address. These objections draw on both common-sense observations of falling bodies and the paradoxes involved in Galileo’s attempt to mathematically model their motion. Are they satisfied by Salviati’s reply? Are you?

See now the power of truth; the same experiment which at first glance seemed to show one thing, when more closely examined, assures us of the contrary.

—Galileo Galilei