Johannes Kepler was born in Weil der Stadt in Swabia, in southwest Germany.
His paternal grandfather, Sebald Kepler, was a respected craftsman who
served as mayor of the city; his maternal grandfather, Melchior Guldenmann,
was an innkeeper and mayor of the nearby village of Eltingen. His father,
Heinrich Kepler, was "an immoral, rough and quarrelsome soldier,"
according to Kepler, and he described his mother in similar unflattering
terms. From 1574 to 1576 Johannes lived with his grandparents; in 1576
his parents moved to nearby Leonberg, where Johannes entered the Latin
school. In 1584 he entered the Protestant seminary at Adelberg, and
in 1589 he began his university education at the Protestant university
of Tübingen. Here he studied theology and read widely. He passed
the M.A. examination in 1591 and continued his studies as a graduate
Kepler's teacher in the mathematical subjects was Michael Maestlin (1550-1635).
Maestlin was one of the earliest astronomers to subscribe to Copernicus's
heliocentric theory, although in his university lectures he taught only
the Ptolemaic system. Only in what we might call graduate seminars did
he acquaint his students, among whom was Kepler, with the technical
details of the Copernican system. Kepler stated later that at this time
he became a Copernican for "physical or, if you prefer, metaphysical
In 1594 Kepler accepted an appointment as professor of mathematics at
the Protestant seminary in Graz (in the Austrian province of Styria).
He was also appointed district mathematician and calendar maker. Kepler
remained in Graz until 1600, when all Protestants were forced to convert
to Catholicism or leave the province, as part of Counter Reformation
measures. For six years, Kepler taught arithmetic, geometry (when there
were interested students), Virgil, and rhetoric. In his spare time he
pursued his private studies in astronomy and astrology. In 1597 Kepler
married Barbara Müller. In that same year he published his first
important work, The Cosmographic Mystery, in which he argued that the
distances of the planets from the Sun in the Copernican system were
determined by the five regular solids, if one supposed that a planet's
orbit was circumscribed about one solid and inscribed in another.
Kepler's model to explain the relative distances of the planets from
the Sun in the Copernican System.
Except for Mercury, Kepler's construction produced remarkably accurate
results. Because of his talent as a mathematician, displayed in this
volume, Kepler was invited by Tycho Brahe to Prague to become his assistant
and calculate new orbits for the planets from Tycho's observations.
Kepler moved to Prague in 1600.
Kepler served as Tycho Brahe's assistant until the latter's death in
1601 and was then appointed Tycho's successor as Imperial Mathematician,
the most prestigious appointment in mathematics in Europe. He occupied
this post until, in 1612, Emperor Rudolph II was deposed. In Prague
Kepler published a number of important books. In 1604 Astronomia pars
Optica ("The Optical Part of Astronomy") appeared, in which
he treated atmospheric refraction but also treated lenses and gave the
modern explanation of the workings of the eye; in 1606 he published
De Stella Nova ("Concerning the New Star") on the new star
that had appeared in 1604; and in 1609 his Astronomia Nova ("New
Astronomy") appeared, which contained his first two laws (planets
move in elliptical orbits with the sun as one of the foci, and a planet
sweeps out equal areas in equal times). Whereas other astronomers still
followed the ancient precept that the study of the planets is a problem
only in kinematics, Kepler took an openly dynamic approach, introducing
physics into the heavens.
In 1610 Kepler heard and read about Galileo's discoveries with the spyglass.
He quickly composed a long letter of support which he published as Dissertatio
cum Nuncio Sidereo ("Conversation with the Sidereal Messenger"),
and when, later that year, he obtained the use of a suitable telescope,
he published his observations of Jupiter's satellites under the title
Narratio de Observatis Quatuor Jovis Satellitibus ("Narration about
Four Satellites of Jupiter observed"). These tracts were an enormous
support to Galileo, whose discoveries were doubted or denied by many.
Both of Kepler's tracts were quickly reprinted in Florence. Kepler went
on to provide the beginning of a theory of the telescope in his Dioptrice,
published in 1611.
During this period the Keplers had three children (two had been born
in Graz but died within months), Susanna (1602), who married Kepler's
assistant Jakob Bartsch in 1630, Friedrich (1604-1611), and Ludwig (1607-1663).
Kepler's wife, Barbara, died in 1612. In that year Kepler accepted the
position of district mathematician in the city of Linz, a position he
occupied until 1626. In Linz Kepler married Susanna Reuttinger. The
couple had six children, of whom three died very early.
In Linz Kepler published first a work on chronology and the year of
Jesus's birth, In German in 1613 and more amply in Latin in 1614: De
Vero Anno quo Aeternus Dei Filius Humanam Naturam in Utero Benedictae
Virginis Mariae Assumpsit (Concerning the True Year in which the Son
of God assumed a Human Nature in the Uterus of the Blessed Virgin Mary").
In this work Kepler demonstrated that the Christian calendar was in
error by five years, and that Jesus had been born in 4 BC, a conclusion
that is now universally accepted. Between 1617 and 1621 Kepler published
Epitome Astronomiae Copernicanae ("Epitome of Copernican Astronomy"),
which became the most influential introduction to heliocentric astronomy;
in 1619 he published Harmonice Mundi ("Harmony of the World"),
in which he derived the heliocentric distances of the planets and their
periods from considerations of musical harmony. In this work we find
his third law, relating the periods of the planets to their mean orbital
In 1615-16 there was a witch hunt in Kepler's native region, and his
own mother was accused of being a witch. It was not until late in 1620
that the proceedings against her ended with her being set free. At her
trial, her defense was conducted by her son Johannes.
1618 marked the beginning of the Thirty Years War, a war that devastated
the German and Austrian region. Kepler's position in Linz now became
progressively worse, as Counter Reformation measures put pressure on
Protestants in the Upper Austria province of which Linz was the capital.
Because he was a court official, Kepler was exempted from a decree that
banished all Protestants from the province, but he nevertheless suffered
persecution. During this time Kepler was having his Tabulae Rudolphinae
("Rudolphine Tables") printed, the new tables, based on Tycho
Brahe's accurate observations, calculated according to Kepler's elliptical
astronomy. When a peasant rebellion broke out and Linz was besieged,
a fire destroyed the printer's house and shop, and with it much of the
printed edition. Soldiers were garrisoned in Kepler's house. He and
his family left Linz in 1626. The Tabulae Rudolphinae were published
in Ulm in 1627.
Kepler now had no position and no salary. He tried to obtain appointments
from various courts and returned to Prague in an effort to pry salary
that was owed him from his years as Imperial Mathematician from the
imperial treasury. He died in Regensburg in 1630. Besides the works
mentioned here, Kepler published numerous smaller works on a variety
His Life, His Laws and Times
A Short Biography
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
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
• First to explain the process of vision by refraction within
• First to formulate eyeglass designing for nearsightedness and
• 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 iimages
• First to explain the principles of how a telescope works;
• First to discover and describe the properties of total internal
• His book Stereometrica Doliorum formed the basis of integral
• 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
• First to derive the birth year of Christ, that is now universally
• 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
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.
Kepler was born
on December 27, 1571 at the Imperial Free City of Weil der Stadt (now
part of the Stuttgart Region in the German state of Baden-Württemberg,
30 km west of Stuttgart's city center). His grandfather had been Lord
Mayor of that town, but by the time Johannes was born, the Kepler family
fortunes were in decline. His father earned a precarious living as a
mercenary, and abandoned the family when Johannes was 17. His mother,
an inn-keeper's daughter, had a reputation for involvement in witchcraft.
Born prematurely, Johannes is said to have been a weak and sickly child,
but despite his ill health, he was precociously brilliant.
Though he excelled in his schooling, Kepler was frequently bullied,
and was plagued by a belief that he was physically repulsive, thoroughly
unlikable and, compared to the other pupils, an outsider. This ostracizing
probably led him to turn to the world of ideas, as well as an abiding
religious conviction, for solace.
He was introduced to astronomy/astrology at an early age, and developed
a love for that discipline that would span his entire life. At age six,
he observed the Comet of 1577, writing that he "...was taken by
[his] mother to a high place to look at it." At age nine, he observed
another astronomical event, the Lunar eclipse of 1580, recording that
he remembered being "called outdoors" to see it and that the
moon "appeared quite red."
In 1587, Kepler began attending the University of Tübingen, where
he proved himself to be a superb mathematician. Upon his graduation
from that school in 1591, he went on to pursue study in theology, becoming
a part of the Tübingen faculty. However, before he took his final
exams he was recommended for the vacant post of teacher of mathematics
and astronomy at the Protestant school in Graz, Austria. He accepted
the position in April of 1594, at the age of 23.
In April 1597, Kepler married Barbara Muehleck. She died in 1611 and
was survived by two children.
In December 1599, Tycho Brahe wrote to Kepler, inviting Kepler to assist
him at Benatek outside Prague. After Tycho's death, Kepler was appointed
Imperial Mathematician (from November 1601 to 1630) to the Habsburg
In October 1604, Kepler observed the supernova which was subsequently
named Kepler's Star. In January 1612 the Emperor died, and Kepler took
the post of provincial mathematician in Linz.
In 1611, Kepler published a monograph on the origins of snowflakes,
the first known work on the subject. He correctly theorized that their
hexagonal nature was due to cold, but did not ascertain a physical cause
for this. The question of snowflakes was not resolved until the 20th
On March 8, 1618 Kepler discovered the third law of planetary motion:
distance cubed over time squared. He initially rejected this idea, but
later confirmed it on May 15 of the same year.
In August of 1620, Katherine, Kepler's mother, was arrested in Leonberg
as a witch; she was imprisoned for 14 months. She was released in October
1621 after attempts to convict her failed. Even though she was subjected
to torture, she refused to confess to the charges. However, only the
courageous personal intervention of Kepler (despite the risk to be arrested
as well) and his reputation as the famous Imperial Mathematician rescued
On November 15, 1630 Kepler died of a fever in Regensburg.
Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum
Like previous astronomers, Kepler initially believed that celestial
objects moved in perfect circles. These models were consistent with
observations and with the Platonic idea that the sphere was the perfect
shape. However, after spending twenty years doing calculations with
data collected by Tycho Brahe, Kepler concluded that the circular model
of planetary motion was inconsistent with that data. Using Tycho's data,
Kepler was able to formulate three laws of planetary motion, now known
as Kepler's laws, in which planets move in ellipses, not circles. Using
that knowledge, he was the first astronomer to successfully predict
a transit of Venus (for the year 1631).
Kepler discovered the laws of planetary motion while trying to achieve
the Pythagorean purpose of finding the harmony of the celestial spheres.
In his cosmologic vision, it was not a coincidence that the number of
perfect polyhedra was one less than the number of known planets. Having
embraced the Copernican system, he set out to prove that the distances
from the planets to the sun were given by spheres inside perfect polyhedra,
all of which were nested inside each other. The smallest orbit, that
of Mercury, was the innermost sphere. He thereby identified the five
Platonic solids with the five intervals between the six known planets
— Mercury, Venus, Earth, Mars, Jupiter, Saturn; and the five classical
Closeup of the model
In 1596 Kepler published Mysterium Cosmographicum, or The Cosmic Mystery.
Here is a selection explaining the relation between the planets and
the Platonic solids:
… Before the universe was created, there were no numbers except
the Trinity, which is God himself… For, the line and the plane
imply no numbers: here infinitude itself reigns. Let us consider, therefore,
the solids. We must first eliminate the irregular solids, because we
are only concerned with orderly creation. There remain six bodies, the
sphere and the five regular polyhedra. To the sphere corresponds the
heaven. On the other hand, the dynamic world is represented by the flat-faces
solids. Of these there are five: when viewed as boundaries, however,
these five determine six distinct things: hence the six planets that
revolve about the sun. This is also the reason why there are but six
… I have further shown that the regular solids fall into two groups:
three in one, and two in the other. To the larger group belongs, first
of all, the Cube, then the Pyramid, and finally the Dodecahedron. To
the second group belongs, first, the Octahedron, and second, the Icosahedron.
That is why the most important portion of the universe, the Earth—where
God's image is reflected in man—separates the two groups. For,
as I have proved next, the solids of the first group must lie beyond
the earth's orbit, and those of the second group within… Thus
I was led to assign the Cube to Saturn, the Tetrahedron to Jupiter,
the Dodecahedron to Mars, the Icosahedron to Venus, and the Octahedron
To emphasize his theory, Kepler envisaged an impressive model of the
universe which shows a cube, inside a sphere, with a tetrahedron inscribed
in it; another sphere inside it with a dodecahedron inscribed; a sphere
with an icosahedron inscribed inside; and finally a sphere with an octahedron
inscribed. Each of these celestial spheres had a planet embedded within
them, and thus defined the planet's orbit.
On October 17, 1604, Kepler observed that an exceptionally bright star
had suddenly appeared in the constellation Ophiuchus. (It was first
observed by several others on October 9.) The appearance of the star,
which Kepler described in his book De Stella nova in pede Serpentarii
('On the New Star in Ophiuchus's Foot'), provided further evidence that
the cosmos was not changeless; this was to influence Galileo in his
argument. It has since been determined that the star was a supernova,
the second in a generation, later called Kepler's Star or Supernova
1604. No further supernovae have since been observed with certainty
in the Milky Way, though others outside our galaxy have been seen.
Remnant of Kepler's Supernova SN 1604.
In his 1619 book, Harmonices Mundi or Harmony of the Worlds, as well
as the aforementioned Mysterium Cosmographicum, he also made an association
between the Platonic solids with the classical conception of the elements:
the tetrahedron was the form of fire, the octahedron was that of air,
the cube was earth, the icosahedron was water, and the dodecahedron
was the cosmos as a whole or ether. There is some evidence this association
was of ancient origin, as Plato tells of one Timaeus of Locri who thought
of the Universe as being enveloped by a gigantic dodecahedron while
the other four solids represent the "elements" of fire, air,
earth, and water.
To his disappointment, Kepler's attempts to fix the orbits of the planets
within a set of polyhedrons never worked out, but it is a testimony
to his integrity as a scientist that when the evidence mounted against
the cherished theory he worked so hard to prove, he abandoned it.
His most significant achievements came from the realization that the
planets moved in elliptical, not circular, orbits. This realization
was a direct consequence of his failed attempt to fit the planetary
orbits within polyhedra. Kepler's willingness to abandon his most cherished
theory in the face of precise observational evidence also indicates
that he had a very modern attitude to scientific research. Kepler also
made great steps in trying to describe the motion of the planets by
appealing to a force which resembled magnetism, which he believed emanated
from the sun. Although he did not discover gravity, he seems to have
attempted to invoke the first empirical example of a universal law to
explain the behaviour of both earthly and heavenly bodies.
Kepler also made fundamental investigations into combinatorics, geometrical
optimization, and natural phenomena such as snowflakes, always with
an emphasis on form and design. He was also one of the founders of modern
optics, defining e.g. antiprisms and the Kepler telescope (see Kepler's
books Astronomiae Pars Optica — i.a. theoretical explanation of
the camera obscura — and Dioptrice). In addition, since he was
the first to recognize the non-convex regular solids (such as the stellated
dodecahedra), they are named Kepler solids in his honor.
In 1632, only two years after his death, his grave was demolished by
the Swedish army in the Thirty Years' War.
Kepler and Astrology
Kepler disdained astrologers who pandered to the tastes of the common
man without knowledge of the abstract and general rules, but he saw
compiling prognostications as a justified means of supplementing his
meagre income. Yet, it would be a mistake to take Kepler's astrological
interests as merely pecuniary. As one historian, John North, put it,
'had he not been an astrologer he would very probably have failed to
produced his planetary astronomy in the form we have it.'
Kepler believed in astrology in the sense that he was convinced that
astrological aspects physically and really affected humans as well as
the weather on earth. He strove to unravel how and why that was the
case and tried to put astrology on a surer footing, which resulted in
the On the more certain foundations of astrology (1601), in which, among
other technical innovations, he was the first to propose the quincunx
aspect. In The Intervening Third Man, or a warning to theologians, physicians
and philosophers (1610), posing as a third man between the two extreme
positions for and against astrology, Kepler advocated that a definite
relationship between heavenly phenomena and earthly events could be
At least 800 horoscopes and natal charts drawn up by Kepler are still
extant, several of himself and his family, accompanied by some unflattering
remarks. As part of his duties as district mathematician to Graz, Kepler
issued a prognostication for 1595 in which he forecast a peasant uprising,
Turkish invasion and bitter cold, all of which happened and brought
him renown. Kepler is known to have compiled prognostications for 1595
to 1606, and from 1617 to 1624. As court mathematician, he explained
to Rudolf II the horoscopes of the Emperor Augustus and Muhammad, and
gave astrological prognosis for the outcome of a war between the Republic
of Venice and Paul V. In the On the new star (1606) Kepler explicated
the meaning of the new star of 1604 as the conversion of America, downfall
of Islam and return of Christ. The De cometis libelli tres (1619) is
also replete with astrological predictions.