Thanks in part to the extensive legal defense Kepler drew up for her, she was released in October after attempts to convict her failed. She was, however, subjected to territio verbalis , a verbal terrorization that included displays of the instruments of torture that awaited her if she did not confess. Throughout the trial, Kepler postponed his other work on the Rudolphine Tables and a multi-volume astronomy textbook to focus on his "harmonic theory.

Kepler completed the last of seven volumes of his textbook Epitome of Copernican Astronomy in It brought together and extended his previous work and became very influential in the acceptance of the Copernican system over the next century. In , he completed the Rudolphine Tables , which provided accurate calculations of future positions of the planets and allowed the prediction of rare astronomical events.

On November 15, , Kepler died of a fever in Regensburg. Two years later, his grave was demolished by the Swedish army in the Thirty Years' War. Kepler inherited from Tycho Brahe a wealth of the most accurate raw data ever collected on the positions of the planets. The difficulty was in terms of making sense of the data. The orbital motions of the planets are observed from the Earth, which is itself orbiting the Sun.

As shown in the illustration below, this can cause the other planets to appear to move in strange loops.

### Johannes Kepler

To understand the orbit of Mars, Kepler needed to know the orbit of the Earth accurately. For that, he needed a surveyor's baseline. In a stroke of pure genius, he used Mars and the Sun as his baseline. He realized that even without knowing the actual orbit of Mars, it would be in the same place in its orbit at times separated by its orbital period.

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His geometrical analysis needed only the ratios of the distances of the planets from the Sun, not the exact distances. Historian of science William Boerst points out in Johannes Kepler, Discovering the Laws of Celestial Motion that Kepler was looking for both the accurate distance of Mars from the Sun and the period it took to move from one degree to the next.

To do so, he meticulously divided the orbit of Mars into segments. When he looked at the measured distances with the Sun at the center for each of the degrees, the variance from an ideal circle was enormous. After five years of painstaking study of the Mars orbit, Kepler began to question his own belief that the orbits must be circular. To attempt a description of the orbit of Earth, Kepler raised the question, how much time does it take for the planet to sweep out certain areas described by a line from Sun to Earth moving through a segment of the orbit?

Through his analysis of the data, he discovered that planets sweep out equal areas in equal times. Mathematical order was preserved in this theory, which seemed to accurately represent the data obtained by empirical observation. Applying this law rigorously to the orbits of the other planets led him to what we now refer to as Kepler's First Law of Planetary Motion.

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Elliptical orbits were the only shape that fit the data accurately. Finally Kepler understood that the planets move in elliptical orbits, with the Sun at one focus. He abandoned the circular theory and wrote that he "felt like I had been awakened from a sleep. Kepler expounded these two laws in his book Astronomia Nova New Astronomy , which was completed in and published in This book captured the imagination of Sir Isaac Newton more than a generation later. After 20 years of painstaking, trial-and-error efforts to make sense out of the data, Kepler arrived at his three laws of planetary motion:.

Kepler's elliptical orbit law : The planets orbit the sun in elliptical orbits, with the Sun at one focus. Kepler's equal-area law : The line connecting a planet to the Sun sweeps out equal areas in equal amounts of time. The constant of proportionality is the same for all the planets. Using these laws, he was the first astronomer to successfully predict a transit of Venus , for the year Kepler's laws were the first clear evidence in favor of the heliocentric model of the solar system, because they only came out to be so simple under the heliocentric assumption.

Kepler, however, never discovered the underlying reasons for the laws, despite many years of what would now be considered non-scientific, mystical speculation. Isaac Newton eventually showed that the laws were a consequence of his laws of motion and law of universal gravitation.

## Johannes Kepler This page is Copyright

From the modern vantage point, the equal-area law is more easily understood as arising from the conservation of angular momentum. On October 17, , Kepler observed that an exceptionally bright star had suddenly appeared in the constellation Ophiuchus. It was first observed by several others on October 9. It has since been determined that the star was a supernova, the second in a generation, later called "Kepler's Star" or Supernova No additional supernovae have been observed in the Milky Way, though others outside our galaxy have been seen.

Kepler also made fundamental investigations into combinatorics a branch of mathematics , geometrical optimization, and natural phenomena such as snowflakes , always with an emphasis on form and design. He was also one of the founders of modern optics, defining, for instance, antiprisms and the Kepler telescope, as detailed in his books Astronomiae Pars Optica and Dioptrice.

In addition, he was the first to recognize non-convex regular solids such as "stellated dodecahedra" , which have been named "Kepler solids" in his honor. Kepler was a Pythagorean mystic who incorporated religious arguments and reasoning into his work. He considered mathematical relationships to be at the base of all nature, and all creation to be an integrated whole. This was in contrast to the Platonic and Aristotelian notion that the Earth was fundamentally different from the rest of the universe, being composed of different substances and with different natural laws applying.

In his attempt to discover universal laws, Kepler applied terrestrial physics to celestial bodies. Moreover, Kepler was convinced that celestial bodies influence terrestrial events.

## Quotations by Johannes Kepler

One result of this belief was his correct assessment of the Moon's role in generating the tides, years before Galileo 's incorrect formulation. Another was his belief that someday it would be possible to develop a "scientific astrology," despite his general disdain for most of the astrology of his time.

Kepler discovered the laws of planetary motion while trying to achieve the Pythagorean purpose of finding harmony of the celestial spheres. According to historian of science James R. Voelkel Johannes Kepler and the New Astronomy , he asked a unique question: "Why did God choose to construct the solar system in this way and not another?

Developing his ideas from the time he taught geometry in Graz, Kepler began to think it was not a coincidence that the number of perfect polyhedra was one less than the number of known planets. Having embraced the Copernican system , he set out to prove a model in which the distances of the planets from the Sun were given by spheres inside perfect polyhedra, all of which were nested inside each other.

The smallest orbit, that of Mercury, was the innermost sphere. He identified the five platonic solidsâ€”cube, tetrahedron, dodecahedron, icosahedron, and octahedronâ€”with the five intervals between the six known planets: Mercury , Venus , Earth , Mars , Jupiter , and Saturn. Kepler wrote to Maestlin, his old astromony professor, expressing his intention to publish this model for the glorification of God. He felt he had found his holy calling in a new venue and wept tears of joy over what he referred to as "stupendous miracles of God.

In his books Harmonice Mundi and Mysterium Cosmographicum , Kepler further associated the platonic solids with the classical concept of elements: the tetrahedron was the form of fire, the octahedron was that of air, the cube was earth, the icosahedron was water, and the dodecahedron was the cosmos as a whole or ether.

There is some evidence that this association was of ancient origin, as Plato tells of one Timaeus of Locri, who thought of the Universe as being enveloped by a gigantic dodecahedron, while the other four solids represented the elements of fire, air, earth, and water. Kepler's attempts to fix the orbits of the planets within spheres separated by polyhedra never worked out. To his credit, he abandoned the theory when he realized that the astronomical data did not support it.

His most significant achievements came from the realization that the planets move in elliptical, not circular, orbits. This realization was a direct consequence of his failed attempt to fit the planetary orbits within polyhedra. Kepler's willingness to abandon his highly cherished theory in the face of precise observational evidence indicates that he had a very modern attitude to scientific research.

Kepler also took important steps in trying to describe the motion of the planets by appealing to a force that resembled magnetism, which he believed emanated from the Sun. Although he did not discover gravity, he seems to have attempted to invoke the first empirical example of a universal law to explain the behavior of both earthly and heavenly bodies. He, however, disdained astrologers who pandered to the tastes of the common man without knowledge of the abstract and general rules. He compiled astrological prognostications as a means of supplementing his meager income, but it would be a mistake to take his astrological interests as merely pecuniary.

As one historian, John North, put it, "had he not been an astrologer, he would very probably have failed to produce his planetary astronomy in the form we have it.

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