Inspired by the heliocentric (sun-centered) theory of Nicholas Copernicus (1473 – 1543), Swedish-Danish astronomer Tycho Brahe (1546 – 1601) devoted much of his adult life to daily observations and systematic measurements of the motions of Mars and the other known planets. Upon his death, most of Brahe’s observational data was inherited by his German assistant, Johannes Kepler (1571 – 1630), who carried on Brahe’s work.[1]

During the early 17th century, Kepler painstakingly developed his three laws of planetary motion, largely by trial and error. At first he attempted to describe Brahe’s observations with circles, but to no avail. He then tried oval shapes, and finally ellipses which seemed to work.[2] Kepler’s three empirical laws of planetary motion describe the observed elliptical motions, velocities, and orbital periods of the then known six planetary orbits around the Sun.[3]

Kepler’s first law (the “Law of Ellipses”) was published in 1609 and states that the planets move around the Sun in elliptical orbits (rather than circular ones), with the Sun at one focus of each ellipse (Figure 5). This empirical law contradicted both the conjectures of the Greeks and of Copernicus, that such orbits are circular.

Kepler’s second law (the “Law of Equal Areas in Equal Times”) was also published in 1609 and states that each planet moves around equal areas of its elliptical orbit during equal time periods (Figure 6). For example, on Figure 6 the shaded area between points A, B, and the Sun is equal in size to the shaded area between points C, D, and the Sun…and each planet traverses the arc from A to B in the same time period as it traverses the arc from C to D.

Kepler’s third law (the “Law of Harmony”) was published in 1619 and states that the square of each planet’s orbital period (P) is equal to the cube of its average distance (D) from the Sun (Chart 7). This empirical law has been called a “law of necessity” for any satellite system.[4] Why? Because the equilibrium of orbital motion is not an arbitrary occurrence, but rather is a mathematical consequence of the mass and orbital velocity of each opposing orbiting body, and their distances apart.[5]

Kepler’s three laws of planetary motion gave the Copernican heliocentric hypothesis the firm empirical and geometrical foundation which it needed. But Kepler had no idea what caused the motions which he described, nor why his laws worked. He even suggested that the motions of the planets were caused by the wings of angels.[6] It remained for Newton a few decades later to explain (mathematically and physically) how and why Kepler’s laws actually worked.