Tycho, Kepler, 11 September 2013!(1546-1601) Tycho Brahe:!1.Background: !A.He was well known nobleman in Denmark, and a relative of the Danish a.King Frederick II.!He was sponsored through university by his relatives, and did well in his b.courses. !Though he was a good mathematician and astronomer, he had a c.ferocious temper and very few friends. !He correctly realized that no one could figure out the movement of the d.planets because all of the current data about the planet's positions was inaccurate and of low quality. !He dedicated his life to acquiring the highest quality data on the e.positions of the planets compared to the stars.!Throughout the 1570s-1590s, Tycho used his connection to King Frederick B.II to acquire funding for the largest (and therefore most accurate) astronomical equipment ever built.!He also devised new, very precise methods for getting the best data out a.of his equipment.!He used a "mural quadrant" (a quarter of a circle on a wall which is b.oriented precisely north-south) to measure the altitude of planets. ! Tycho looked through the center of the arc of the mural quadrant 1.and aligned an indicator on the arc to an astronomical object as it passed through a window of the southern wall. !This gave the object's height in degrees. !A.When the object disappeared behind the horizon, he would then tell 2.his assistants to mark the time from two separate clocks. !The timing gives the right ascension of each objects, and the A.attitude of the actual observatory will give the declination. !Tycho Brahe also had to correct for the inaccurate clocks of his B.time by measuring the clocks against the stars. !He also used other specialized astronomical instruments. !3.For a time before the telescope, the data is amazingly good. !c.People still use it now.!1.Though he spent the majority of his energy collecting data, Tycho Brahe C.also wrote books that explained his methods and equipment. !This was so that people could theoretically replicate his data. !a.His work was interrupted when he lost funding from the Danish monarchy D.and had to leave the country. !Tycho's patron King Frederick II died in 1588, and his son Christian IV a.was not a fan of Tycho (understandable, because Tycho had a horrible personality).!As Christian IV gained power, he began to cut Tycho's privileges and 1.funding. !Since Tycho was also generally unpopular in Denmark, he decided to 2.leave after 1597. !Though Tycho was a premier astronomer and had a lot of very good b.astronomical equipment, his bad temperament prevented him from landing more than a couple of short visiting professorships !Tycho realized he needed a king to be a court astronomer for in 1.order to continue his work. !He found another royal sponsor in Rudolph II of Bohemia.!E.Rudolph II of Bohemia: !a.Ruled over the Holy Roman Empire (really a loose confederation of 1.german or czech states)!He wanted his capital Prague to be the cultural center of Europe!2.Prague was located too out of the way to organically become a A.cultural capital, so he invited all the scholars and artists who were rejected from their own countries. !For example: !a.Giuseppe Arciboldo, who became unpopular with the Church 1.father in Italy because of his non-representational portraits.!John Dee, the astronomer of Elizabeth 1 !2.Along with legitimate scholars, he also brought many fakers to b.his court, and believed all of them !By 1599, Tycho and Rudolph had a solid professional relationship. !b.Tycho even became a major counselor of Rudolph. !1.Partially to test his status with Rudolph and partially because he had 2.enough astronomical data, Tycho asked for a mathematical assistant, and got one. !His assistant was Kepler, a great austrian mathematician. !A.Tycho and Kepler instantly hated each other, but Rudolph II B.mediated.!Tycho died in 1601 before any major developments happened. !F.After Rudolph II bought Tycho's data from his widow, Kepler took over. !G.(1571-1630) Johannes Kepler: !2.Background: !A.Kepler came from poor family, but was sponsored through upper a.education by his uncle because of his genius. !He learned from an astronomy professor named Michael Maestlin from b.the University of Tübingen who was known for his quality teaching. !Kepler wrote a book in his twenties about the great distance between c.Jupiter and Mars in the Copernican model: !He that this could be possible if the planets were on circles whose 1.placement and sizes are described by inscribing and circumscribing the five platonic solids (solid figures that have equal edges and equal faces) !He didn't convince anyone, but gained respect for his slick 2.mathematics. !He had a genius geometric mindset. !3.Since Kepler was a Protestant in Catholic Graz, he was banished. !d.Becoming an assistant to Tycho in Prague gave he and his family a new 1.place to live. !In 1605, Tycho was able to prove that no combination of perfect circles in B.Ptolemy or Copernicus' system could describe Mar's movement. !It was all calculated by long hand, which was time consuming. !a.In 1609, he realized that Mar's orbit was an ellipse, and the sun is at a focus C.of the ellipse. !The other focus is empty. !a.He wrote and published a fundamentally correct book called b."Astronomia Nova" describing how the planets moved.!Though it did change all of astronomy, it is no longer new ("nova").!1.Kepler's laws:!D.These are things that Kepler said which astronomers later condensed a.into laws. !The planets orbit the Sun in ellipses, with the sun at one focus.!1.Ellipses are conic sections (a slice of a cone from an angle).!A.Ellipses have two focuses which determine their shape: !a.If you add the lengths of two lines connecting both foci to 1.any single point on the edge of the ellipse, you will get the same sum. !The line joining the Sun and a planet sweeps through equal areas in 2.equal times. !The green triangle and the blue triangle have the same area, so the A.planets moving along those sections will take the same amount of time. !As a result, the planets move faster nearest to the sun and slowest B.farther from the sun.!The square of the orbital period of a planet is proportional to the 3.cubes of the semimajor axis of its orbit– half the longest dimension of the ellipse. !P^2 = A^3!A.The square of how long it takes for a planet to orbit the sun is B.proportional to the cube of the planet's distance from the sun. !This was published later in a different book in 1619. !C.Kepler was right.
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