Scientific Revolution: Discoveries by Brahe, Kepler, Galileo, and Newton in Cosmology - Pr, Study notes of Astronomy

Download Scientific Revolution: Discoveries by Brahe, Kepler, Galileo, and Newton in Cosmology - Pr and more Study notes Astronomy in PDF only on Docsity! 1 9/7/06 1 Lecture 3: Cosmology of the Scientific Revolution Tycho Brahe Kepler Galileo Newton http://www.physics.fsu.edu/users/Lind/AST1002/ 9/7/06 2 Tycho Brahe (1546-1601) • Flamboyant and tyrranical aristocrat, but devoted to science • Lived and observed on island off the coast of Denmark • Last of the great “naked eye” observers • Made planetary observations much more accurate than any previous • Observed “new star” (Tycho’s supernova) in 1572 • Demonstrated that comet was beyond Moon’s orbit • From parallax observations of new star, comet: • knew they were not in Earth’s atmosphere • evidence that heavens were not immutable 9/7/06 3 Tycho’s cosmological model  Tycho used parallax observations to explore heliocentric model:  If Earth moves, then parallax of stars should be observable  Tycho could not detect any significant parallax; he concluded Earth is stationary  In fact, stellar parallax is 100× too small for naked-eye observation to measure; largest values are about 1 arcsecond=(1/3600)°  Tycho settled on combined geo/helio-centric model  Sun orbits Earth; all other planets orbit Sun http://clyde.as.utexas.edu 9/7/06 4 Johannes Kepler (1571-1630)  Born in Germany; originally planned to be ordained as Lutheran minister  Convinced God made the Universe according to a mathematical plan; saw his Christian duty as understanding works God had created  Studied mathematics; published in 1596 his Mystery of the Cosmos proposing that planetary orbits lie in spheres nested within a series of the Platonic solids (wrong!)  Was hired as Tycho Brahe’s assistant in Prague; his job was to make sense of Brahe’s extremely accurate observations of Mars  Kepler became Imperial Mathematician after Brahe’s death (1601)  Kepler’s “war with Mars” amounted to a thousand sheets of arithmetic; resulted in publishing Kepler’s “First Law” and “Second Law” in 1609 as part of his New Astronomy  Kepler’s “Third Law” was published in 1619 as part of his Harmony of the World 9/7/06 5 Kepler’s first law Planets move around the Sun in ellipses, with the Sun at one focus. perihelion aphelion 9/7/06 6 Kepler’s second law The line connecting the Sun and a given planet sweeps out equal areas in equal times. Therefore, planets move faster when they are nearer the Sun Consequence of angular momentum conservation. http://home.cvc.org/science/kepler.gif 2 9/7/06 7 Kepler’s second law with high- and low- eccentricity orbits 9/7/06 8 Kepler’s third law The square of the period P of the orbit is proportional to the cube of the semi-major axis R Period (P) = time it takes for planet to complete one orbit  Semi-major axis (R) = half of the length of the “long” (i.e. major) axis of the ellipse. P2=constant × R3 9/7/06 9  For the Earth, we know that: P=1 year =3×107 seconds R=150 million km (1 Astronomical Unit, A.U.) Kepler’s 3rd law says that, for other planets, 32 ! " # $ % & =!! " # $$ % & AU R yr P 9/7/06 10 Solar system orbits Inner planets Outer planets + http://www.rasnz.org.nz/SolarSys/Orbits06.htm Note the low eccentricities! 9/7/06 11 Kepler in perspective  Based on Tycho Brahe’s accurate observations, Kepler calculated and thought his way to a major breakthrough in cosmology  Kepler’s three laws of planetary motion  Represented a very simple (and correct!) model of the solar system  Swept away thousands of years of prejudice – and his own previous pet theory!  Were driven fundamentally by the data, including Tycho’s error estimates  Unlike previous models which quantified only what was observed already, Kepler’s Laws had predictive power, consistent with modern idea of a meaningful scientific theory 9/7/06 12 Galileo Galilei (1564-1642)  Born in Pisa; worked as professor of mathematics  Built one of the first telescopes in 1609  Published “The Starry Messenger” with first telescopic discoveries in 1610  Telescopic observations:  Saw craters and mountains on the Moon  Realized sunspots were on surface, not foreground; rotated with Sun  Identified four satellites of Jupiter (“Galilean moons”)  Saw rings of Saturn  Resolved the diffuse Milky Way into many faint stars  Observed phases of Venus including gibbous and full