Early Years
Following his exile, Kepler was
employed as an astrologer for Albrecht von Wallenstein (1583-1632), the duke of
Friedland, who led his armies to many victories during the Thirty Years War
(1618-1648). Kepler was disdainful of conventional astrology and presented
interpretations based on the angles between planets and stars. He died while on
route to collect money owed him in relation to his work, The Rudolphine
Tables, a collection of observations and calculations made during under the
rule of Holy Roman Emperor Rudolf (Kepler 235, 250).
The Mystery of the Universe
Kepler's first major work, Mysterium Cosmographicum (The Mystery of the Universe), was
published in 1596. In it, he supports the Copernican heliocentric model with
numerous arguments, and in more detail than did Copernicus himself. Kepler
applied the full force of mathematics in providing proofs of his positions,
moving discussion of the Copernican model to another level. Copernicus, while
moving the Earth out of the center of the model of the universe, persisted in
attributing special qualities to the Earth regarding its orbit and relationship
to other heavenly bodies. Kepler rightly proves in Mysterium Cosmographicum that the Earth should be treated no
different than any other planet (Kuhn 209-210).
Influences
Michael Maestlin introduced Kepler to
the Copernican heliocentric model at the University of Tübingen (a theological school). Maestlin was a lecturer who served
as an early mentor to Kepler and encouraged him in his studies. A series of
letters in 1595 from Kepler to Maestlin outlined Kepler's thoughts on proofs
regarding the Copernican system. These letters showed Kepler's thoughts on
using three-dimensional polyhedrons as mathematical models to be used to figure
the orbit and arraignments of the planets instead of the two-dimensional
figures that Copernicus and others had been using (The Secret of the Universe 18, 22).
Maestlin helped Kepler by providing
methods for calculating distances of the planets to the Sun and serving as a
sounding board for his ideas. Maestlin suggested that Kepler present his
information supporting the Copernican system as a mathematical hypothesis so as
to avoid a confrontation with the Lutheran Church. Although Kepler suspected
his mentor of privately supporting the Copernican system, Maestlin never made
an overt declaration in support of it. In 1616, the same year the Vatican
condemned the Heliocentric model, Maestlin would publicly reject the idea in a
letter, but this did not stop Kepler from pursuing his ideas (The Secret of the Universe 17).
The Church Intercedes
Kepler required the permission of the
Rector and Senate of the University of Tübingen in order to publish Mysterium Cosmographicum (The Mystery of the Universe). A chapter
that tried to reconcile the Copernican system with the Bible was removed as a
result of the University's review (The
Secret of the Universe 21). While the work itself was approved to be
published, the rector who approved it, Matthias Hafenreffer, would later rail
against it in a sermon. This was not the first time Kepler encountered the
religious intolerance. As a student at Tübingen University a professor rejected
an essay he wrote on the Copernican system. Later, in 1620 he would
successfully defend his mother against charges of witchcraft (Somnium xvii, xix).
The Noble Dane
In December 1597, Kepler sent to Tycho
Brahe, “the Noble Dane,” a copy of Mysterium
Cosmographicum. In response, Brahe sent a letter to Kepler's mentor
Maestlin noting his disagreement with Kepler’s conclusion regarding the heliocentric.
However, Brahe did assert that progress could not be made through a priori
deductions, but only through accurate observations and calculations. As a
consequence, Brahe was sufficiently intrigued by Kepler's work to invite him to
Uraniberg; although, frankly, Brahe was more interested in Kepler’s
mathematical ability than in his theories (The
Secret of the Universe 22-23).
Kepler refined the art of observation
and data collection under Brahe. Equipped with the Noble Dane's extensive data
from a lifetime of obsessive observation, Kepler applied the research towards
his next published work, Astronomie Nova
(The New Astronomy) (Stephenson 21).
Despite religious convictions that prevented Brahe from seeing the logic of a
heliocentric model, his dedication to accurate scientific data and mathematical
calculations is a lasting tribute to the Danish astronomer and a major
contribution to the Copernican Revolution.
The New Astronomy
Astronomie Nova, published in 1609, introduces Kepler's first two laws of motion.
Ptolemy, Copernicus, and Brahe all explained the apparent retrograde orbit of
the planets as the result of a series of epicycles that take place within a
planet's orbit, both of which were assumed to be perfect circles (Kuhn 212).
This was in accordance with the belief that the heavens were divine in origin.
Since anything divine was assumed to be perfect, the orbits must therefore be
perfect 360-degree circles. Kepler's observations proved this doubtful and he
used Brahe's data to establish the first two of three laws that would serve as
the foundation of Isaac Newton's Principia
Mathematica (Stephenson 1).
Kepler's Laws of Motion
Kepler's First Law: Planets move in simple elliptical orbits around a focal point,
the Sun (Kuhn 212).
This is the equation for an ellipse:
X2
A2
|
+
|
Y2
B2
|
= 1
|
Kepler's Second Law: The speed of the
orbit of each planet varies in proportion to its distance. The closer to the
focal point, the Sun, the faster the speed (Kuhn 212).
 |
| Fig. 2. The space between the lines represents a unit of time. |
This means that a planet will cover
the same distance in one hour, for example, whether moving quickly close to the
Sun, or slowly further away from it. Ironically, even though Kepler's Second
Law was proven true, Isaac Newton showed Kepler's mathematical methodology and
premise regarding velocity were fallacious (Westfall 8).
The Harmony of the World
Ten years after Astronomie Nova, Kepler publishes Harmonices Mundi (The Harmony
of the World). In it, he establishes a third law regarding the motion of
the planets.
Kepler's Third Law: The squares of the periods of the
planets are proportional to the cubes of their semi-major axes. In other words,
as a planet moves away from the Sun its orbital speed decreases (Westfall 216).
T= The orbits of two planets
R= Mean distance between planets and
sun
Ta2 / Tb2
= Ra3 / Rb3
Based on the second law it may be
logically assumed that the further away from the Sun a planet got the slower it
would go, but Kepler had insufficient data to support a third law to be
published in Astronomie Nova. By 1619,
however, he had sufficient data to back a third law and presented it in Harmonices Mundi. It is this third law,
and the data that supports it, that inspired Newton's law of gravitation; an
idea that Kepler himself touched upon via his "theory of heaviness" that
he mentions briefly in the introduction to Astronomie
Nova (Stephenson 4).
With the publication of Astronomie Nova by Kepler in 1609, yet
another figure enters the stage whose personality and assiduous dedication to
the scientific method will bring Copernicus’ theories into full direct conflict
with religious authority…Galileo Galilei.
Related Content
Burne, Jerome, ed. Chronicle
of the World. Paris: Jacques
LeGrand S.A.
International Publishing, 1989. Print.
Field, J.F. The MacTutor
History of Mathematics Archive:
Johannes
Kepler The
University of St. Andrews, Scotland, School of Mathematics and Statistics, 1997. Web. 7 Dec.
2000. <http://www-groups.dcs.st-and.ac.uk/~history/
Mathematicians/Kepler.html>.
Kepler, Johannes. The Secret
of the Universe. Trans. A.M.
Duncan. New
York: Abaris Books, 1981. Print.
---. Somnium. Trans.
Edward Rosen. Madison,
Milwaukee and
London: The University of Wisconsin
Press, 1967. Print.
Kuhn, Thomas, S. The
Copernican Revolution: Planetary
Astronomy
in the Development of Western Thought.Cambridge: Harvard University Press, 1957. Print.
Stephenson, Bruce. Kepler's
Physical Astronomy. New York,
London,
Paris, Berlin and Tokyo: Springer-Verlag, 1987. Print.
Westfall, Richard, S. The
Construction of Modern Science.
Cambridge,
New York and Melbourne: CambridgeUniversity Press, 1971. Print.
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