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1、Copernicus, Kepler, Galileo, Newton,How did we Discover the Earth is Round?,Traditional: as a ship sails away, the hull diasppears below the horizon before the sails Problem: ancient ships were so tiny they would be mere specks on the horizon. More likely: someone on a ship saw the land come into vi
2、ew,How did we Discover the Earth is Round?,Other possibilities: storm clouds with bases below the horizon Why is there a horizon at all? Why cant we just see forever? Contrary to myth, the knowledge of a round earth was never, NEVER forgotten during the Middle Ages,Constellations and Culture,A Myth
3、in the Autumn Sky,A Portion of the Northern Sky,The Northern Cross,The Traditional Constellation,Why Didnt the Ancients Picture this as a Cross?,The Southern Cross,A Star Map,Western Constellations,Chinese Constellations,The Inca “Dark Constellations”,Copernicus: Precursory events,Thomas Aquinas rec
4、onciles Aristotelian Philosophy with Christianity. King Alfonso the Wise of Castile publishes Alfonsine tables, based on Ptolemaic System, late 1200s. Concept of “Law of Nature“ arises from medieval theology and philosophy. Ideal motion thought to be perfectly circular in heavens, rectilinear on ear
5、th.,Immediate Setting,Printing invented 1457. Michelangelo, 1475-1564. Luther, 1483-1546. Protestant Reformation begins ca. 1520. Shakespeare 1564-1616. Age of Exploration, Colonization. Supernovae, 1572, 1604 shook idea of heavens as unchanging.,Ptolemaic System,Planets appear to reverse motions at
6、 times. Ptolemy explained motions in terms of orbits (epicycles) carried on a larger orbit (deferent).,Ptolemaic System,Epicycle deferent ratios were very close to modern values of planet/earth orbit ratios. System worked very well. Contrary to popular myths, Ptolemys system was not overly cumbersom
7、e, and it accounted for subtleties like the uneven motion of the Sun It is not Ptolemys fault he did such a good job that it took 1500 years to improve on him!,How Ptolemy Dealt With Unequal Speeds,Why this was a hot topic,Alfonso the Wise of Castile published tables based on Ptolemy, 1200s Tables w
8、ere out of date by 1500 System began to seem cumbersome and inelegant Need for calendar reform Gregorian Calendar, 1582 System was beginning to seem clumsy,Nicolaus Copernicus 1473-1543,First known modern person to propose the Earth circles the Sun Not known how he arrived at the idea Died just as t
9、heory was published Not much story to tell Luther; “this fool wants to overturn the whole science of astronomy”,Possible clues to Copernican idea,Epicycle motions for Venus and Mercury opposite other planets. Epicycle for Suns motion appeared in schemes for all other planets. References to now-lost
10、ideas of Aristarchus of Samos,Johannes Kepler 1571-1630,A thoroughgoing medieval mystic Left detailed accounts of his reasoning Generally a much more interesting story than Copernicus,The Platonic Solids,Keplers Nested Spheres,How Did Kepler Know the Spacing?,The Kepler Solids,The Poinsot Solids,Str
11、ange Start - Good Finish,Kepler started off with mystical ideas, and ended up correctly describing the motions of the planets. How can this be?,Science often proceeds by a process of successive approximation,Make an assumption See how it fits reality, Modify it (junk it if necessary) and try again.
12、After a few iterations of successive approximation you can be very far from your starting point, Even fairly strange initial assumptions can lead to correct results.,Successive Approximation differs profoundly from circular reasoning,In circular reasoning, you start off with an assumption, Accept, r
13、eject, or modify observations to fit the assumption, Then use the results as proof of the assumption. People who engage in circular reasoning almost never scrap or modify their initial hypothesis The whole point of circular reasoning is to justify the initial hypothesis at all costs.,Keplers Laws,Pl
14、anets travel around the Sun in elliptical orbits with the Sun at one focus. A line from the planet to the Sun sweeps out equal areas in equal times. The square of a planets period in years and its distance cubed are proportional.,How Did Kepler Do It?,One Mars year (687 days) = 2 Earth years (730 da
15、ys) minus 43 days After 687 days, Mars is in the same place in its orbit, but Earth is not Mars appears to be in a different location in the sky,How Did Kepler Do It?,Tycho Brahe 1546-1601,Tycho really did live the outrageous lifestyle shown in the video Really did have a gold nosepiece. He died the
16、 way he lived. He was hitting up some noble personage for patronage and support and, fearing that somebody else might upstage him, refused to leave to go to the bathroom. He developed a bladder infection and died.,A Neat Coincidence thats Too Neat,Rosenkranz and Guldenstern are Dead,Who were they?,Hamlet,Hamlets Uncle has: Murdered his father Married his mother Usurped Hamlets Crown Hamlet is Depressed How Much does Hamlet Know?,Enter Rosenkranz and Guldenstern,Hamlet is supposed t
