Kepler's Observations

Mysterium Cosmographicum

center piece of Kepler's 1596 The secret of the universe
Kepler's sketch shows an ordering of the five planetary orbits in terms of the nesting of the five regular solids.

Published in July 19, 1596, Johannes Kepler's first major astronomical work, "Mysterium Cosmographicum (The Cosmographic Mystery)", was the first published defense of the Copernican system. He hypothesized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the Universe. Despite rather poor agreement between his model and his observations, Kepler would cling to this idea to the end of his life. He issued a second edition of the book in 1621.

Kepler sought the opinions of many of his astronomical contemporaries to whom he had sent copies of his Mysterium, among them, Tycho Brahe. On February 4, 1600, Kepler met Tycho Brahe and his assistants, in Prague, the site where Tycho's new observatory was being constructed. Over the next two months he stayed as a guest, analyzing some of Tycho's observations of Mars. In August of 1600, Kepler returned to Prague, with his family, to collaborate on the Rudolphine Tables.

New Astronomy

Title page of Kepler's New Astronomy
"New Astronomy."

Kepler's "New Astronomy (Astronomia Nova)" was completed and published in Linz in 1609. Buried deep in this, at times very mystical book, is Kepler's first formulation of his first and second Laws of planetary motion, which in modern parlance can be stated as follows:

  1. Planetary orbits are ellipses, with the Sun located at one focus;

  2. Planets move along their elliptical orbit with a speed such that a line segment joining the planet to the Sun sweeps equal surface areas in equal time intervals.

Another important novelty is Kepler's attempt to justify the above two Laws on physical grounds, by ascribing planetary motions to a form of magnetically-mediated action-at-distance. This insight is what led him to formulate planetary orbits in relation to the Sun, as opposed to the center of the Earth's orbit (or "mean sun"), and in turn to his first two Laws. This idea, interestingly, also led him to postulate a movement of axial rotation for the Sun, two years before telescopic observations of sunspots would establish solar rotation as an observational fact.

The Rudolphine Tables

image of panel showing Kepler laboring by candlelight
Frontispiece of the "Rudolphine Tables" of planetary positions.

The "Rudolphine Tables" was published by Kepler in 1627 in Ulm and dedicated to Tycho's and Kepler's deceased patron, Emperor Rudolph II. The frontispiece is an allegoric depiction of the Temple of Astronomy. Taking center stage are Nicolaus Copernicus and Tycho Brahe, while Hipparchus and Claudius Ptolemy look on. The central panel on the base is a map of the island of Hveen. The panel to the left shows Kepler, himself, laboring by candlelight.

The Rudolphine Tables were the first to make use of Kepler's newly formulated "Laws on Planetary Motions", calibrated using Tycho's store of accurate planetary observations. They received a spectacular validation on November 7, 1631, when the French philosopher and sometimes astronomer Pierre Gassendi (1592–1655) observed a transit of Mercury across the solar disk, as predicted by Kepler. Kepler's prediction of this event was far more accurate than those based on the Copernican Tables. This success paved the way for the general acceptance, not only of the Rudolphine Tables, but also by extension, of Kepler's three Laws of planetary motions.

Harmonices Mundi

Title page of Kepler's Harmony of the World
"Harmony of the World."

Kepler's "Harmony of the World (Harmonices Mundi)" was completed in the spring of 1618 and finally published in Linz in 1619. Again of a rather mystical flavor at times, the book contains Kepler's first formulation of his Third Law of planetary motion:

"The square of a planet's orbital periods is proportional to the cube of its mean distance to the Sun."

Kepler was to formulate the final versions of his Three Laws of planetary motions much more clearly in book IV of his textbook "Epitome of Copernican Astronomy (Epitome Astronomiae Copernicanae)", published in 1620.

Epitome of Copernican Astronomy

Kepler's textbook Epitome of Copernican Astronomy
"Epitome of Copernican Astronomy."

Kepler's "Epitome of Copernican Astronomy (Epitome astronomiae Copernicanae)", was one of his most ambitious and life long projects, second perhaps only to his "Rudolphine Tables". Books I through III, appeared in 1618, Book IV in 1620, and Books V-VII in 1621. The complete work was reprinted in 1635, and for a long time remained one of the few comprehensive textbooks on the topic. Kepler applies his Third Law of Planetary Motion to infer the sizes of the orbits of the Galilean moons of Jupiter.

Kepler, J. 1609, Astronomia Nova, trans. W.H. Donahue 1992, Cambridge University Press.
Stephenson, B. 1994, The Music of the Heavens,Princeton University Press.
Stephenson, B. 1987, Kepler's physical astronomy, [1994 reprint, Princeton University Press].