Johannes Kepler

Johannes Kepler was born at 2:30 PM on December 27, 1571, in Weil der Stadt, Württemburg, in the Holy Roman Empire of German Nationality. He was a sickly child and his parents were poor. But his evident intelligence earned him a scholarship to the University of Tübingen to study for the Lutheran ministry. There he was introduced to the ideas of Copernicus and delighted in them. In 1596, while a mathematics teacher in Graz, he wrote the first outspoken defense of the Copernican system, the Mysterium Cosmographicum.

Kepler's family was Lutheran and he adhered to the Augsburg Confession a defining document for Lutheranism. However, he did not adhere to the Lutheran position on the real presence and refused to sign the Formula of Concord. Because of his refusal he was excluded from the sacrament in the Lutheran church. This and his refusal to convert to Catholicism left him alienated by both the Lutherans and the Catholics. Thus he had no refuge during the Thirty-Years War.
The Holy Roman Empire of German Nationality at the Time of Kepler


Kepler was forced to leave his teaching post at Graz due to the counter Reformation because he was Lutheran and moved to Prague to work with the renowned Danish astronomer, Tycho Brahe. He inherited Tycho's post as Imperial Mathematician when Tycho died in 1601. Using the precise data that Tycho had collected, Kepler discovered that the orbit of Mars was an ellipse. In 1609 he published Astronomia Nova, delineating his discoveries, which are now called Kepler's first two laws of planetary motion. And what is just as important about this work, "it is the first published account wherein a scientist documents how he has coped with the multitude of imperfect data to forge a theory of surpassing accuracy" (O. Gingerich in forward to Johannes Kepler New Astronomy translated by W. Donahue, Cambridge Univ Press, 1992), a fundamental law of nature. Today we call this the scientific method.

In 1612 Lutherans were forced out of Prague, so Kepler moved on to Linz. His wife and two sons had recently died. He remarried happily, but had many personal and financial troubles. Two infant daughters died and Kepler had to return to Württemburg where he successfully defended his mother against charges of witchcraft. In 1619 he published Harmonices Mundi, in which he describes his "third law."

In spite of more forced relocations, Kepler published the seven-volume Epitome Astronomiae in 1621. This was his most influential work and discussed all of heliocentric astronomy in a systematic way. He then went on to complete the Rudolphine Tables that Tycho had started long ago. These included calculations using logarithms, which he developed, and provided perpetual tables for calculating planetary positions for any past or future date. Kepler used the tables to predict a pair of transits by Mercury and Venus of the Sun, although he did not live to witness the events.

Johannes Kepler died in Regensburg in 1630, while on a journey from his home in Sagan to collect a debt. His grave was demolished within two years because of the Thirty Years War. Frail of body, but robust in mind and spirit, Kepler was scrupulously honest to the data.
A List of Kepler's Firsts
First to correctly explain planetary motion, thereby, becoming founder of celestial mechanics and the first "natural laws" in the modern sense; being universal, verifiable, precise.

In his book Astronomia Pars Optica, for which he earned the title of founder of modern optics he was the:
First to investigate the formation of pictures with a pin hole camera;
First to explain the process of vision by refraction within the eye;
First to formulate eyeglass designing for nearsightedness and farsightedness;
First to explain the use of both eyes for depth perception.

In his book Dioptrice (a term coined by Kepler and still used today) he was the:
First to describe: real, virtual, upright and inverted images and magnification;
First to explain the principles of how a telescope works;
First to discover and describe the properties of total internal reflection.

In addition:
His book Stereometrica Doliorum formed the basis of integral calculus.
First to explain that the tides are caused by the Moon (Galileo reproved him for this).
Tried to use stellar parallax caused by the Earth's orbit to measure the distance to the stars; the same principle as depth perception. Today this branch of research is called astrometry.
First to suggest that the Sun rotates about its axis in Astronomia Nova
First to derive the birth year of Christ, that is now universally accepted.
First to derive logarithms purely based on mathematics, independent of Napier's tables published in 1614.
He coined the word "satellite" in his pamphlet Narratio de Observatis a se quatuor Iovis sattelitibus erronibus
Kepler's Laws of Planetary Motion

Kepler was assigned the task by Tycho Brahe to analyze the observations that Tycho had made of Mars. Of all the planets, the predicted position of Mars had the largest errors and therefore posed the greatest problem. Tycho's data were the best available before the invention of the telescope and the accuracy was good enough for Kepler to show that Mars' orbit would precisely fit an ellipse. In 1605 he announced The First Law:

Planets move in ellipses with the Sun at one focus.


The figure below illustrates two orbits with the same semi-major axis, focus and orbital period: one a circle with an eccentricity of 0.0; the other an ellipse with an eccentricity of 0.8.
Circular and Elliptical Orbits Having the Same Period and Focus

Prior to this in 1602, Kepler found from trying to calculate the position of the Earth in its orbit that as it sweeps out an area defined by the Sun and the orbital path of the Earth that:

The radius vector describes equal areas in equal times. (The Second Law)


Kepler published these two laws in 1609 in his book Astronomia Nova.

For a circle the motion is uniform as shown above, but in order for an object along an elliptical orbit to sweep out the area at a uniform rate, the object moves quickly when the radius vector is short and the object moves slowly when the radius vector is long.

On May 15, 1618 he discovered The Third Law:

The squares of the periodic times are to each other as the cubes of the mean distances.


This law he published in 1619 in his Harmonices Mundi . It was this law, not an apple, that lead Newton to his law of gravitation. Kepler can truly be called the founder of celestial mechanics.