Johannes Kepler
15711630
The German astronomer Johannes Kepler was one of the chief
founders of modern astronomy because of his discovery of three
basic laws underlying the motion of planets.
Johannes Kepler was born on Dec. 27, 1571, in the Swabian town
of Weil. His father, Heinrich Kepler, was a mercenary; although
a Protestant, he enlisted in the troops of the Duke of Alba
fighting the Reformed insurgents in the Low Countries. Kepler's
grandmother brought him up; for years he was a sickly child. At
13 he was accepted at a theological seminary at Adelberg.
Kepler wanted to become a theologian, and following his
graduation from the University of Tübingen, as bachelor of arts
in 1591, he enrolled in its theological faculty. But he was also
interested in French literature and astronomy. His poor health
and proclivity to morbidness singled him out no less than did
his precocious advocacy of the doctrine of Copernicus.
It seems that the University of Tübingen gladly presented Kepler
for the post of the "mathematician of the province" when request
for a candidate came from Graz. He arrived there in April 1594
and set himself to work on one of his duties, the composition of
the almanac, in which the main events of the coming year were to
be duly predicted. His first almanac was a signal success. The
occurrence of two not too unlikely events, an invasion by the
Turks and a severe winter, which he had predicted, established
his reputation.
Far more important for astronomy was the idea that seized Kepler
on July 9, 1595. It appeared to him that the respective radii of
the orbits of the planets corresponded to the lengths determined
by a specific sequence in which the five regular solids were
placed within one another, with a sphere separating each solid
from the other. The sphere (orbit) of Saturn enveloped a cube
which in turn enveloped another sphere, the orbit of Jupiter.
This circumscribed a tetrahedron, a sphere (the orbit of Mars),
a dodecahedron, a sphere (the orbit of earth), an icosahedron, a
sphere (the orbit of Venus), an octahedron, and the smallest
sphere (the orbit of Mercury). The idea was the main theme of
his Mysterium cosmographicum (1596).
The next year Kepler married Barbara Muehleck, already twice
widowed, "under an ominous sky," according to Kepler's own
horoscope. Of their five children only one boy and one girl
reached adulthood. It was with reluctance that Kepler, a
convinced Copernican, first sought the job of assistant to Tycho
Brahe, the astrologermathematician of Rudolph II in Prague. He
took his new position in 1600. On the death of Tycho the
following year, Kepler was appointed his successor.
His Three Laws
Kepler's immediate duty was to prepare for publication Tycho's
collection of astronomical studies, Astronomiae instauratae
progymnasmata (16011602). Kepler fell heir to Tycho's immensely
valuable records. Their outstanding feature lay in the precision
by which Tycho surpassed all astronomers before him in observing
the position of stars and planets. Kepler tried to utilize
Tycho's data in support of his own layout of the circular
planetary orbits. The facts, that is, Tycho's observations,
forced him to make one of the most revolutionary assumptions in
the history of astronomy. A difference of 8 minutes of arc
between his theory and Tycho's data could be explained only if
the orbit of Mars was not circular but elliptical. In a
generalized form this meant that the orbits of all planets were
elliptical (Kepler's first law). On this basis a proper meaning
could be given to another statement of his which he had already
made in the same context. It is known as Kepler's second law,
according to which the line joining the planet to the sun sweeps
over equal areas in equal times in its elliptical orbit.
Kepler published these laws in his lengthy discussion of the
orbit of the planet Mars, the Astronomia nova (1609). The two
laws were clearly spelled out also in the book's detailed table
of contents. Thus they must have struck the eyes of any careful
reader sensitive to an astronomical novelty of such major
proportion. Still, Galileo failed to take cognizance of them in
his printed works, although he could have used them to great
advantage to buttress his advocacy of the Copernican system.
The relations between Galileo and Kepler were rather strange.
Although Galileo remained distinctly unappreciative of Kepler's
achievements, the latter wrote a booklet to celebrate Galileo's
Starry Messenger immediately upon its publication in 1610. On
the other hand, Kepler argued rather vainly in his Conversation
with the Starry Messenger (1610) that in his Astronomiae pars
optica (1604), or Optics, which he presented as a commentary to
Witelo's 13thcentury work, one could find all the principles
needed to construct a telescope.
In 1611 came Rudolph's abdication, and Kepler immediately looked
for a new job. He obtained in Linz the post of provincial
mathematician. By the time he moved to Linz in 1612 with his two
children, his wife and his favorite son, Friedrich, were dead.
Kepler's 14 years in Linz were marked, as far as his personal
life was concerned, with his marriage in 1613 to Suzanna
Reuttinger and by his repeated efforts to save his aged mother
from being tried as a witch.
As for Kepler the scientist, he published two important works
while he was in Linz. One was the Harmonice mundi (1618), in
which his third law was announced. According to it the squares
of the sidereal periods of any two planets are to each other as
the cubes of their mean distances from the sun. The law was,
however, derived not from celestial mechanics (Newton's
Principia was still 6 decades away) but from Kepler's conviction
that nature had to be patterned along quantitative relationships
since God created it according to "weight, measure and number."
Shortly after his first book appeared, he wrote in a letter:
"Since God established everything in the universe along
quantitative norms, he endowed man with a mind to comprehend
them. For just as the eye is fitted for the perception of
colours, the ear for sounds, so is man's mind created not for
anything but for the grasping of quantities." In the Harmonice
mundi he wrote merely a variation on the same theme as he spoke
of geometry which "supplied God with a model for the creation of
the world. Geometry was implanted into human nature along with
God's image and not through man's visual perception and
experience." The second work was the Epitome astronomiae
Copernicanae, published in parts between 1618 and 1621. It was
the first astronomical treatise in which the doctrine of circles
really or hypothetically carrying the various planets was
completely abandoned in favor of a physical explanation of
planetary motions. It consisted in "magnetic arms" emanating
from the sun.
Kepler was already in Ulm, the first stopover of the wanderings
of the last 3 years of his life, when his Tabulae Rudolphinae
(1628) was published. It not only added the carefully determined
position of 223 stars to the 777 contained in Tycho's
Astronomiae instauratae progymnasmata but also provided
planetary tables which became the standard for the next century.
Kepler died on Nov. 15, 1630. He was a unique embodiment of the
transition from the old to the new spirit of science.
~~~<"((((((><~~~<"((((((><~~~<"((((((><~~~<"((((((><~~~<"((((((><~~~
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
student.
Kepler's teacher in the mathematical subjects was Michael
Maestlin (15501635). 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 reasons."
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.
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
(16041611), and Ludwig (16071663). 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 radii.
In 161516 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 of subjects.
~~~<"((((((><~~~<"((((((><~~~<"((((((><~~~<"((((((><~~~<"((((((><~~~
Kepler, Johannes (1571–1630), German astronomer and
mathematician; discoverer of the laws of planetary motion. Born
into the Protestant minority in the free city of Weil der Stadt,
within the Lutheran duchy of Württemberg, Kepler's family was
poised at the boundary between the aristocracy and the artisan
class. His father and brother Heinrich both served as soldiers;
his youngest brother worked as a tinsmith. Kepler was educated
at religious schools supported by the duke of Württemberg, and
at the University of Tübingen. Here he studied with theologians
trained by Philipp Melanchthon (1497–1560), the great German
religious and educational reformer, and began a lifelong
friendship with his mathematics teacher, the Copernican
astronomer Michael Mästlin (1550–1631).
Unable to follow a church career because his scruples prevented
him from signing the Formula of Concord, Kepler began his
professional life as a teacher in the Protestant gymnasium at
Graz, in southern Austria. From here he rose to become an
imperial courtier, and achieved lasting fame as an innovator in
astronomy. Kepler married twice (1597 and 1613). He was a
devoted father who suffered deeply at the early deaths of many
of his children, and he seems to have used mathematical research
as a solace. Kepler's publication of the Mysterium
Cosmographicum (1596; The secret of the universe) began a
meteoric rise. Compelled to leave Graz with other Protestants in
1598, he attached himself to the court of Emperor Rudolf II
(ruled 1576–1612) in Prague, and succeeded Tycho Brahe as
imperial mathematician in 1601. Thus, in only three years,
Kepler ascended from the position of a provincial schoolteacher
to become the astrological and astronomical adviser to the most
powerful monarch in the Christian world, although the emperor
proved unreliable as a source of financial support. Kepler
immediately began to produce a series of major works, especially
the Optics (Astronomiae pars Optica, 1604) and the New Astronomy
(1609), which extended and refounded their subjects. Other works
(1601, 1610) attempted to reform astrology. In 1612, after the
forced abdication and death of Rudolf, Kepler left Prague, but
retained his title of imperial mathematician under later
emperors. From 1612 to 1626 he and his family made their home in
Linz, in Upper Austria, although Kepler traveled widely. While
in Linz he produced the Epitome of Copernican Astronomy
(1618–1621) and the Harmony of the World (1619). The latter
precipitated a violent exchange with the English theosophist
Robert Fludd (1574–1637), but Kepler declined an invitation to
visit England despite his longstanding admiration for King
James I (ruled 1603–1625). During this period his mother was
accused of witchcraft. Kepler directed the defense that led to
her acquittal in 1620–1621. The work that had secured the favor
of the imperial house for so long, the Rudolfine Tables, was
completed in 1627.
With the increasing violence and disorder of the Thirty Years'
War, Kepler again sought the protection of a powerfulpatron, and
he became astrological adviser to A. W. E. von Wallenstein, the
leading Catholic general, in 1628. His patron's fall from power
immediately preceded his own death, at Regensburg, in 1630. In
the Mysterium Cosmographicum, Kepler presented the most
important defense of Suncentered astronomy since the appearance
of Nicolaus Copernicus's De Revolutionibus Orbium Coelestium in
1543. Uniting ideas from his education in mathematics and
religion, Kepler proposed that God had employed each regular
geometrical solid exactly once in the plan of the world. Nesting
the solids within each other, the orbs defining the limits of
the planets' motions could be inscribed between them. The five
regular solids provided the spacing between six orbs, explaining
both their relative distances and the number of planets (the
EarthMoon system forms one unit). On both counts Kepler's Suncentred
model could be argued to be superior to the Earthcentred
Ptolemaic system. But Kepler's defense of Copernicus faced
another rival: the newly proposed hybrid system of Tycho Brahe,
in which Earth was central and stationary, the Moonand Sunwent
aroundthe Earth, butall the other planets circled the Sun.
On arriving in Prague in 1600, Kepler was effectively
subordinated to Brahe, who first set him to writing an attack on
an earlier imperial mathematician (A Defense of Tycho against
Ursus). Although not actually published during Kepler's
lifetime, this work gives valuable insights into both the state
of astronomy and Kepler's novel methodological ideas. Brahe had
presented Kepler to Rudolf II as the man who would distill
Brahe's decades of observations into new astronomical tables
that would carry the emperor's name. When Brahe died
unexpectedly in 1601, the importance of this project helped
Kepler to succeed Brahe as imperial mathematician. Kepler used
the superlatively accurate and complete observations to show
that Brahe's cosmic scheme was untenable, and to replace
Copernicus's circlebased models with elliptical orbits.
In 1604 Kepler published an important work on optics, which
treated the nature of light and vision, the phenomena of
refraction, and the applications of optics in astronomy. During
the same period he established that the path of Mars was an
ellipse and introduced a new way of calculating the planet's
position based on the novel concept of an orbit with the Sun at
one focus (a principle now called the first law of planetary
motion). He showed that his new approach was superior not only
to the models of Ptolemy and Brahe, but also to the original
form of Copernicus's system. Also improving on Copernicus, he
was able to show that the planes of the planet's orbits
intersected in the Sun. He also suggested that the Sun was the
origin of a quasimagnetic force responsible for the planets'
motions. Based on these physical ideas, he argued for a
connection between the speed of a planet along its path and the
area swept out by the line connecting it to the Sun (now called
the second, or area, law). He demonstrated this result first for
a circular path, then for an ellipse. Although originally
presented only for the case of Mars, the elliptical orbit and
the mathematical principles governing its motion were intended
to extend to all planets, based on universal physical
principles. Kepler advertised the new connection between physics
and astronomy in his book's title, A New Astronomy, Based on
Causes, or Celestial Physics. It appeared in 1609 after a delay
caused by Brahe's heirs.
In Prague, Kepler also produced two important works attempting
to reform astrology, On More Certain Foundations for Astrology
(1601) and Tertius Interveniens (1610; The intermediary third
position [between two extremes]). He rejected the traditional
astrological machinery of houses, but retained the idea that
geometrical configurations of celestial objects influenced human
judgment and caused terrestrial weather. Also in 1610 he gave
enthusiastic support to Galileo Galilei (in Conversation with
the Sidereal Messenger, 1610, and preface to the Dioptrice,
1611), and confirmed the latter's telescopic discovery of the
moons of Jupiter.
During his time in Linz, Kepler's two most important productions
were the Harmony of the World (1619) and the Epitome of
Copernican Astronomy (which appeared in several volumes,
1617–1621). The former attempted a grand synthesis of geometry,
harmonics, astrology, and astronomy, and presented the music of
the spheres, in the form of tones generated as planets vary in
speed throughout their orbits. Here also Kepler stated the third
law of planetary motion, connecting the square of the planetary
year with the cube of its mean distance. The Epitome of
Copernican Astronomy was a systematic presentation of Kepler's
version of the Copernican system, intended as a textbook, and as
a basis for understanding Kepler's approach in the Rudolfine
Tables. Appearing in 1627, the tables successfully predicted
that Mercury would pass across the face of the sun in November
1631, showing that Kepler had improved the accuracy of
positional calculations by a factor of ten.
Kepler was an innovator where Copernicus was a renovator.
Copernicus had recentred the planetary system, but his
calculations of planetary positions took as their geometrical
centre the mean sun, a constructed point, located elsewhere than
the Sun itself. The Sun played no physical role in Copernicus's
system and he retained celestial spheres to move the planets.
Like Ptolemy, Copernicus continued to use circles carrying
circles to predict the positions of planets against the
background of fixed stars, and although distances were
calculable in his system, they played no role in predicting
positions. Kepler introduced the modern form of Copernicanism.
His planets moved freely through the heavens, propelled by a
force originating in the Sun, along orbits that intersected at
the Sun. They obeyed mathematical laws that united physics and
astronomy in a new way. Their path through space was an ellipse,
not a circle, and their distances and velocities were linked in
the second law.
Kepler's insights were not immediately accepted by
contemporaries, but they were vindicated by Isaac Newton
(1642–1727), who replaced Kepler's solar force with universal
gravitation, and demonstrated that the three laws of planetary
motion followed from his own more general laws of motion in the
case of a planet moving around the Sun. Although the laws of
planetary motion became central results of the later mechanical
philosophy, Kepler himself was not a mechanical philosopher.
Kepler's sun rotates because of an animating spirit; the planet
Earth has a spirit that perceives celestial alignments and
creates weather; in the 1609 presentation of Kepler's theory,
planets are capable of directing their own motion of approach to
or recession from the Sun. In his last work, the Somnium,
published posthumously in 1634, another kind of spirit narrates
the appearance of the heavens as seen from the Moon. In Kepler's
cosmos, mathematical regularities are evidence of controlling
minds, and the structure of the universe, which Kepler spent his
life uncovering, testifies to the architectonic mind of its
Creator.
JACANA HOME PAGE

CLASSIC VIDEO CLIPS

JACANA ASTRONOMY SITE
JACANA PHOTO LIBRARY 
OLD MAUN PHOTO GALLERY 
MAUN PHONE DIRECTORY
FREE FONTS 
PIC OF THE DAY

GENERAL LIBRARY 
MAP LIBRARY 
TECHNICAL LIBRARY
HOUSE PLANS LIBRARY

MAUN EMAIL, WEBSITE & SKYPE LIST

BOTSWANA GPS COORDINATES
MAUN SAFARI WEB LINKS 
FREE SOFTWARE 
JACANA WEATHER PAGE
JACANA CROSSWORD LIBRARY 
JACANA CARTOON PAGE 
DEMOTIVATIONAL POSTERS
This web page was last updated on:
09 March, 2009
