Presentation Transcript

1. SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond Lecture 3 3 February 2014 Science Center Lecture Hall A
2. Outline of Lecture 3 New TF (BuLentKiziltan - astronomy) Ptolemy’s Model Copernicus’ Model Tycho Brahe’s Observations (and Model) Kepler’s Three Laws Galileo’s Telescope Revolution iSite Alert Weather Advisory
3. Claudius Ptolemy (c. 90 – c. 160 AD) Greek-Egyptian-Roman Wrote “Syntaxis.” Later known as “Almagest” Also wrote “Tetrabiblos” Almagest gives prescription for positions among stars of sun, moon, and planets Almagest held sway in astronomy for ~1.5 millennia
4. Early (Aristotelian) Setting For Ptolemy’s Model Circle and sphere supreme: perfect geometrical figures Uniform motion: perfection in action
5. Six Basic (Early) Assumptions Stars move affixed to sphere, make uniform daily circuit of sky Sun, moon, and planets each moves uniformly in its circuit of the sky Earth is in center of the sky Earth is spherical 5. Earth tiny compared to size of sky 6. Earth stands still
6. Nature’s Ideas Different Sun does not move uniformly in orbit In addition, planets move backwards (retrograde) in orbits at some times
7. What To Do? Preserve uniform motion, but: 1. For sun, move center of uniform motion away from center of earth For planets, in addition add epicycle (see next slide)
8. Offset Center Yields Non-Uniform Rotation As Viewed From Earth; Epicycle Yields Retrograde Motion(Deferent Is Large Offset Circle)
9. Still Headaches! Especially for Mars. No model could both match: 1. lengths of retrograde periods; and successive positions in sky of successive intervals of retrograde motion
10. Ptolemy’s Brilliant Idea He maintained idea of uniform motion, but created new point (“equant”) about which motion would be uniform (next slide)
11. Ptolemy’s Equant: “Solves”Retrograde Problem
12. How Match Observations? Longitude model: Direction of large circle’s center from earth’s center Ratio of offset of large circle’s center from earth’s center to radius of large circle Ratio of epicycle radius to large circle’s radius Angular rates (2) of center of epicycle viewed from equant and of planet on epicycle Positions (2) of center of epicycle and of planet on epicycle at (some) epoch
13. Procedure To Match Need 7 values, one for each of 7 parameters Choose 7 “good” observations and determine corresponding values for parameters 3. Calculate for any desired epoch (used Julian calendar, in use from before Ptolemy’s time until after end of Almagest’s tables’ widespread use)
14. Conclusion Ptolemy’s model: 1. Was purely a geometric/arithmetic one; no underlying principle(s) Far from perfect fit to observations; glaring discrepancies remained (see later slide) Unexplained peculiarities, e.g., retrograde motion took place only when sun was on (extended) line joining earth and planet
15. What Came Next? Copernicus! Nothing substantially changed for ~1.5 millennia (as already twice noted) Nicolas Copernicus (1473-1543), Polish cleric in RCC, worked on theory in which all planets move around sun; not clear why he chose this theory Revival of old Greek idea, but with specific details Retained concept of circles Required circles centered off from sun, each with own (small) epicycle, as with Ptolemy’s model
16. Comment A lot unclear; mostly just guesses as to from where and why Copernicus worked on heliocentric model. He apparently abhorred equant. (Did he feel was cheating as means to preserve Aristotelian uniform motion?) Did he delay publication of his De RevolutionibusOrbiumCoelestium because of fear of the reaction of the RCC? Good reason to disbelieve this common belief: Two friends, a bishop and a cardinal, urged him to publish; Giordano Bruno, burned at stake for heresy in 1600, claimed that his heliocentric cosmology was not relevant. But also reason on other side, as in reading assignment
17. Copernicus vs. Ptolemy Accuracy: About same (see next slide) Difficulty calculating: About same What governs choice? Two main advantages of Copernicus’ model: 1. Retrograde motion explained naturally (see next slide plus one) vs. merely an “accident,” requiring special feature in model (equant) 2. Planets’ distances from sun ordered as orbital periods vs. no model of relative distances/orbital periods One main “advantage” of Ptolemy’s model: 1. Earth (nearly) at center of universe
18. Comparison of Ptolemy’s and Copernicus’ Sky Position Errors for Mars
19. Copernicus’ Theory: Schematic Of Retrograde Orbit Of Mars
20. Copernican Model Consequence Big change in world view: Earth displaced from center of universe; replaced by sun Humanity thereby downgraded, big time Eventually led to big struggle with RCC (read Galileo discussion)
21. The World of Tycho Brahe (1546-1601) Next noteworthy contribution by Danish nobleman; convinced King of Denmark to support his construction of world’s best observatory. (Aside on Tycho’s nose) Made four or so times more planet observations, especially of Mars, than did all of humanity up to that time, a treasure trove waiting for exploitation Also developed “compromise” model of solar system: Sun and moon orbit earth; planets orbit sun; earth remains center of universe
22. Johannes Kepler’s Contributions Tycho’s last brilliant move: hired Kepler (1571-1630) to analyze data under his (Tycho’s) direction Tycho died 10 months later; nasty fight followed over data access Kepler trained as mathematician; very tenacious; looked for models to accurately represent data, Mars especially. Felt physical cause needed: violated by models with offset centers of motion. Thought planetary motions due to magnetic effect of sun Success came slowly; long books much faster
23. Kepler’s Contributions (Concluded) Broke from (offset) circle tradition (brilliant stroke!): Found that planets move about sun in ellipses, with sun at one focus (see next slide) Noticed (more or less) that each planet swept out equal areas in equal times (see next slide plus one) More than a decade later in ca. 1618 established relation between orbital periods of planets and their distances from sun: P2 = Constant x a3 Square of period, P, proportional to cube of (near to) average distance, a, of planet from sun. One constant for all planets; notice implication of using astronomical unit for distance and year for time Codified and called “Kepler’s 3 laws of planetary motion” over 150 years later by J. J. Lalande, French astronomer No more offset circles, no more epicycles, no more equants, just ellipses! And model much better fit to data. Occam wins.
24. Definition Of Ellipse
25. Kepler: Equal Areas Swept In Equal Times
26. Key Philosophical Point Did Johannes Kepler’s findings prove that his model was correct? More basic question: What constitutes proof? No established framework, as in Euclid’s geometry We seek in science, noted last week, a model that accurately predicts phenomena not yet observed. To be viable, model must also predict phenomena already observed The key to choice is based, overall, on persuasion, influenced primarily – one would like to believe – on evidence
27. Meanwhile, South of the Border… Simultaneously with Kepler’s labors, Galileo Galilei (1564-1642) also at work Word of invention in northern Europe of telescope reached Italy. Instead of having spying on armies and similar endeavors in mind, Galileo had simple telescope made and looked up. Amazing surprises were in store.
28. The Telescope Revolution Galileo built, with optician’s help, own tiny telescope (refractor type); contemporary binoculars now better Targets: Jupiter. Made major discovery; not obvious: four moons (see next slide) Venus. Observed phases (see next slide plus one) Moon. Observed craters Milky Way. Observed individual stars Trouble with RCC
29. Copies Of Galileo’s 1610 Drawings OfJupiter And Its Moons
30. Galileo’s Views Of Phases Of Venus(Simulations By O. Gingerich)
31. iSite Alert Tonight we will post the first homework assignment. If you find anything difficult to grasp or confusing in any way, please ask your TF (if you know by then who it is) or me for clarifications Tonight we will also post the first installment of the course book for your critical feedback Email to class accompanies each posting
32. Weather Advisory If commute from Lexington to Cambridge (and/or back) seems problematic: Look for relevant email and/or posting on course site