Presentation Transcript

1. SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond Lecture 5 12 February 2014 Science Center Lecture Hall A
2. Outline of Lecture 5 Discovery of planet Uranus Discovery of Planet Neptune Anomaly in Mercury’s Orbit Short course in relativity: special and general The Cosmic Distance Ladder (CDL): first rung
3. Discovery Of Planet Uranus Herschel thought was comet Took months to realize was planet First named GeorgiumSidus Later named “Uranus” by Bode
4. Comparison Of Observations and Model Predictions For Uranus
5. What Could Be Wrong? Limitation of Newton’s law? Or another planet waiting in outer wings for discovery? Independently, young Englishman, John Couch Adams, and established French astronomer, Urbain J. J. Le Verrier, in early 1840s set about to test new-planet idea
6. Hunt Is On! Not feasible to directly determine orbit of possible new planet from Uranus observations alone Assumptions necessary! Each man made nearly same ones: New planet orbits in circle in same plane as Uranus; distance from sun taken from Bode’s law Abstruse and lengthy calculations still required (Le Verrier’s occupied >200 pages)
7. How To Be Taken Seriously? Calculations completed ≈same time, Adams ≈fortnight earlier; both noted ≈sky location and ≈brightness of new object Best telescopic equipment needed. Neither man experienced observer. Each asked national observatory to look
8. Denouement English Astronomer Royal in July 1846 authorized observations; assistant dutifully recorded locations of objects in relevant part of sky; no one then bothered to check on (unexpected) object nearpredicted position French astronomers refused to make observations on “mere theoretical predictions” Undaunted, Le Verrier sent message to Galle, assistant at Berlin Observatory; with crucial aid from graduate-student-rank assistant, Heinrich d’Arrest, Galle, after pleading with Director Encke, made observations on night request received, 23 September 1846 (see next two slides) Discovery made! World-shaking event - for two reasons: enormous triumph of science; battle royal over credit between England and France (see third slide); big flap over name Note extreme difference between prediction and discovery
9. Berlin Observatory’s 9” Refractor(Used To Discover Neptune)
10. Predicted vs. Observed Position Of New Planet
11. View Of Adams From France
12. Triumph To Tragedy? Another Test Looms 13 years later, Le Verrier uncovers problem at other “end” of solar system: Closest point to sun (perihelion) in Mercury’s orbit moves faster than Newton’s laws predict, by about 43 arcseconds per century (see next slide) What could be cause? Count the ways: 1. Error in prediction and/or measurement? 2. Interior planet, “Vulcan,” and/or swarm of tiny planets (“asteroids”)? 3. Rotation-induced bulge at sun’s equator? 4. Small flaw in Newton’s law?
13. Precession of Mercury’s Perihelion(NOT To Scale)
14. Process of Elimination Observations and calculations, effectively ruled out all but flaw in Newton’s law Modifications to inverse-square law were unavailing: fixing Mercury problem caused others What to do? No one knew. Big Mystery!
15. Next Seeming Digression: Special Theory of Relativity Einstein’sbasic postulates: 1. Nothing travels through vacuum faster than light; and 2. speed of light is independent of speed of source or of receiver of light Two, especially second, dramatically original, with startling consequences. Effects most pronounced for relative speeds close to c. Consider clock comparisons and aging
16. Einstein’s Theory Of General Relativity Special relativity silent on masses Newton’s law of gravity proposes simple model Einstein’s problem: instantaneous action at any distance (see hand-waving illustration) Inventing new law of gravity consistent with special relativity took Einstein about 8 years; approach entirely novel
17. Model And Comparison With Observations Einstein’s equations of general relativity: Gυν = - 8πGTυν Compact notation hides complications. Note: left side depends only on geometry of space-time; right side only on mass, energy, and momentum in space-time Solution for single planet yields elliptical orbit for Mercury with precession of perihelion of 43 arc seconds per century, in precise accord with Le Verrier’s result and later observations and data analyses This accomplishment of Einstein’s was - and is – an achievement for the ages. His theory of general relativity has withstood all challenges for nearly one century Tests about 6 in number now; first 3proposed by Einstein, 4thby me (also involved with last 2) Applications in astrophysics abound (from overall structure of universe to extreme conditions at or near many individual objects) Next year, in 2015, worldwide celebrations likely of centenary of development of theory, although not published until 1916
18. The CDL Universe literally unimaginably vast Getting handle on distances no trivial matter Determining distances on earth hard enough (see Part 2 of course) Ladder needed for surmounting vastness Not your ordinary ladder: Rungs very unevenly spaced. Ladder grandiosely named: “the cosmic distance ladder”
19. How Large The Solar System? First substantive step on CDL: earth to sun By definition one astronomical unit; who needs more? Need to know value of astronomical unit in terrestrial distance units How determine value? Not easily
20. Size Of Solar System (SSS) Measure distance earth to otherplanet; if successful, game over. Why? Kepler’s 3rd law Long history of attempts; late as 1950s, claimed accuracy one part in 104, proved tenfold optimistic Modern method disclosed over optimism: radar. How does it work? (See next slide)
21. Radar Acronym: RAdioDetection And Ranging Basic radar equation: Prec= …Ptrσ A/r4 Prec, Ptr = Power received, transmitted σ = radar cross section of target A = area of antenna r = distance, radar antenna to target Hand demo: inverse square (twice)
22. Radar Astronomy Moon detected (barely) in 1946 Venus nearly 107 as difficult; detected in 1961 (x3 average improvement per year: ~50 yr) Technique: Transmit “coded” signal; shut down for receive cycle (house-fly analogy)
23. Millstone Hill (MIT) Radar, 1958
24. SSS (Concluded) Astronomical unit (a.u.) determined in km to ~2 parts in 106, nearly 103 better than optical Saved day for Mariner 2 in 1962 Now a.u. known to better than ~1 part in 1010! Why care?
25. Scale Model Of Solar System Suppose earth shrank to peppercorn What size sun? What distance sun?