Johannes Kepler / KEP-lur /
German Astronomer and Mathematician
Mathematics Ranking 17th of 46
Illustration from Kepler’s book New Astronomy,
where he is working out elliptical orbits of the planets. Issued by Germany in 1971 to commemorate
the 400th anniversary of his birth.
Johannes Kepler settled in Prague in 1599, becoming Tycho Brahe’s assistant and later court mathematician to the emperor. Kepler’s analysis of Brahe’s planetary observations enabled him to discover the three principles governing planetary motion, by which he clarified the spatial organization of the solar system. The first two laws recognized the elliptical orbits of the planets; in Harmonices Mundi (Harmonics of the World, 1619, 78 pages) he expounded the third law of planetary dynamics, relating the distances of the planets from the sun to their orbital periods.(1) This foreshadowed the general application of the scientific method to astronomy, specifically helping Isaac Newton in his exposition of universal gravitation, which affects all of the material bodies in the physical universe.
Finally, he founded modern optics by presenting the earliest correct explanation of how human beings see.
Born in the town of Weil der Stadt, then a “free city” within the Holy Roman Empire, Kepler was born prematurely, the offspring of an unhappy marriage. His father was a mercenary soldier, his mother the argumentative daughter of an innkeeper. Small in stature, Johannes never enjoyed robust health, but his superior intelligence was recognized even when he was a young child. Coming from a poor family, he would have received no education had not the dukes of Wurttemberg adopted the enlightened policy of providing generous scholarships for the bright sons of their impoverished subjects. With such help, Kepler in 1587 was able to attend the University of Tubingen. He had the good fortune to study astronomy under Michael Mastlin, a professor who was convinced that the Copernican astronomical model was basically true: The Earth is a planet that rotates daily around its own axis and revolves annually around the sun.
In 1595, Kepler became a math teacher in the Lutheran high school of Graz, Austria. The same year, a spectacular idea flashed through his mind. Ancient Greek geometry had proved that there were only five ways to construct a three-dimensional solid using regular polygons: the tetrahedron (pyramid), the cube, the octahedron (formed by eight equilateral triangles), the dodecahedron (12 pentagons), and the icosahedron (20 equilateral triangles). The ancients knew that these five solids could be enclosed in a sphere, and that there can be no additional regular solids. Excited by a vision of mathematical harmonies in the skies, a vision he derived from the philosophy of Plato and the mathematics of the Pythagoreans, Kepler tried to relate planetary orbits with geometrical figures. According to Copernican astronomy, there were six planets, whose orbits were regulated by the turning of invisible spheres. But why were there only six planets and not nine or one hundred? Was the cosmos so constructed that one of the five regular solids intervened between each pair of the unseen spheres, which carried the six Copernican planets? This nest of alternating planets and regular solids constituted the main theme in Kepler’s Cosmographic Mystery of 1596. The Platonic and Pythagorean components in Kepler’s conception of celestial harmony, however mystical in origin, helped lead him to the three principles of planetary motion now known by his name.
Kepler sent copies of the Cosmographic Mystery, his first major work, to a number of scientists, including Tycho Brahe, later to become the imperial mathematician of the Holy Roman Empire. Four years later, Brahe invited him to join his research staff in the observatory outside Prague. Kepler now had access to Brahe’s incomparable collection of astronomical observations, the result of decades of persistent, careful work by the greatest naked-eye observer of the heavens and the leader of a highly qualified team of astronomers.
Optics–Structure and Function of the Human Eye
As a member of the team, Kepler was to investigate the planet Mars. But before he could use the raw observations, Kepler felt that he had to solve the problem of atmospheric refraction: how is a ray of light, coming from a distant heavenly body located in the less-dense regions of outer space, deflected when it enters the denser atmosphere surrounding Earth?
Kepler published his results in 1604. His analysis of the process of vision provided the foundation for all of the advances in the understanding of the structure and function of the human eye. Kepler wrote that every point on a luminous body in the field of vision emits rays of light in all directions, but that the only rays that can enter the eye are those that hit the pupil, which functions as a diaphragm. He stated that the rays coming from a single luminous point form a cone, the circular base of which is in the pupil. All of the rays are then refracted within the normal eye to meet again at a single point on the retina, identified by Kepler as the sensitive receptor of the eye. If the eye is not normal, the second short interior cone comes to a point not on the retina but in front of it (nearsightedness or myopia) or behind it (farsightedness), causing blurred vision. For more than three centuries (c. 1300–1600), eyeglasses had helped older persons to see better. But nobody before Kepler was able to explain how these little pieces of curved glass had worked.
By 1609, Kepler demonstrated that the orbit of Mars is an ellipse. He extended this idea to all the planets and it became his first principle of planetary motion—all the planets rotate around the sun in elliptical orbits. The second principle required an explanation of uniform motion for the planets, given his new idea of elliptical orbits. The pre-Keplerian dogma that permitted only circular paths entailed the concept of uniform motion—i.e., the moving body or point must traverse equal arcs in equal intervals of time. Such a conception of uniform motion as measured along an arc was, of course, incompatible with an elliptical orbit. But Kepler found an alternative form of uniformity.
This new uniformity equated equal areas with equal times. With the sun remaining stationary in one focus of the ellipse, the planet, while revolving along the periphery of its elliptical orbit, would sweep out, in equal intervals of time, equal areas of the ellipse, not equal arcs along the periphery of the ellipse. In other words, the straight line joining the sun and any planet sweeps out equal areas in equal periods of time. (This means a planet’s speed increases as its distance from the sun decreases.)
In 1619, ten years after Kepler published his first two principles of planetary motion (the elliptical orbit and equality of areas), he published the Harmonics of the World, which expounded his third principle, which related a planet’s mean distance from the sun to the time it takes to complete its elliptical orbit around the sun. The cube of the distance proved to be in a constant ratio to the square of the time required for all the planets to complete such an orbit. “The enunciation of this rule (which is sometimes called the 3/2 ratio) completed Kepler’s contribution to the understanding of planetary motion.”(2) This foreshadowed the general application of scientific method to astronomy, specifically helping Isaac Newton in his exposition of universal gravitation, which affects all of the material bodies in the physical universe.
(1) Judy Pearsall and Bill Trumble (editors), The Oxford Encyclopedic English Dictionary (New York, 1996), p. 777.
(2) Encyclopaedia Britannica, Macropaedia, Volume 22, 1993, 15th Edition, pp. 485.