Kepler’s Laws of Planetary Motion Summary

  • Last updated on November 10, 2022

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.

Summary of Event

The first serious challenge to the earth-centered universe of the ancient Greeks was Nicolaus Copernicus’s Copernicus, Nicolaus sun-centered (heliocentric) model, published in 1543 as De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres, 1939; better known as De revolutionibus De revolutionibus (Copernicus) . Unfortunately, because Copernicus, like the Greeks, assumed the planets moved in circular orbits, his theory was inaccurate and offered no practical improvement on the ancient model. Johannes Kepler, by shear dogged persistence over many years, derived the correct mathematical form of planetary orbits—his first law—as well as two additional laws of planetary motion [kw]Kepler’s Laws of Planetary Motion (1609-1619) [kw]Laws of Planetary Motion, Kepler’s (1609-1619) [kw]Motion, Kepler’s Laws of Planetary (1609-1619) [kw]Planetary Motion, Kepler’s Laws of (1609-1619) Science and technology;1609-1619: Kepler’s Laws of Planetary Motion[0540] Astronomy;1609-1619: Kepler’s Laws of Planetary Motion[0540] Mathematics;1609-1619: Kepler’s Laws of Planetary Motion[0540] Physics;1609-1619: Kepler’s Laws of Planetary Motion[0540] Cultural and intellectual history;1609-1619: Kepler’s Laws of Planetary Motion[0540] Austria;1609-1619: Kepler’s Laws of Planetary Motion[0540] Bohemia;1609-1619: Kepler’s Laws of Planetary Motion[0540] Planetary motion, laws of Astronomy;laws of planetary motion Kepler, Johannes

Tycho Brahe, Brahe, Tycho the first person since the Greeks to improve astronomy, devoted his life to the patient observation of planetary motion, measuring this motion with incredible accuracy years before the invention of the telescope. Kepler assisted Tycho during Tycho’s last two years of life, acquiring his voluminous collection of data upon Tycho’s death in 1601. Kepler had long been convinced of the correctness of the Copernican theory, but he knew that it was seriously flawed. He therefore turned his considerable mathematical skills to solving the problem of planetary orbits. To Kepler this was a religious quest; the key to God’s mind was harmony and simplicity manifested in geometric order. To solve the mysteries of the solar system was to understand the grand secret of the universe.

Kepler assumed Tycho’s post of imperial mathematician to Emperor Rudolf II Rudolf II (Holy Roman Emperor) of Bohemia in 1601, a position he occupied until Rudolf’s death in 1612. Although there were royal astrological duties to attend to, the position gave him status, a salary, and, most important, time to pursue his scientific interests. During this most fruitful period of his professional life, he single-handedly founded scientific astronomy and invented instrumental optics.

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 b.c.e. as the ellipse. Kepler’s first law of planetary orbits, building on this ancient knowledge, states that all planets move in elliptical paths, with the Sun at one of the foci of each ellipse. (Mathematically, an ellipse is a curve for which the sums of the distances of any point on the curve from two internal fixed points, the foci, are equal to the sums of distances from the foci to any other point on the curve.)

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 New Astronomy (Kepler) , 1992).

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 Optics (Kepler) , 2000). This work showed that light intensity decreases as the inverse square of the distance from a source, explained the principle of the camera obscura (precursor to the photographic camera), elucidated how spectacles for near and far sightedness worked, explained light refraction by lenses, and showed that the eye’s lens projects an inverted image on the retina. This was followed by another great work on optics, Dioptrice Dioptrice (Kepler) (1611; partial English translation of preface, 1880), which applied the principles discussed in the earlier work to the newly invented telescope.

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 Harmony of the World, The (Kepler) , 1997), with no intended irony.


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 Calculus (invented by Isaac Newton Newton, Sir Isaac;calculus ), the three laws show no apparent connection to each other. The connection was revealed eighty years later when Newton proved that an elliptical orbit is one of the logical consequences of his laws of motion and gravitation. The objective importance of Kepler’s third law to Newton is inestimable, as it provided the final clue for Newton to deduce and verify his law of universal gravitation.

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.

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">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.
  • citation-type="booksimple"

    xlink:type="simple">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.
  • citation-type="booksimple"

    xlink:type="simple">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.
  • citation-type="booksimple"

    xlink:type="simple">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.
  • citation-type="booksimple"

    xlink:type="simple">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.
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