JOHANNES KEPLER AND THE ENTRENCHMENT OF THE HELIOCENTRIC CONCEPT
By: Tara Beheshti
For: Professor Clarke
Due:
"The diversity of the phenomena of nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment." – Johannes Kepler (1)
On
Kepler was introduced to astronomy at a very early age, which is probably why
he developed such a strong interest in the discipline. He observed the Comet of
1577 with his mother at the age of five and the Lunar Eclipse of 1580 at the
age of nine. (3) Unfortunately, the small pox that Kepler suffered through
childhood weakened his vision so he was more inclined to work with mathematics
rather than naked eye observations. In 1587, Kepler attended the
At this school Kepler published his first work in 1596 which was called Mysterium Cosmographicum or The Sacred Mystery of the Cosmos. This book presented Kepler’s cosmological theory based on the Copernican system and explained how five of the Pythagorean (perefect) polyhedra dictate the sturcture of the universe. Perefect polyhedra are hollow polyhedra with all the faces made of identical regular polygons and which has the same number of faces meeting all its verticies. For example, Kepler’s Great Dodechahedron has twekve pentagon faces, twelve verticies, and thirty edges. In his work Kepler explained that the distances from the planets to the sun were given by spheres inside perfect polyhedra. With this he identified five intervals between the six known planets at that time: Mercury, Venus, Earth, Mars, Jupiter and Saturn. Kepler’s measurements were very close to the accurate distances we have today, and this was considered a great accomplishment for a scientist in his time.
In 1599, after reading Kepler’s book, which showed his impressive talent as a mathematician with his use of geometry, Tycho Brahe invited Kepler to Prague to work as his assistant. Although the two scientists did not agree on Kepler’s strong belief in the Copernican system, they still had a mutal respect for each other’s talents. Brahe had been observing the orbit of Mars and transferred this work to Kepler. Brahe and Kepler worked together collecting data to add to Brahe’s already vast collection for two years, until Brahe’s death in 1601. Kepler was appointed Imperial Mathematician in his place, which was the most prestigous role for a Mathematician in Europe. He continued to study Mars and had vast amounts of data to use in testing his theories. Kepler finally concluded that Mars’s orbit was an ellipse and this would inspire a later book and two ground breaking laws.
In 1604, Kepler presented Astronomia pars Optica or The Optical Part of Astronomy. This work made his the first to explain “atmospheric refraction”. This phenomena occurs when a ray of light changes direction as it passes from space through the atmosphere. This would cause heavenly bodies to appear in a different location then they actually are. Also at this time, Kepler observed a supernova in the Milky Way and used it as evidence to argue that the universe is not changeless. Kepler’s agruement would later support Galileo’s work. After this, Kepler began to develop the first astronomical model of the solar system that did not use circular orbits. In 1609, he published Astronomia Nova or New Astronomy. This book conatined Kepler’s very important first and second laws of planetary motion.
Kepler’s first law was called “The Law of Ellipses”. This stated that the orbits of the planets are ellipses with the Sun at one of the foci. An elipse is a closed curved shape that is defined by two foci. If the two foci were in the same place the ellipse would actually become a circle. An ellipse has two axis, the major and the minor. The shape of an ellipse is measured by its “eccentricity”. The flatter an ellipse the closer the eccentricity is to one. A cricle would have an eccentricity of zero. (4)
Kepler’s second law is “The Equal-Areas Law”. It claims that the line that connects the planet to the Sun sweeps out equal areas in equal times. This conclusion was drawn from Kepler’s observation that the speed of a planet’s orbit would vary throughout its journey. Planets would move the fastest when closest to the Sun at a point called perihelion. Planets would move the slowest when farthest from the Sun at a point called aphelion. The motion that Kepler’s law describes gives the distance from a planet to the Sun is equal to the length of the semimajor axis. This is half the distance of the major axis of the planet’s ellipse.
In 1610, Galileo discovered four moons of Jupiter with a spyglass. Later that year, Kepler used a telescope to observe Jupiter’s moons and published Narratio de Observatis Quatuor Jovis Satellitibus or Narration about Four Satellites of Jupiter observed. This book was a very good suport for Galileo because many other scientists at the time either doubted or denied the existence of the moons. Kepler also coined the term “satellite” through this work.
Kepler was comissioned by the Emporer Rudolf II to use Brahe’s extensive catalogue of raw observational data to produce the “Rudolphine Tables”. This constisted of star catalogues and planetary tables that conatained positions for 1,005 stars, with directions and tables for locating the planets in the solar system. However, he postponed his work on a multi-volume astronomy textbook and the tables when his mother was being hunted down for suspicion of witchcraft. During this time Kepler focused on his harmonic theory and as a result published Harmonices Mundi or Harmony of the Worlds in 1619. This contained Kepler’s third law of planetary motion.
The third and final law of planetary motion was “The Harmonic Law”. This law states that the squares of the orbital periods of the planets around the Sun are proportional to the cubes of the orbital semimajor axis. The law is often written as:
p2 = a3
Where p is the orbital period in Earth years and a is the length of the semimajor axis (average distance from the Sun) in astronomical units. So if the time of a planets orbit around the Sun can be used to calculate its average distance from the Sun or vice-versa.
Kepler’s three laws were finally complete and brought great success to him when he was the first astronomer to correctly predict the transit of Venus in 1631. A transit occurs when Venus passes directly between the Sun and the Earth and covers a small portion of the Sun’s disc. Kepler’s laws were controvsersial during his time because they were the first concrete evidence for the Heliocentric model of the solar system. They simply would not work under the Geocentric model. Later on Issac Newton would further support these laws by explaining them using his laws of motion and law of universal gravitiation. Kepler simply could not provide more evidence to support his laws because he tended to use “non-scientific mystical speculation”. (3) This simply refers to Kepler’s deep belief in God, and that despite the use of his mathematics simply left some phenomena to be worked “by the hand of God”.
Harmony of the Worlds also contained a connection between Platonic or perefect solids and classical elements. The tetrahedron was fire, the octahedron represented air, the cube was earth, the icosahedron was water, and the dodecahedron was the matter of the cosomos or ether. Ether was Aristotle’s fifth element, which he believed that the whole universe except for Earth was made of. Although Kepler seemed to have an obsession with the geometry of the universe, he proved to have a modern attitude compared to his predessors in being able to abandon his theories when they began to appear incorrect. Despite his impressive first astronomical model, Kepler was never able to fit the planetary orbits within polyhedra as he wished to do. Abandoning a theory which had seemed to be a great work of his, proved that Kepler was more interested in the discovery of truth rather than satisfying his own very strong beliefs.
In 1627 Kepler completed the Rudolphine Tables, which allowed for the calculation of the position of any planet in the past, present, or future. This would prove to be a very useful tool for astrologers to use in their predictions of the future. The tables are impressively accurate with their margin of error satying within 10 seconds of current measurements, unlike some earlier tables which were five degrees off.(5) The longitude of any planet could be found at any time using Kepler’s equation, which used logarithims for calculation. The Kepler equation is:
E - e sin E = M
The “E” stands for eccentric anomoly, “e” is the eccentricity of the ellipse, and “M” is the mean anomoly. An eccentic anomoly is the angle between the direction of the periapsis and the current position of an object in its orbit, which is projected on to a point perpendicular to the major axis that is measured from the centre of the ellipse. In astronomy, an apsis is a point of greatest or least distance of the elliptical orbit of a celestial body from its centre of attraction (in Kepler’s case the Sun). From this, the closest point of approach is called the periapsis. The mean anomoly is a measure of time specific to an orbiting body, which is a multiple of two radians at periapsis. The eccentricity of an ellipse denoted by “e” can be very simply defined in nonmathematical terms as “the degree of flatness of an ellipse”. This equation is introduced in Kepler’s work called the Epitome of Copernican Astronomy. Brahe had origionally wished for the tables to be based on the Geocentric system, but Kepler ignored his wish and based the calculations on elliptical orbits in the Heliocentric system.
After the Rudolphine Tables, Kepler was left with no work and no salary. This was a result of the Thirty Year’s War that had been taking place between Germany and Austria since 1618. Protestants were being presecuted in Linz where Kepler had lived so he was forced to leave and attempted to find work in other courts. Kepler was unsucessful in finding work for the rest of his life and died in Regesburg, Germany in 1630.
Some may argue that Kepler was simply a scientist that was capable only of building upon the work of others before him, and could not innovate his own successful ideas. However, Kepler seems to have formed the beginings of our first modern scientists. He was able to recognize the valuable work of those before him, such as Copernicus and Brahe, and use the already available data to move forward toward new discoveries. His life’s passion was to have the Heliocentric model accpeted throughout the world as the true workings of our solar system. Kepler was able to entrench the Heliocentric system into society through his ability to recognize the capability of human error. Unlike those before him, he was able to put aside his work when he could not prove it and strived to test his theories until they were proven through universally accepted tools of calculation such as mathematics. All of Kepler’s accomplishments, along with those of his peers, made the Scientific Revolution an important milestone in the history of humanity and its evoltion.
BIBLIOGRAPHY
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5. Kusukawa, S. (1999). Kepler and astronomical tables. Retrieved
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kepler. Retrieved