Johannes Kepler
Johannes Kepler is now remembered for discovering the three laws of planetary motion, and writing about them in books that were published in 1609 and 1619. He also did important work in optics, discovered two new regular polyhedra, gave the first mathematical treatment of close packing of equal spheres, gave the first proof of how logarithms worked, and devised a method of finding the volumes of solids of revolution. This can be seen as contributing to the development of calculus. Not only did he help the development of calculus, but he calculated the most exact astronomical tables known today. This accuracy did much to establish the truth of heliocentric astronomy, which states that the sun, and not the earth, was the center of the planetary system.
Kepler was born in the small town of Weil der Stadt in Swabia, and moved to nearby Leon berg with his parents in 1576. His father was a mercenary soldier and his mother the daughter of an innkeeper. Johannes was their first child. His father left home for the last time when Johannes was five, and is believed to have died in the war in the Netherlands. As a child, Kepler lived with his mother in his grandfather’s inn. He tells us that he used to help by serving in the inn. It was said that the customers of the inn were sometimes startled by the child’s unusually high math skills. Kepler’s early education was in a local school and then at a nearby seminary, from which he went on to enroll at the University of Tubingen.
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At this time, it was usual for all students at a university to attend courses on mathematics. These courses usually included the four mathematical sciences: arithmetic, geometry, astronomy and music. However, what was taught depended on the university. At Tubingen, Kepler was taught astronomy by one of the leading astronomers of the day, Michael Maestlin. The curriculum included geocentric astronomy. This is the study of how all seven planets at the time – Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn – moved around the Earth. Their positions to the stars were being calculated by combining circular motions. This system was what worked with the current physics of the time, although there were certain difficulties. However, these astronomers, who also saw themselves as mathematicians, were content to carry on calculating positions of planets. They figured they would leave it to natural philosophers to worry about whether the mathematical figures added up to the physical ones. Kepler, however, did not take like this attitude. His earliest published work in 1956 says that people should consider the actual paths of the planets, and not just the circles used to construct them.
At Tubingen, Kepler studied Greek and Hebrew as well as mathematics. Ironically, at the end of his first year Kepler got A’s in every subject except mathematics. It is supposed that Maestlin was trying to tell him he could do better, because Kepler was one of the select pupils that Maestlin chose to teach more advanced astronomy to. He was teaching them the new, heliocentric cosmological system that was formed by Copernicus. Kepler almost instantly accepted that the Copernican system was physically true.
It seems that even in Kepler’s student days there were signs that his religious beliefs were not entirely in tune with the orthodox Lutheranism religion that was prominent in Tubingen. This ties up with Kepler’s astronomy because he apparently found difficulties in explaining how force from the Sun could affect the planets. In his writings, Kepler usually is known for laying his opinions on the line. This led officials at his university to doubt his religious beliefs. These might be why Maestlin persuaded Kepler to abandon plans for ordination and instead take up a post teaching mathematics in Graz. Religious intolerance began to become much more strict in the years to come. Kepler was asked to leave his church and his religion in 1612. This caused him much pain, and even though he had relatively high social standing, as Imperial Mathematician, he never succeeded in getting the ban lifted from his church.
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... had constructed the Universe in accordance to a mathematical scheme, he saw his ideas as a progression ... by Kepler, which came to be known as his Second Law, revealed that a line joining the planet to ... he saw his progression in the fields of astronomy and mathematics as a "fulfillment of his Christian ... to defend Copernicus and his Copernican system. The theory that the planets revolve around the sun not ...
Even before this ban though, was when Kepler began his findings. The life-long question that concerned Kepler was the nature of the timing and motion of the celestial bodies in space. He was convinced that simple mathematical concepts existed that could make sense of the planetary system. He saw the planetary system operating according to its own set of mathematical laws, and not previous ones, which was quite a radical idea for those times.
Kepler was a mathematician rather than an observer. To make his calculations, Kepler was supplied with years of impeccable data by his elder, Tache Brahe, who had carefully marked the position of Mars in relationship to the rest of the bodies in space. Kepler rejected many ideas, such as circular orbits, because they did not fit Brahe’s observations. He stuck very close to the observations that Brahe had made for him, as he was certain that they would be very accurate. In 1609, Kepler finally published his first two laws of planetary motion in a book entitled New Astronomy. A decade later, in 1619, his third law was published in The Harmonies of the World.
Through these works, Kepler can be credited, in many respects, to mark the beginnings of what we call modern science. Kepler developed his empirical laws from Brahe’s data on Mars. “By the study of the orbit of Mars,” he said, “we must either arrive at the secrets of astronomy or forever remain in ignorance of them.” However, in what proved to be a step that would change science, Kepler then went on to say that his laws applied to all the planets, including the Earth, without ever actually checking to make sure that this was true. Today we know that his laws even apply to comets. Though Kepler may not have expected this, his laws can also predict and explain the motion of satellites orbiting the earth. The expectation that the mathematical laws of science are universal is very accepted in our time. This makes it difficult to imagine just how important Kepler’s observations and calculations actually were.
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Kepler’s work put to rest any ideas that planets move in perfectly circular orbits, because nature has decided that the celestial bodies must show perfection in their movements. He also put to rest, in the scientific community, the ancient idea that there existed a complex motion of planets that somehow effects what we do. Although Kepler never knew why planets move by the empirical relationships that he explained in his three laws, he tried to find a cause of which these three laws applied. He stated, “I am much occupied with the investigation of physical causes. My aim in this is to show that the celestial machine is rather a clockwork.” Kepler sensed that two bodies have a natural magnetic attraction to each other and guessed that the Sun had an attractive force. However, his theory carried on to Newton, half a century later, to formulate a theory of motion, which involved gravity as the cause of planetary motion.
Without Kepler’s great observations and calculations, the world would be very different today. Many would go on thinking that the entire solar system orbited around the Earth, instead of the Sun. Due to the fact that Kepler spent his life trying to disprove this theory, our world is very much changed today. We now understand that the solar system orbits around the sun, and that the planets are attracted to this center because of the natural gravitational attraction between two bodies. His observations were very important to physicists and mathematicians alike. His calculations are still being used today, which shows exactly how accurate they were. His death in 1630 was a great loss to the science world, but his contributions will last forever.
