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Download Eratosthenes (250 B.C) Ptolemy`s Geocentric Model
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Another demonstration-- Earth was round: •the altitudes of stars change with latitude— latitude—Greeks sailed the seas! •Erasthatenes (who?) first realized this several decades earlier Eratosthenes (250 B.C) •measured the circumference of the Earth-Earth--Used "the shadow in the well" method. •At S, sun is straight overhead. •At A, sun is at an angle to zenith (about 7o) •Here, α is the same as β. •Proportion: AS/β AS/β = 360/(circumference of Earth). Star Trails Above Mauna Kea Credit & Copyright: Peter Michaud (Gemini Observatory), AURA, NSF Star trails from the Oregon Star party: http://www.keteu.org/images/astro/osp-trails.web.jpg Aristarchus of Samos (300 B.C.): . •"Heliocentric" argumentsargumentsdetermined relative distances of the Earth and the sun, •Based on angles between Earth Moon and Sun at various phases. But….Aristotle argued for the Geocentric Model Observed no stellar parallaxes no winds— winds—shouldn’ shouldn’t 1000 km/hr wind blow as earth spins through it? spinning Earth would hurl its inhabitants into space. No mechanism to keep it in a circular orbit. • • •From size of eclipse shadow, determined relative sizes of Earth moon… moon…and sun! •Deduced: sun is 90 x farther than moon, moon is 1/3 size of earth, sun is about 30 x as large. • angles are harder to measure than it looks here! •Concluded earth must orbit much larger sun! • • Click on image to play MPEG move on the web. From: www-astronomy.mps.ohio-state.edu Main difficulty with Geocentric Model: Retrograde motion •Why do some celestial objects move in backward loops? •“obvious” obvious” solution was “wheels upon wheels” wheels” •But how many wheels? From: http://www.earth.uni.edu/~morgan/astro/course/retrograde_mars.jpg Ptolemy’s Geocentric Model •Plato, Eudoxes, Eudoxes, Aristotle, and finally Ptolemy (100AD) developed geocentric “systems” systems” •These used Deferents (large orbits) and epicycles (small orbits” orbits” •The trick was to use these to make accurate predictions of positions in the future •i.e. Mars will be near Antares in Scorpius on winter solstice… solstice…etc. 1 Ptolemy’s was most accurate… •Ptolemy (pronounced Tolemy) was professor in Alexandria during the Roman Era. •A mathematician, physicist, astronomer, and foremost geographer of his era. •Created elaborate system of 88 epicycles and deferents, not precisely centered on earth, to model the motion of the heavens. •Proved accurate in making predictions for over a thousand years Dark Ages-Aristotelian beliefs Mandatory •The defeat of the Rome and the empire by Germanic tribes (Aric the brave!) led to withdrawal of roman troops across Europe •Infrastructure, commerce, education, and defense of cities crumbled to dust… dust…. •Highly divided Christian Europe was battling Vikings from the North, Mongols from the east, and the Plague. •The Church began to seize power through various means… means… http://www.coam.org.uk/Events/event2006/Dark%20Ages.jpg http://www.newizv.ru/images/photos/other/20050126210812_4-VIKINGS.jpg Copernicus (1473 - 1534) • by 1400 the planetary positions were no longer predicted by the “almagest” almagest” • Copernicus Proposed all the following “fix” fix”: 1. Earth spins on its axis once every 23 hrs, 56 min 2. Earth and all known planets orbited the sun in circular orbits with sun at center. 3. distant stars were so far that no parallax could be seen . 4. Polar axis precessed every 26,000 years. 5. All the above just a mathematical model to make accurate predictions… predictions…easier than updating the Ptolemaic model Johannes Kepler (1571 - 1630) •Mathematician...sought out Brahe for his famous data, and was hired by Brahe to fit data to the tyconic model universe. But… But…. •Kepler was trying to fit data to the “Kepler model" Universe •the orbits of the six known planets fit into the largest spheres which could be inscribed into the six regular geometric solids •--crazy --crazy by today's standards, but at least the orbits were centered on the sun! •Wrote: Harmony of the worlds relating music, geometry, astronomy So was Copernicus or Ptolemy’s model correct? •Tycho Brahe, Johanes Kepler, and Galileo were the greatest contributors to the debate. •Brahe (pronounced Bray) was the last and greatest prepre-telescopic astronomer. •Brahe felt that better observations were needed . •interested in proving that the “Tyconic Universe" was correct Kepler and Brahe...continued •Brahe died and family wouldn't release data after Brahe died (don’ (don’t ask how he died). : •Eventually Kepler "acquired" Brahe's data and found that: •--the --the orbit of Mars just isn't a circle! •Plato was wrong! •The door to a true understanding of the solar system was now wide open! Brahe’s tombstone, from: www.nada.kth.se/~fred/tycho/tychotomb.jpg 2 Kepler’s results • From Brahe’ Brahe’s data, Kepler deduced three laws: 1. Planets orbit the sun in Ellipses with the sun at one focus 2. A line joining a planet and the sun sweeps out equal areas in equal times These three relations are now known as Kepler's three laws. Extra for experts: x and y are the positions of the Earth with 0,0 at intersection of major and minor axis. After Kepler •an accurate description of the Solar system •definitive proof that the Earth orbited the sun, and spun on its axis (most of that due to Galileo—stay tuned! Missing: an explanation of Why the planets orbited the sun and why Kepler's mysterious laws NASA’s Project were true! Kepler—to detect terrestrial planets orbiting other stars! • What did Galileo observe with his telescope? •Venus had phases like the Moon: •Size always changed with phase •At Crescent Phase Venus was always closest to Earth •At Full Phase, Venus was always farthest Kepler’s third law 1. The cube of a planets semisemimajor axis is proportional to the square of its orbital period a3 = T2 2. a = semisemi-major axis –also average distance from planet to sun (also written as d or r). Units are AU’ AU’s. 3. T = orbital period (also written as P). Units are years. 4. Newton later used this A graph of semi-major axis cubed on discovery to develop and vertical axis, and orbital period squared on prove the law of universal horizontal axis. Clearly not a coincidence! gravitation. Galileo(1564 -1642) •Mathematician, physicist, astronomer •If you take a course in either Area, Galileo’ Galileo’s name comes up often •Heard about telescope and built one to explore the heavens •Proved the Copernican model and developed physics to explain Earth could orbit sun, etc. •Paid a price for his curiosity Conclusion? •Venus orbited sun: •Not the Earth •Clearly not in keeping with the official Geocentric model! •What else could be wrong? The Trial of Galileo from: http://astro.ysc.go.jp/venus-phases.jpg 3 Jupiter has moons that Orbit Jupiter( not the Sun) The Sun has spots photo from: http://www.ladeltascience.com/astronomy/kisatchie04/ju piterand moons.jpg The Galilean Moons the Moon has craters •So the Moon was a world like the Earth… Earth… •Not a perfect geometric object as Plato taught. http://solar.physics.montana.edu/canfield/ssu_images/sunspots.gif Plato to Galileo: review Write down one important idea or contribution for each of the following people. One sentence each. Give approximate date as well. 1. Aristotle 2. Plato 3. Brahe 4. Copernicus 5. Galileo 6. Kepler 7. Ptolemy Important terms—define in one or two sentences • • • • • • • • • • Parallax shift Sidereal day and month Epicycle Geocentric Heliocentric Precession cycle (include period) Retrograde motion Centripetal acceleration Kepler’s laws Phases of Venus 4