Johannes Kepler, using the extremely accurate astronomical data inherited from Tycho Brahe, and over years of diligent persistence, single-handedly derived the three laws of planetary motion. Without these laws, Sir Isaac Newton might not have realized his law of universal gravitation.
The first serious challenge to the earth-centered universe of the ancient Greeks was Nicolaus Copernicus’s
Tycho Brahe,
Kepler assumed Tycho’s post of imperial mathematician to Emperor Rudolf II
He began the astronomical analysis of planetary orbits almost immediately by attempting to meld Tycho’s data on the orbit of Mars into a Copernican system of simple uniform circular motion about the Sun. Over the next four years Kepler failed repeatedly; Tycho’s data placed the orbit eight minutes of arc outside the predicted Copernican orbit, an error exceeding the accuracy of the measurements by at least a factor of four. Not willing to overlook this difference, Kepler had to assume that the Copernican scheme was seriously flawed. To rectify it he had to abandon the one assumption Copernicus had lifted directly from the ancient Greeks: that the planets moved in circular paths (or combinations of circles) at uniform speeds. By trial and error he discovered that the planetary orbits corresponded to a simple geometrical figure known to mathematicians since the third century
Kepler realized that his first law by itself was incomplete because it provided absolutely no information about how the speed of a planet in its orbit was related to its orbital position. If such a relationship could be found the features of any planet’s motion could be elegantly and succinctly summarized. Although Kepler had no guarantee that such a relationship even existed or could be found, such was his faith in the order of the universe that he proceeded on the basis that it lay hidden in Tycho’s voluminous data. By sheer persistence and ingenuity Kepler revealed another simple law, to be called the second law of planetary motion: During any given time interval, the imaginary line connecting a planet and the Sun sweeps out the same area anywhere along the elliptical path. As a result of this law, it follows that the distance from the Sun to a planetary position multiplied by the speed at that point is equal to a constant, thus giving Kepler his simple relationship. His second law establishes the possibility of accurate astronomical prediction, without resort to the multiplicity of geometric artifices employed by previous systems utilizing circular orbits.
Kepler labored for several years on a book detailing these laws, readying it for publication in 1606. Three more years were required to find a publisher and to raise the money to pay the printing costs, an expenditure he had to assume since no wealthy patron offered support. Printing began 1608, and the book was released the following summer as Astronomia nova (1609; New Astronomy
During the time he was theorizing planetary orbits, Kepler also researched optics, particularly lenses, publishing Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur (1604, also known as Astronomiae pars optica; Optics
Kepler’s first and second laws of planetary motion were discovered by a bizarre combination of blundering intuition and an astute alertness for hidden clues. The laws were phenomenally successful at predicting planetary positions, but Kepler remained dissatisfied because no overall pattern connecting the orbits of different planets existed. Although there was no good reason why the motions of unrelated planets should be connected, Kepler, who was obsessed with the conviction that nature was simple and harmonious, believed a relationship did exist. Consequently, he spent a decade relentlessly pursuing this quest despite the many personal misfortunes that plagued the latter part of his life. (After Rudolf II died, Kepler lost his position at court and was forced to accept a lesser position in Austria.)
After years of unceasing toil, he found that there was indeed a pattern connecting the orbits of different planets: the third law of planetary motion. This law states that the square of the period of revolution of a planet about the Sun is proportional to the cube of the mean radius of the planetary orbit. Produced against the backdrop of European turmoil and personal tragedy, Kepler published Harmonices mundi (1619; The Harmony of the World
Not only are Kepler’s three laws the foundation upon which modern astrophysics was constructed, but the intervening centuries has verified their accuracy for all types of orbits, including those followed by charged particles moving under the action of electrical forces.
Kepler never realized the true significance of his laws, because without differential calculus
Although Kepler is honored for his work in astronomy, a subtle and perhaps even more important contribution was his innovative attitude toward astronomy, an attitude destined to have profound effects on the future of the physical sciences. This was a shift from attempting to fit the universe to preconceived geometrical models to a new emphasis on the mathematical relationships underlying the observations. His successful attempt to formulate physical laws in mathematical form, based on precise quantitative data, established the equation as the prototypical essence of physical law.
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Applebaum, William. “Keplerian Astronomy after Kepler: Researches and Problems.” History of Science 34, no. 4 (December, 1996): 451. Applebaum argues that Kepler was more influential on astronomy in his own time than is commonly thought. -
Casper, Max. Kepler. New York: Abelard-Schuman, 1959. A translation of the 1947 edition of the definitive biography of Kepler and his time, including discussions of his laws and how he arrived at them. Includes an index and excellent bibliography. -
Ferris, T. Coming of Age in the Milky Way. New York: Doubleday, 1989. Chapter 4 of this well-written summary of science history presents a comprehensive overview of how Copernicus, Tycho, and Kepler advanced human understanding of the solar system. -
Hathaway, N. The Friendly Guide to the Universe. New York: Penguin Books, 1994. This entertaining, idiosyncratic synopsis of astronomy, among other areas, explains Kepler’s laws with easy-to-read prose and simple diagrams. -
Koestler, Arthur. The Sleepwalkers. New York: Penguin Books, 1989. An easy to read compendium tracing the evolution of human understanding of astronomy from the ancient Greeks through Isaac Newton. Eleven chapters are devoted to Kepler.
Galileo; Johannes Kepler; Gottfried Wilhelm Leibniz; Sir Isaac Newton.