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SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond

SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond. Lecture 4 10 February 2014 Science Center Lecture Hall A. Outline Of Lecture 4 (Fun Day: Hand Drawings!).

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SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond

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  1. SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond Lecture 4 10 February 2014 Science Center Lecture Hall A
  2. Outline Of Lecture 4(Fun Day: Hand Drawings!) Speed of light (strange saga) Newton’s law of gravitation (another saga) Discovery of Uranus and Bode’s “law” (for yet another discovery)
  3. Speed Of Light Ancient views: Infinite versus finite First serious attempt (Galileo): True or apocryphal? (See next slide)
  4. Trying To Measure The Speed Of Light(Galileo Style)
  5. Speed Of Light(cont’d) “Inner digression” (unity of science: another case): Navigation needed for commerce: world’s opened! Latitude straightforward (see next slide) Longitude ambiguous (see next slide + 1) Clock in the sky resolves ambiguity? Galileo suggests eclipses of Io. How work?
  6. Latitude Via Star Observations (One Example Only)
  7. Tradeoff: Longitude And Time(Unrealistic In Time Difference Shown)
  8. Schematic Of Io Eclipses
  9. Domenico Cassini (1625-1712) and Ole Roemer (1644-1710) Cassini, Paris Observatory Director, undertook program to monitor eclipses of Jupiter’s satellites Sent Jean Picard to Denmark to locate Brahe’s Observatory relative to Paris. Picard brought back Ole Roemer Roemer noted strange pattern in Io eclipse observations (see last slide again)
  10. Speed Of Light Unmasked Roemer deduced speed of light; gave as time to cross sun- earth distance and back; equivalent to ~ 2x105 km/sec Talked to French Academy; written up by unknown person; published in French journal and shortly thereafter in British journal Cassini apparently disowned this technique: Didn’t get consistent results from other three satellites of Jupiter. But see contrary view (Reading Assignment No. 2)
  11. Speed Of Light Refined Roemer’s result obtained in 1676 Unsurprisingly, much progress since. Latest measurements yielded299,792.458 km/sec So accurate that value now used to define meter with second defined by an atomic property
  12. On to Isaac (1642-1727) Backdrop: “Forces” in air; Kepler early proponent of “causes” Famous dinner: Christopher Wren (designed St. Paul’s in London); Robert Hooke (polymath in Newton’s shadow); and Edmund Halley (comet fame) mused about inverse square law for gravity (see demo) Halley’s talk with Newton; Principia followed in 18 months. (More than one story on timing of publication: Picard – radius of earth story)
  13. Newton’s Laws Principia contained Newton’s laws of motion and gravity: F = m x a (Net force, F, on body equals product of its mass, m, and acceleration, a. NB: Different use of letter “a” than earlier. Why? Universally used for both purposes; more needs than letters!) F = Const x M x m / r2 (Force of gravity between two bodies equals product of two masses divided by square of distance between them; constant “universal,” symbol universally “G.”)
  14. Newton’s Laws Applied Amazing consequence of putting these two laws together: F = ma = GMm/r2 or a = GM/r2 The acceleration undergone by body under these laws is independent of its mass! Example of Jupiter and pea Recall demonstration in Lecture 1. How accurate is the agreement with Nature’s behavior? How do large bodies such as spheres interact under Newton’s laws? Application of laws to solar system led to flowering of applied mathematics for almost (or, in views of some, more than) two centuries
  15. Discovery Of Planet Uranus: First In Historic Times In 1781, William Herschel noticed “star” in sky not in any star catalog Interloper moved day to day with respect to position of other (nearby in sky) stars: hallmark of planet Continued observations, and handful of “pre-discovery” observations from 1690 on, led with Kepler’s third law to determination of distance from sun of newly-discovered planet. Remarkably, value agreed well - to within 2% - with prediction from Bode’s law (see next slide)
  16. Bode’s (1772) Law And Uranus’ Orbit Law: an = 0.4 + 0.3 x 2n astronomical units (au), where n= -infinity, 0, 1, 2, 3, 4, 5, 6, 7,… predictedobserved a= -infinity for Mercury = 0.4 au 0.387 au 0 Venus 0.7 0.723 1 Earth 1.0 1.000 2 Mars 1.6 1.524 3 “Empty” 2.8 2.767 (1801 discovery of Ceres; asteroid “belt”) 4 Jupiter 5.2 5.203 5 Saturn 10.09.540 6 Uranus 19.6 19.18 7 ?? 38.8 ?? Contrast Bode’s with Newton’s laws in terms of foundations
  17. Follow-On Uranus Observations First new planet since antiquity garnered great interest; observed intensely Orbit accurately determined and predictions made of future sky positions Systematic deviations between predicted positions and observed positions seemed clear by about 1820; unmistakable by about 1840
  18. Comparison Of Observations and Model Predictions For Uranus
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