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JOHANNES KEPLER: THE SEARCH FOR "HARMONIES"

by Neal McLain, CSBE

For hundreds of years, up until the 16th Century, mankind had accepted the idea that the earth is the center of the universe. The Greek astronomer and mathematician Ptolemy (A.D. 85-165) had published a unified theory supporting the idea, and it was not seriously challenged for the next fourteen centuries.

But by the middle of the 16th Century, a new idea was beginning to take hold: that the sun is the center of the universe. The Polish monk Nicolaus Copernicus (1473-1543) had published the idea, but it was only after his death that the idea began to spread.

During the latter half of the 16th Century, the principal exponent of this idea was the Danish nobleman Tycho Brahe (1546-1601). Using funds provided by his patron, King Frederik II of Denmark, Tycho built an observatory on the Island of Hven. He called it Uraniborg, The Castle of the Heavens, and he filled it with the best astronomical instruments of the day -- many designed and built to his own specifications. Over the next 25 years, he proceeded to assemble the most precise set of astronomical observations the world had ever known.

After the death of King Frederik, Tycho fell out of favor with the Danish government, and eventually moved his observatory to Prague. It was in Prague that he met the young German mathematician Johannes Kepler (1571-1630). He agreed to take Kepler on as a student and apprentice. He gave him access to the astronomical tables he had compiled at Uraniborg, and assigned to him the task of calculating the orbit of Mars. Shortly before his death, he formally presented his tables to Kepler.

Kepler believed fervently in the idea of divine creation, and he was convinced that God had created a universe based on mathematical "harmonies". It seemed obvious to him that these harmonies would turn out be elegantly simple, if only he could discover them.

Kepler spent the last thirty years of his life searching for harmonies. He studied Tycho's tables, and added many of his own observations, all the while pursuing his old problem: the mathematical definition of the orbits of the planets. He tried and rejected many theories: concentric circles based on regular geometrical figures, concentric bowls based on regular geometrical solids, and an endless variety of numerical series.

It was out of this work that Kepler's three great laws eventually emerged. When he finally determined the orbit of Mars, he had discovered what turned out to be the First and Second Laws, which he published in 1609. It took him another nine years to discover the mathematical connection between orbit radius and orbit period; this became the Third Law, published in 1618.

Kepler was never able to explain the theoretical basis for the laws; indeed, there is little evidence that he ever tried. He derived the laws solely from empirical observation. But in his own mind, he had proven his thesis: God had indeed created a universe based on simple mathematical harmonies.

It would be another 70 years before Kepler's laws were finally proven mathematically. This was the work of the English mathematician Isaac Newton (1642-1727), who developed the fundamental theory that made the mathematical proof possible: the theory of universal gravitation. Once universal gravitation was understood, the proof of Kepler's laws followed directly.

But it is Kepler who first discovered the laws that bear his name. Like all significant physical laws, Kepler's laws have stood the test of time: they are as clear and true today as they were in Kepler's day. Indeed, Kepler's Laws form the fundamental basis for the entire modern field of satellite communications.

Further readings:
•  Kepler's Laws of Planetary Motion from University of British Columbia, Vancouver, British Columbia, Canada.
•  Johannes Kepler Biography from Rice University, Houston, Texas, USA
•   Johannes Kepler Biography from St. Andrews University, Scotland, U.K.
•   Johannes Kepler Biography by Eric W. Weisstein, Urbana, Illinois, USA.
•  Physics for the Inquiring Mind by Eric M. Rogers. Princeton: Princeton University Press, 1960.

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