Giants of Science Part Two Tycho Brahe & Johannes KeplerTycho Brahe and UraniborgTycho Brahe’s DiscoveriesTycho Brahe & Johannes KeplerKepler’s ModelsKepler’s BreakthroughProperties of EllipsesKepler’s 3 Laws of Planetary MotionKepler’s First Law of Planetary MotionKepler’s Second Law of Planetary MotionKepler’s Third Law of Planetary Motion1Giants of Science Part TwoTycho Brahe & Johannes KeplerThese two scientists showed that the Universe was not some ideal perfection as Ptolemy proposed and worked towards acceptance of Copernicus’ heliocentric model Tycho Brahe –made the most accurate observations of stars and planets up to that time.–was a flamboyant Danish nobleman who wore a silver nose when part of his nose was cut off in a duel!Tycho Brahe (1546-1601)2Tycho Brahe and Uraniborg•He lived in a mansion/observatory on an island off the coast of Denmark.•The mansion had very sophisticated equipment (but no telescopes!) to help him and his assistants to measure the positions of stars and planets.•He named the mansion Uraniborg (Sky Castle).Some of the equipment used at Uraniborg3Tycho Brahe’s Discoveries•As a young man he proved that comets had to be farther from Earth than the Moon.•He also proved that a star which appeared to brighten dramatically over a few weeks was also beyond the Moon.•Both observations showed that the heavens could change like the Earth.•He also came up with his own compromise model of the Universe. Brahe’s compromise:All the planets went around the Sunwhile the Sun moved around a fixed Earth4Tycho Brahe & Johannes Kepler•A few years before he died, Brahe hired Johannes Kepler to help in analyzing the data he had collected.•Brahe started him out on his hardest problem: determine the orbit of Mars. •Mars has the largest observed retrograde motion and no circular orbit could be found to match Brahe’s observations.Brahe and assistants making observations5Kepler’s ModelsAfter years of work, the most accurate circle he could find for Mars’ orbit still left an error of 8 arcminutes (about 1/4 the angular size of the full Moon).“If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy”- KeplerJohannes Kepler (1571-1630)6Kepler’s Breakthrough•Kepler’s key discovery –planets do not orbit in circles but rather in ellipses. –the Sun was not at the center of the ellipse but rather at one focus.•With this breakthrough he obtained excellent agreement between his model and observations.7Properties of Ellipses•Each point marked by a tack is called a focus.•The farther apart one focus is from another the more eccentric the ellipse.•The line cutting the ellipse in half that passes through each focus is called a major axis. Half the major axis is called a semimajor axis.•The semimiajor axis is the average distance of the planet from the Sun8Kepler’s 3 Laws of Planetary MotionThese laws describe the observed planetary motions but do not describe why these motions occur as they do.9Kepler’s First Law of Planetary MotionThe orbit of each planet around the Sun is an ellipse with the Sun at one focus.–There is nothing at the other focus.–The average distance of the planet from the Sun is the semimajor axis.–Throws out Ptolemy’s perfect circular orbits.10Kepler’s Second Law of Planetary MotionAs a planet moves around its orbit, it sweeps out equal areas in equal times.–A planet travels faster when it is nearer the Sun and slower farther away–Throws out Ptolemy’s uniform motion11Kepler’s Third Law of Planetary MotionThe amount of time it takes a planet to orbit the Sun is related to the size of its orbit by P2(years) = a3(AU)–1 AU (astronomical unit) is the semimajor axis of the Earth’s orbit. Earth’s average distance from the Sun.–It doesn’t matter how elliptical the orbit as long as the average distance is the