# Kepler

The work of Kepler rests on the observations made by Tycho Brahe throughout many years. Tycho Brahe was a Danish nobleman born in 1546. He studied law at the University of Copenhagen in his youth and was first attracted to Astronomy by the occurrence of a predicted eclipse. He began to make astronomical instruments, then to take observations at Augsburg and Wittenberg. In the meantime he married a peasant girl, and became interested also in alchemy and astrology.

In 1576 he established the first observatory at Huen, where he remained for twenty years. After being banished from Germany and impoverished he was invited by the Emperor Rudolph to Prague. Here he began the work of compiling the Rudolphine Tables. These embodied a great series of observations upon the various apparent locations of the planets. He soon afterward invited Kepler, a young astronomer, to be his assistant. Tycho Brache died in 1601, but Kepler went on with his work.

John Kepler was born in 1571 in Würtemberg. His father lost his money through indorsing paper for a friend, and John was taken from school for three years and kept at work in his father’s tavern until twelve years old. Then he was sent to a monastic school and finally to the University of Tübingen. He was very sickly, but a good student, and ranked second in his class. He became interested in the Copernican system and in 1599 was invited by Tycho Brahe to be his assistant.

Tycho Brahe had assigned him the study of the planet Mars, and Kepler followed up this work after Tycho’s death.

KEPLER

After and Old Engraving

Tycho’s tables were very accurate and Kepler used them to try to discover some regular motion of the planet that would account for its apparent positions.

Copernicus had thought the planets revolve in circles tracing also epicycles in so doing. Kepler tried this theory by his tables and found it would not account for the positions of the planet Mars. He tried hypothesis after hypothesis, but each time after the most arduous calculations he proved the theory wrong. His problem was to choose such an orbit for both Mars and the earth that a line run from the earth through Mars into the heavens would always follow the apparent positions of Mars. The difficulty of the problem, with his facilities, may be imagined. Sometimes he came as close as an eighth of a degree to getting the theory to fit in with the observations, but he had faith in the tables and refused to be satisfied. He tried various circles with epicycles, also tilting the planes of the orbits. Then putting the sun away from the center of the circle, he thought of varying the rate of speed, keeping the areas marked off equal in equal times. This helped, but not enough. He thought of ovals, and worked out the problem for several, but became almost discouraged by the enormous and practically impossible calculations involved. He had been working six years and no solution was in sight. He tried a circle with Mars oscillating to the extent of the diameter of an epicycle, and at last found that he could represent the movements of the planet in that way. He looked at it again and saw that the curve described is an elipse with the sun in one focus. He feverishly made a test of his idea that the areas swept out by the planet in equal times are equal and was overjoyed to find it correct. In his delight he drew a figure of victory on his diagram. The orbit of Mars was found.

In 1611 his patron Rudolph was forced to abdicate and Kepler was left penniless. His wife died and one of his three children. Kepler then moved to Linz and accepted a professorship there.

His mother had been a virago and his father had abandoned her. Now she was accused of witchcraft and Kepler had to hurry to Würtemberg to save her.

He was interested in the idea of the "music of the spheres," and actually wrote out the notes they sang. Then he began to brood over the relation of the distances of the planets from the sun and their times of revolution.

He did not know the actual distances of the planets from the sun but all he needed was the relative distances, and the lengths of theiryears (also known). After a great many experiments he finally thought of comparing the cubes of their relative distances with the squares of the times, and to his intense joy saw that they agreed—the squares of the times of revolution of the planets are proportional to the cubes of their distances. This third law was found in 1618. His delight is shown by the following letter:

"What I prophesied twenty-two years ago, as soon as I found the heavenly orbits were of the same number as the five (regular) solids, what I fully believed long before I had seen Ptolemy’s Harmonies, what I promised my friends in the name of this book, which I christened before I was sixteen years old, I urged as an end to be sought, that for which I joined Tycho Brache, for which I settled at Prague, for which I have spent most of my life at astronomical calculations—at last I have brought to light, and seen to be true beyond my fondest hopes. It is not eighteen months since I saw the first ray of light, three months since the unclouded sun-glorious sight! burst upon me. Let nothing confine me: I will indulge my sacred ecstacy. I will triumph over mankind by the honest confession that I have stolen the golden vases of the Egyptians to raise a tabernacle for my God far away from the lands of Egypt. If you forgive me I rejoice; if you are angry, I cannot help it. The book is written; the die is cast. Let it be read now or by posterity, I care not which. It may well wait a century for a reader, as God has waited six thousand years for an observer."

He died in 1630, but his work is deathless. He had seen and proved the solar system, and that there is unity in the universe.

Probably the most characteristic passage in his writings in regard to his discoveries is that just given. We give below the beginning of his Epitome of Astronomy, a book that had an enormous influence in spreading the new ideas of the science.