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Chapter 4: Renaissance Astronomy Astronomy after Ptolemy [http://www.thenagain.info/WebChron/WestCiv/WestCiv.html] Decline of Western Civilization (extended) knowledge of ancient astronomy lost Islamic Astronomy [Astrolabium.jpg,Astrolabio_andalusí_Toledo_1067.jpg,arabic_astronomers.gif] Incorporated knowledge (and preserved writings) of Greeks and other ancient civilizations Measurements and observations, improved calculations, but no critical developments in models First “modern” observatories a1c4:1 Rebirth of Western Astronomy (~1400) [figure 4-2] rediscovery of ancient writings observation/hypothesis testing challenges to ancient models only relative motion is observable beginnings of impetus theory Ptolemy's geocentric model largely accepted [fig 4.1 the Universe according to Dante's Devine Comedy]] a1c4:2 Copernicus (1473-1543, the height of the Renaissance ) heliocentric model (Sun centered) [copernicus.gif] planets orbit in perfect circles about the Sun apparent path of the sun is the ecliptic [fig 4-3, zodiac.avi] model provides apparent paths’ of planets, including prograde and retrograde motion [figure 4-4, heliocentric_retrograde.mov, copernicus_m.avi,copernicus_v.avi] sidereal period: 1 actual revolution (P) longer sidereal period => greater distance from sun synodic period: apparent period, relative to sun as seen from earth (S) [fig 4-5,6] Sidereal period determined from apparent period and earth’s period Superior Planets Planet’s orbit about Sun is outside Earth’s orbit about sun 1/P=1/Pearth-1/S Inferior Planets Planet’s orbit about Sun is inside Earth’s orbit about sun 1/P=1/Pearth+1/S a1c4:3 Geometry + Observations → size of a planet’s orbits [figure 4-7] Greatest Elongation: greatest angular distance between Sun and planet. Astronomical Unit (AU): Earth’s orbital distance (average distance from the Sun). Motion and Observations: Earth Rotates: Daily motion of Sun, Moon, Stars and Planets [diurnal.avi] Inferior Planet overtakes Earth: Planet undergoes retrograde motion Earth overtakes Superior Planet : Planet undergoes retrograde motion Moon’s motion about Earth: Phases of the Moon (and occasional eclipses) [eclipser_shadowsB_2010_v2.mov] Earth moves about Sun: Sun appears to move west to east along ecliptic, through zodiac [zodiac.avi] Earth's Axis has constant Tilt + Earth's Orbit: Seasons [seasons_large.mov] a1c4:4 PLANET Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Synodic Period (days) Sidereal Period (days) 116 584 − 780 399 378 370 367.5 88 225 365 687 4,332 10,750 30,590 59,800 Orbital Distance (AU) 0.39 0.72 1.0 1.52 5.2 9.6 19.2 30.1 a1c4:5 More on Copernicus’s model Orbits are perfect circles. Epicycles were required to account for variation in planet’s orbital speed. (just as complex as Ptolemy’s model) [fig4.8] Astronomical observations did not favor either Copernicus’s model or Ptolemy’s model. (Both about as good/bad) Violation of Aristotle’s theory of motion. •No stellar parallax is observed (yet)! [fig 4.9, 4.11, parallax.avi, 16_1.mov] → not accepted at the time a1c4:6 Tycho Brahe, the Great Observer (1546-1601) regular observations of Sun, Moon and Planets large number of observations greatest precision to date did not detect any stellar parallax [parallax.avi] heliocentric model rejected due to lack of observed stellar parallax Tycho Brahe’s geocentric model [figure 4-12] Sun and Moon orbit Earth, while planets orbit sun. Similar to Ptolemy’s and Copernicus, no more or less accurate. Tycho met Johannes Kepler 2 years before Tycho’s death. 30 years of Tycho’s observations went to Kepler when Tycho died. a1c4:7 Kepler (1571-1630) colleague of Tycho Brahe analyzed Tycho Brahe’s vast, accurate collection of astronomical data => Kepler’s Laws of planetary motion, a model for the solar system Kepler’s First Law: Orbital shapes are ellipses with the Sun at one focus [figure 4-13,kepler_1.avi] An ellipse is a close curve for which the sum of the distances from two fixed points (the foci) is the same for every point on the curve. [figure 4-14, ellipse.avi] semi-major axis: farthest distance from center eccentricity: how “squashed” the ellipse is perihelion: point of orbit closest to the sun aphelion: point of orbit farthest from the sun complete description of orbit: orbital elements [orbital_elements.avi] a1c4:8 Kepler’s Second Law: how orbital speed varies along the orbit equal areas in equal time [figure 4-15,kepler_2.avi, KeplerThird_Nav.swf] (orbital speed) x (distance to sun) = constant fastest at perihelion, slowest at aphelion Kepler’s Third Law: Period-Orbit relation square of sidereal period proportional to cube of semi-major axis P 2 ∼ a3 use period in earth-years, a = 1 Astronomical Unit Astronomical Unit = average Earth-Sun distance P 2 = a3 [KeplerThird_Nav.swf] Kepler’s Laws gave better agreement with observation than any earlier model! a1c4:9 Galileo (1564-1642) early use of Astronomical Telescope stars: not magnified like planets & the moon Sun & Moon: not perfect smooth spheres [fig 4.16,17] Jupiter’s satellites: another “center of rotation”[fig 4.18] phases of Venus: inconsistent with Ptolemy’s model [fig 4-19, ptolemy_v_phases.avi, copernicus_v_phases.avi] “Dialogue Concerning the Two Chief World Systems, the Ptolemaic and the Copernican” a1c4:10