Kepler Motion Viewed from Either Focus

Abstract

In the first chapter we analyzed a Babylonian planetary text and saw that the Late-Babylonian astronomers had shaped arithmetic into a powerful tool for addressing astronomical problems. In contrast, the Greek planetary models, qualitative as well as quantitative, employed geometrical models with moving parts and a knowledge of how to combine velocities. We call such models cinematical, for cinematics is the branch of mathematics concerned with motion but without regard to masses and forces. Finally, dynamics—the study of the behavior of a system of masses in terms of the forces that act upon them—was created in its useful form by Isaac Newton (1642–1727). In his Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy), usually called the Principia (1687), he formulated the basic rules of dynamics and successfully applied them to a variety of physical problems, among them that posed by the solar system.