Jonathan Oster
Math 475W
First Minor Paper
Kepler
Johannes Kepler was a great mathematician and astronomer of the Renaissance period.
He was born on December 27, 1571 in the Holy Roman Empire in what is now Germany. His
father left home and likely died in a war in the Netherlands when Kepler was five. In his
childhood Kepler lived in his grandfather’s inn with his mother. He attended a local school and
then a seminary. His original aspiration was to be ordained as a Lutheran minister (1). Kepler
once said, “For a long time I wanted to become a theologian. Now, however, behold how
through my effort God is being celebrated through astronomy.” Kepler’s faith in God was the
source of his belief in the rational order of nature. His most famous accomplishment was his
three laws of planetary motion which demonstrated the importance of mathematics to the study
of nature. (1)
Kepler received his college education at the University of Tubingen, an orthodox
Lutheran school. He learned geocentric astronomy from Michael Mastlin. In geocentric
astronomy the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn were considered to be
the seven planets that orbited the Earth. Mastlin selected Kepler as one of the few students to
teach the new, heliocentric astronomy of Copernicus. In the Copernican system there were only
six planets including the Earth that orbited the Sun and the Moon was defined to be a new and
different type of body. Kepler quickly became a believer in the heliocentric system. He thought
this view agreed with observations such as the fact that Venus and Mercury are always observed
near the Sun. The Copernican system explains that this is because Venus and Mercury are
between the Earth and the Sun but the geocentric system cannot explain this. (1)
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Jonathan Oster
Math 475W
First Minor Paper
While Kepler agreed with Copernicus’s heliocentric model of the solar system he
disagreed with the idea that planetary orbits are circular. Instead Kepler believed that planets
orbit the Sun in an elliptical path. Kepler’s great scientific achievement was his three laws of
planetary motion that accurately describe the orbit of planets. His three laws are known as The
Law of Ellipses, The Law of Equal Areas, and The Law of Harmonies (2). The first two of these
laws were published in 1609 but the third wasn’t published until 1619 (5).
His first law, the Law of Ellipses, says that planets orbit the Sun in an elliptical path
where the center of the Sun is one of the two foci (2). Kepler discovered this when studying the
planet Mars. Kepler’s teacher Mastlin helped him get a job as a mathematical assistant for the
observational astronomer Tycho Brahe in Prague. Brahe got Kepler working on the issue of
Mar’s orbit. When Brahe died in 1601 Kepler became the Imperial Mathematician. Kepler used
the massive amount of observations that Tycho made to conclude that Mar’s orbit was an ellipse
and the Sun was one of the foci. Kepler found that this applies to all planets. (1)
The second law, the Law of Equal Areas, states that a line from the center of the Sun to
the center of a planet will cover an equal area in equal segments of time. For example, that
means that in every 31 day period the line from the center of a planet to the center of the Sun will
cover the same amount of area. A planet accelerates as it gets closer to the Sun and decelerates as
it gets further from the Sun. So a planet’s speed is the highest when it is closest to the Sun and
the lowest when it is furthest from the Sun. A planet’s speed is constantly changing as it goes
through its orbit of the Sun (2). Kepler also discovered this law while studying the orbit of Mars
(1).
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Jonathan Oster
Math 475W
First Minor Paper
The third law, the Law of Harmonies, says that the square of the period of time of a
planets orbit of the Sun divided by the cube of its average distance from the Sun is the same for
all planets. Algebraically the ratio T²/R³, where T is the period of orbit for a particular planet and
R is the mean distance from the Sun to the same planet, is the same for all planets (2). The third
law has been proven by observation and data to be correct. Kepler didn’t discover this until ten
years after his other two laws. It first appeared in his famous book “The Harmony of the World”
in 1619 and was added at the last minute after the book was already in press. (1)
Kepler’s three laws of planetary motion are natural scientific laws that the Universe
obeys and that are written in the language of mathematics. It is remarkable that nature follows
laws that are mathematical. In “The Unreasonable Effectiveness of Mathematics in the Natural
Sciences” the physicist Eugene Wigner wrote, “Why nature is mathematical is a mystery… The
fact that there are rules at all is a kind of miracle.” Kepler was a devout Christian who believed
this natural order was imposed by God. He once said, “The chief aim of all investigations of the
external world should be to discover the rational order and harmony which has been which has
been imposed on it by God, and which he revealed to us in the language of mathematics.” Kepler
believed that since human beings were created in the image of God they were able to understand
the Universe He created. Kepler thought of his scientific work as his Christian duty to study and
understand the works of the Creator. (1)
However there were some disagreements within the Church over the Copernican system.
But Kepler didn’t see any contradiction between the Copernican theory and the Holy Scripture.
In 1609 he wrote, “To teach mankind about nature is not the purpose of Holy Scripture, which
speaks to people about these matters in a human way in order to be understood by them and uses
popular concepts.” Thus, Kepler viewed science and religion as being perfectly compatible with
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Jonathan Oster
Math 475W
First Minor Paper
each other. In 1956 Kepler wrote, “I undertake to prove that God, in creating the universe and
regulating the order of the cosmos, had in view the five regular bodies of geometry known since
the days of Pythagoras and Plato, and that he has fixed according to those dimensions, the
number of heavens, their proportions and the relations of their movements.” He also said, “It is
an act of piety at the very beginning of this discourse about Nature to see whether it says
anything contrary to Holy writ. Nevertheless, I believe that is premature to raise this question
here before I am assailed. In general I promise to say nothing harmful to Holy Writ, and if
Copernicus is convicted of anything with me, I shall consider him finished. And this was always
my intention from the time when I began to examine the six books of Copernicus’s Revolutions.”
(3)
Kepler was married twice. His first marriage to a woman named Barbara was for love but
he married his second wife Susanna mostly because he needed someone to take care of the
children. At the wedding celebrations for his second marriage in 1613, after seeing the volume of
wine barrels estimated using a rod inserted diagonally through a hole, Kepler was inspired to
study the volumes of solids of revolution. He used a method based on Archimedes’ work that
used ‘indivisibles’ that is a predecessor to infinitesimal calculus. (1)
Kepler died November 15, 1630 in Regensburg, which is now in Germany. But the tomb
where he was buried was destroyed during the Thirty Year’s war (1). Kepler’s work did much to
advance mathematics and science. According to Wikipedia, “Kepler’s laws are part of the
foundation of modern astronomy and physics.” Later in the seventeenth century, Issac Newton’s
laws of motion and law of universal gravitation did more to explain Kepler’s laws and astronomy
(5). Kepler was an important part of the Scientific Revolution and a man of faith, “for whom
understanding the nature of the Universe included understanding the nature of its Creator.” (1)
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Jonathan Oster
Math 475W
First Minor Paper
Works Cited
1) J.V. Field, http://www-history.mcs.st-andrews.ac.uk/Biographies/Kepler.html
2) The Physics Classroom, http://www.physicsclassroom.com/class/circles/Lesson4/Kepler-s-Three-Laws
3) J.J. O’Connor and E.F. Robertson, http://www-history.mcs.standrews.ac.uk/HistTopics/Heliocentric.html
4) A.E.L. Davis, http://www-history.mcs.st-andrews.ac.uk/Extra/Keplers_laws.html
5) http://en.m.Wikipedia.org/wiki/Kepler’s_laws_of_planetary_motion
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