Johannes Kepler is born on on December 27th, 1571 close to Weil (Wurtemberg), in the south of Germany, west of Stuttgart. He remains there little, his family settling in 1575 in Leonberg (city located a little more at north). Kepler are Protestant and pride itself on nobility, but on a rather remote nobility since the father of Johannes is not that a mercenary - it will disappear during a military campaign - and that his/her mother, Catherine, orphan, were raised by an aunt who was burned alive like witch.  

Johannes Kepler exerts various modest trades: he is in particular waiter in an inn, then farm laborer, before beginning his studies, at the twelve years age, the small seminar of Adelberg. Its work and its intelligence enable him to obtain a purse of the dukes of Wurtemberg to continue its studies at the university of Tübingen, where it is allowed in 1589. This university (as that of Wittenberg) was created by the dukes to form the future Protestant elites. One teaches there theology, Latin, the music, mathematics; in fact, for this last discipline, geometry and astronomy. The Kepler young person has as professor one of the best astronomers of his time, Michael Maestlin. This last unambiguous ensign the system of Copernic, which places the Sun in the center of the round of planets, including the Earth. Maestlin, by its observations, made it possible to make evolve the design of the Universe; thus it showed that the nova of 1572 is “a new” star, which contradicts the Aristotelian dogma of the immutability of the skies.

The first work of Kepler

Kepler intended himself for the ecclesiastical career when, in 1594, the Protestant school of Graz requires of the university of Tübingen a mathematics professor. He is selected for this load, which leaves him sufficient time for its personal work. Graz is a tolerant city, for the time, and still a Protestant school and a catholic university mix with there. He will convert with the Calvinism, giving up the Lutheranism, which will attract later troubles with the religious authorities to him and will be cause of its excommunication. He regularly publishes astrological calendars and predictions which are carried out, which ensures its reputation.  

Kepler astrologer
Most reflections of Kepler on astrology are scattered in its various works, but it publishes also fundamentis astrologiae, in 1601, and Astrologicus, in 1620. It can appear curious that an astronomer can deal with astrology, fabric of beliefs without any scientific base; but, of the time of Kepler, the current distinction between science and belief (or religion) did not exist yet. It is difficult to imagine the opinion that a “scientist” could then have astrology.  

For Kepler, this discipline is “a licentious girl who nourishes her poor mother, astronomy”. This is why he does not hesitate to publish, at the same time as his almanacs, of the horoscopes and the astrological predictions. However, faithful to its ideas, Kepler seeks to give bases rigorous to astrology, which leads it to reject certain parts of what was taught then (and that he regards as nonsense), to retain others of them and, finally, to add some while being based on physical reasoning or which he holds for such (belief in a clean light of planets, heart of the world located in the Sun and maintaining the movement planets). On the other hand, he refuses any symbolic system relationship between word and thing: he knows that the name of the constellations is arbitrary and that the division of the zodiac is only one convenience mathematical, also finishes he by rejecting all the theories relative to the principal “house” of a planet like at the twelve astrological houses. Besides he finds in these beliefs a stink of paganism, even of satanism, bad quality.  

The “Mysterium cosmographicum”
But it is especially the publication in 1596 - publication to which Maestlin contributed - of Mysterium cosmographicum, fruit of its first meditations on the structure of the Universe, which establishes the notoriety of Kepler. The work is known to have introduced the idea (which appears whimsical today) of the theory of the regular polyhedrons. Kepler associates the five convex regular polyhedrons of the geometry with the solar system while being based on the ideas, into force at the end of the XVI E century, according to which the orbits of six planets known then are more or less material spheres; Kepler one in another explains the relative distances from planets by registering the various polyhedrons: each sphere circumscribed with a polyhedron and registered in the following corresponds to “the sphere” of a planet. This work makes it possible to discover an expansion of ideas sometimes exact, sometimes false, hard and tedious calculations intersected with fulgurating flashes of imagination, an empirical frame of mind and, invaluable thing for us, the account by Kepler himself of his thought processe, its gropings, its methods.  

In spite of the mistakes of its theory, the work ensured the fame of Kepler and opened to him many doors; thus it corresponded with the Danish astronomer Tycho Brahe, whom it met in February 1600 with the castle of Benatek, close to Prague.  

The meeting of Kepler with Tycho Brahe
Association between the powerful one and touchy Tycho Brahe and likely Johannes Kepler will be short. Their reports are tended; inter alia, Brahe does not believe in the heliocentrism of Copernic, and Kepler does not believe in the hybrid system of Tycho Brahe. Kepler sees himself entrusting the study of the orbit of Mars that he praises himself to be able to determine in eight days: he will work eight years there. The choice of Mars will prove to be the good, because except Mercure, not easily observable, it is one of the planets then known whose orbit has the strongest eccentricity.  

In October 1601, Tycho Brahe dies, and Kepler succeeds to him in the load of imperial mathematician. Profiting from the excellent astronomical observations of Tycho Brahe (precise 1 minute from arc near; the preceding ones had a margin of error higher than 10 minutes of arc), Kepler, who is a poor observer because of his myopia and his bad health, will successively solve the various parameters of the orbit of Mars, thus stating the first two laws of the planetary movements which will be published in Astronomia nova, in 1609, in Prague.  
 
The work of Kepler

Kepler is at the same time pilot and actor of the transition between the Middle Ages and the Rebirth. Its work, in which it gives the primacy to the observation, marks the beginning of the scientific method. But its ideas in astrology or dynamics show what remains to be traversed to lead to the ideas of Newton.  

The “Astronomia nova” of Kepler
The reception made with this work is not as enthusiastic as that reserved for Mysterium cosmographicum, because Kepler then upsets the dogmas of his time. Thus he writes: “If one places two stones some share in space, far from any other body, then they approach like magnets, each one traversing a distance proportional to the mass of the other.” The work constitutes also a testimony of the difficult birth of the scientific step, i.e. of the recognition of the primacy of the experiment and fact on the ideas. One sees Kepler indeed there making various assumptions, confronting them with the observations and rejecting them if they do not adapt to it with precision. The discovery of the elliptic trajectory of the orbit of Mars is typical of this step: in agreement with the ideas of Aristote into force at that time and which make circle the most perfect figure and possible one to the only rule over the skies, Kepler will seek for a long time to adjust a circle with measurements of the positions of Mars. It will reach that point almost, but there remains a variation of 8 ' (higher than the errors of observation) for two positions; and this fact will lead it to give up the assumption of the circle for that of an oval, more exactly of an ellipse, and it will be what is called today the first law: “The orbits of planets are ellipses whose Sun occupies one of the hearths.”  

This abandonment of the Aristotelian dogma is confirmed when Kepler also gives up the uniform movements with the statement of the second law: “In the movement of a planet, the radius vector sweeps equal surfaces in equal times.” The planet thus has a faster movement when it is close to the Sun that when it of it is distant.  

Works of optics of Kepler
The astronomer and German physicist left two important works on optics. AD vitellionem, published to Frankfurt in 1604, gives tables of the atmospheric refraction, means of calculation of longitude and law of weakening of the light in 1/r2, reflections on the mode of vision and the use of moods of the eye. In Dioptrice, published in Augsburg in 1611, Kepler seeks to explain the principle of the telescope which has just invented Galileo, with which it has an enthusiastic correspondence.  

“Harmonices mundi”
In 1612, Kepler is named in Linz (in High-Austria), where he will discover the third law, which will be published in Harmonices mundi in 1619. This law shows that the movements of various planets are not independent from/to each other, since dimensions of the orbits are related to the durations of revolution (i.e. at the time necessary to make a turn around the Sun), very exactly: “The squares of the periods of revolution are proportional to the cubes of the average distances to the Sun.”  

Numerical tables
To publish tables of numbers is an ungrateful task although essential; it will occupy many scientists. For all his calculations, Kepler profited from the discovery of the logarithms by Napier (discovery published in 1614), but it improved this invention and, independently of Briggs, it built in Chilias logarithmorum (“Thousand Logarithms”), published with Marburg in 1624, a table of logarithms much more practical: for the same decimal precision, Kepler carries out only about thirty extractions of square roots, instead of 54 at Briggs, and later calculations are made in a way much more direct and simple.  

The “tables rudolphines”
The table of logarithms which it contributed to improve him will be of a great help for focusing into 1627 of its star catalog, known under the name of Tables rudolphines, which reexpresses in the system of Copernic, i.e. in the heliocentric system, the data of the observations (geocentric by the force of the things) of Tycho Brahe. This catalog gives, inter alia, the position of 1 ' 005 stars.  

Kepler leaves Linz then and settles in Sagan (city currently located in Poland), near the duke of Wallenstein. He is bored and seeks a more interesting situation, but dies during a voyage to Ratisbon, on on November 15th, 1630.

The posterity of the work of Kepler

It remains, for the astronomers in particular, the author of three fundamental laws. If, such as it stated them, these laws correspond only to measurements accessible to its time, one can currently deduce them from the laws of Newton. It is shown that they correspond if the planet would be alone vis-a-vis the Sun and of negligible mass in front of that of this last. This is why, for more precision, the third law is usually amended by writing that a3/P2 (where has is the average distance to the Sun, and P the period of revolution) is proportional to the sum of the masses of the Sun and planet (but the largest planet, Jupiter, have a mass about the thousandths of that of the Sun, which explains the good approximation of the statement of Kepler).  

For the first two laws, it is the center of gravity of the solar system, rather than the Sun itself, which is taken as hearth. The orbits defined by Kepler are always used today to describe the trajectories on a short amount of time, what is called an osculatory orbit: it is considered that parameters of the orbit (eccentricity, slope…) vary very slowly; it is the theory of the disturbances (the purely elliptic movement is disturbed by the presence of the other celestial bodies). This theory, resulting from work of Kepler and Newton, allows the precise guidance of the interplanetary probes, but also the measurement of the masses of double stars as well as theirs distance to the Sun, stage necessary to evaluate dimensions of the Universe.