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Tycho Brahe 1546-1601

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Tycho Brahe 1546-1601

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    1. Tycho Brahe (1546-1601) 1

    2. Brahe’s Quadrant 2

    3. Brahe’s Observations Observed Supernovae ? changes in heavens 3

    4. Brahe’s Observations (cont.) 4

    5. Making sense of it all 5

    6. Johannes Kepler (1571-1630) 6

    7. Kepler as lecturer 7

    8. Mysterium Cosmographicum (1595) Tried to the distances of the planets from the Sun in the Copernican system to the five “perfect” solids of the neo-platonists He pursued this model till his death but it never worked satisfactorily 8

    9. Because of talent as a mathematician: He was invited by Tycho Brahe to become his assistant in 1600 Task: calculate the orbit of Mars Tycho's observations He bet his fellow workers that he could solve the problem in 8 days… 9

    10. Tycho’s Tables 10

    11. 8 days ends up 8+ years He first tried a heliocentric model with circular orbits but Sun not at the center 900 pages of calculations Mars’ orbit fit Brahe’s data to within 2’ of celestial arc (= 2/60th of a degree) Vast improvement on Copernicus 11

    12. Failure … New observations ? errors of up to 8’ Rejected his model: “… if I had believed we could ignore these 8’, I would have patched up my hypothesis accordingly. But since it was not permissible to ignore them, these 8’ point the road to a complete reformation of astronomy.” 12

    13. … and new models He next tried a model based on oval orbits – spent 3 years on them Wrote in 1603 “if only the shape were a perfect ellipse all the answers could be found in Archimedes’ and Apollonius’ works” Wrote 18 months later that the truth must lie between a circle and an oval, “just as if the Martian orbit were a perfect ellipse.” 13

    14. It turned out the orbit of Mars … 14

    15. More than 8 years of work He later wrote “I thought and searched, until I nearly went mad, for a reason why the planet preferred an elliptical orbit . . . Ah, what a foolish bird I have been.” 15

    16. Small eccentricity is the problem 16

    17. Astronomia Nova (1609) 17

    18. Harmonices Mundi (1619) 18

    19. Tabulae Rudolphinae (1625) Astronomical tables which reduced errors in planetary position to < 1% 19

    20. Kepler’s First Law 20

    21. Kepler’s Second Law 21

    22. A bit like Ptolemy’s Equant Circle 22

    23. Kepler’s Third Law 23

    24. Kepler’s Third Law 24

    25. Kepler’s Laws are: 25

    26. If there are no crystalline spheres, what moves the planets? 26

    27. A web site about Kepler’s Laws 27

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