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Natural Science - Year I

Unit 27: Brahe, Kepler, and Elliptical Orbits

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History Weblecture for Unit 27

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History Lecture for Unit 27: Kepler and Epicycles

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Lecture outline:

The Followers of Copernicus

Continuing with our study of the "New Astronomy", we look at the accomplishments of Copernicus' followers and competitors.

Copernicus published his textbook and died--he never saw the furor it eventually raised. But that furor was a long time coming. For the first 70 or so years after the printing of the De Revolutionibus, there wasn't enough physical evidence or good observations to choose between Copernicus' model and the old Ptolemaic model of the solar system -- and in scientific terms, there really wasn't any evidence for the actual movement of the earth through space until Bessel managed to detect stellar parallax for 61 Cygni. That didn't happen until 1838, long after most of Europe had accepted Copernicus' heliocentric theory. So why did philosophers and scientists agree to his theory, if there was no direct observational evidence that the earth moved, to support it?

Tycho Brahe

In the late 16th century, two observers provided evidence that at least some of Aristotle's claims about the nature of celestial matter and the motion of planetary objects were wrong. Tycho Brahe was a very eccentric Danish astronomer who had some of his own funds and a position as the royal astronomer to the Danish king. He built a new observatory on Hveen, and improved or invented a number of devices to make better astronomical observations. He had the good fortune to observe carefully two major astronomical phenomena: a supernova in 1572, and a great comet in 1577.

Brahe's observations of the nova showed that the heavens changed: this was a new star, coming into being, growing in brightness, in contravention of the Aristotelian principle that stars made of the quintessence suffered no change, and could not be generated or corrupted.

When the comet appeared in 1577, Brahe carefully plotted its changing position against the background sky, and determined that it was not an atmospheric phenomenon (as Aristotle had claimed), but a body moving beyond the orbit of the moon. Moreover, it moved between the orbits of the planets, coming from as far away as Jupiter to within the orbit of the sun. If the crystalline spheres of Aristotle existed, than the comet was crashing through them!

Tycho was well aware of Copernicus' theory, but he did not agree that the earth could move in space. Instead, he proposed that all the other planets orbited the sun, while the sun circled the earth. This theory, while ingenious, had some severe flaws when applied to his own observations: it suggested that Mars would sometimes cross between the earth and the sun, which never happens.

Read about Tycho Brahe's life.

  • How was Tycho educated?
  • Who supported his astronomical research?

Examine several of Tycho's instruments from the High Altitude Observatory historical pages.

  • What improvements did Tycho make to his instruments?
  • How did this improve his measurements?

Johannes Kepler

One of Brahe's assistants was the German astronomer, Johannes Kepler.

Read the short biography of Johannes Kepler at St. Andrew's Mathematical History Site.

  • How was Kepler educated?
  • Who supported his astronomical research? (What are the implications of this kind of support to science and its advancement?)
  • How was Kepler influenced by Pythagorean ideas of proportion and harmony?

Read about ellipses and Kepler's Three Laws (you can stop at "Calculations using Kepler's Third Law — unless you want to read it all, of course).

  • Kepler's First Law: Planets move in orbits that have the shape of an ellipse. An ellipse is a set of points, the sum of whose lengths to two foci is constant. A line through the ellipse that passes through both foci is called the major axis. The semi-major axis is half of this line, from the center through one focus to the edge of the ellipse. A line perpendicular to this through the center of the ellipse is the minor axis. If the distance between the foci is zero, the ellipse becomes a circle. If the distance between the foci is infinite, the ellipse becomes a line. This distance is a measure of the eccentricity of the ellipse. The greater the eccentricity, the further apart the foci are, and the flatter the ellipse is (less like a circle).
  • Kepler's Second Law: The area "swept out" by a line between the planet and the sun covers equal areas in equal time. When the planet is far from the sun, this shape is long, so the planet does not have to travel far to sweep out a large area. When the planet is close to the sun, this shape is short, and the planet has move further and go faster along its orbital path to cover the same amount of area in the same time.
  • Kepler's Third Law: The period of a planet is related to its distance in a particular way: the square of the period is a ratio of the cube of the semi-major axis of the planet's ellipse.

After Brahe's death, Kepler studied the observations of Mars that Brahe had made. He carefully plotted the positions of Mars in space, based on the relative positons of the earth, the sun, and Mars at each observation, and assuming the Copernican idea that the earth was moving. It took him nine years to complete all his calculations, and at the end of his analysis, he proposed an even more radical approach to astronomy than Copernicus's heliocentricity: throw out the perfect circles of Aristotle and get rid of the eccentrics and the epicycles altogether, because the planets move in elliptical orbits.

An ellipse, you may recall, is one of the mathematical shapes that occurs when you slice a cone at an angle, that is, when you imagine a plane surface intersecting a cone at a tilt.

Kepler's laws of planetary motion are what we call empirical laws. There is no fundamental universal cause for why planets should move in ellipses present in his statement of the laws themselves. A relationship like this one, though, is often a motivating observation for someone to look for a reason, a cause, some force, that will keep planets moving in this particular way.

John Dee

There were other philosophers and mathematicians who were influenced by Copernicus' work, and who supported his theory of a heliocentric system, and who ran into difficulties with their neighbors or princes because of their views. Dee was an Oxford educated mathematician whose father was arrested and deprived of his lands and wealth during the reign of Mary Tudor. As a mathematician, Dee was also suspect, since some people then (and perhaps now!) thought the ability to perform calculations was tantamount ot magic. After Mary's death, Dee prospered for awhile as an advisor to Queen Elizabeth. He provided astrological readings for many court members. He consulted with the Muscovy company on the route they were to take to reach Russia by sailing north around Norway and Sweden, and approaching Moscow from the north. In this capacity, he provided the mathematical methods necessary to use Copernicus' theory and observations of stellar positions and planetary positions to help ships navigate on the open sea. He also proposed calendar reform to Elizabeth; her failure to adopt it (because the Archbishop of Canterbury refused to support Dee) meant England had a calendar out of step with the rest of Europe for over a hundred years. Despite Dee's lack of personal success, his proposals for practical applications of Copernicus' theory helped popularize it in England.

Giordano Bruno

On the continent, another adherent of Copernican theory made a name for himself by associating his own calculations using Copernicus' planetary models with magic and astrology. Giordano Bruno was a radical thinker, always on the edge of the religious community. He spent some time in Geneva, where he was excommunicated by the Calvinist Council for showing disrespect to the heads of the (Protestant) church there. He later maintained that he had never joined the Reformed church there, but during a stay in England, he attacked the Catholic Church, then the Oxford University professors. He returned to the continent and eventually to Italy, where he ran afoul of the Roman Inquisition. After six years in prison, a trial by the Roman curia determined that he was guilty of heresy. He refused to recant of his statements that Christ was not God but only a skilled magician, and was executed.

Bruno is important to our consideration of how Copernican astronomy was viewed, because in addition to his rather radical religious positions, he also defended the Copernican heliocentric system and the possibility that other worlds could be inhabited. Some people in his own time, and some historians since, have interpreted the heresy judgment as a condemnation of Copernicus as well as Bruno.

Study/Discussion Questions:

Further Study/On Your Own