Shattering the Celestial Sphere Shattering the Celestial Sphere Key Concepts 1) Thomas Digges discarded the celestial sphere, advocating an infinite universe. 2) Johannes Kepler discarded epicycles, and set forth three laws of planetary motion. 3) Galileo Galilei, using a telescope, provided observational evidence for heliocentrism. William Cunningham, The Cosmologicall Glasse, 1559 Startling implication of the Copernican model! Planets are opaque spheres orbiting the Sun just like the Earth! Another Startling Implication! Stars look small & dim because they re far away; they re actually large, glowing spheres just like the Sun! Earth is a planet: there s no division between perfect heavens and corrupt Earth. Sun is a star: universe is full of glowing, spherical, Sun-like objects. Early adopter of the Copernican model: Thomas Digges (English: 1546-1595) Cosmological model version 5.1: Heliocentric, with no celestial sphere More distant Very distant Nearby Infinite universe, filled with stars. Nearby stars are brighter. More distant stars are dimmer. Very distant stars are too dim to be seen. 1
Johannes Kepler (German: 1571-1630) discarded epicycles. Ellipse = oval built around two points, called focuses (or foci). Kepler s 1st Law of Planetary Motion: Orbits of planets around the Sun are ellipses with the Sun at one focus. Take a line from one focus, to any point on ellipse, to other focus: length = constant. To measure SIZE of ellipse: Kepler s Second Law of Planetary Motion A line from a planet to the Sun sweeps out equal areas in equal time intervals. Major axis = longest diameter of ellipse Semimajor axis = half the major axis Consequence of Kepler s 2 nd Law: Planets move fastest when closest to the Sun. 2
Kepler s 3 rd Law of Planetary Motion: The square of a planet s orbital period is proportional to the cube of its average distance from the Sun. Kepler s Third Law in mathematical form: 2 3 P a P = orbital period (in years) a = semimajor axis of orbit (in AU) Cube of average distance (in A.U.) Square of orbital period (in years) What is the average distance from the Sun of a planet whose orbital period is 8 years? a) 8 AU b) 4 AU P 8 c) 1 AU d) 0.25 AU 3 a e) It depends on the eccentricity. a 4 P 2 64 64 With his laws of planetary motion, Kepler made more accurate predictions of planetary positions. Galileo Galilei (Italian: 1564-1642) Among the first to observe with a telescope. Johannes Kepler, Rudolphine Tables, 1627 This was a big selling point for the heliocentric model. portrait by Ottavio Leoni, 1624 3
Observations supporting the heliocentric model: 1) The Sun has spots. 2) Jupiter has moons. Motion of spots indicates the Sun is rotating. If the Sun rotates, why not the Earth? There are four Galilean moons of Jupiter. The Earth can t be the center of all orbits in the universe. 3) Venus shows phases. Observations consistent with Copernicus, inconsistent with Ptolemy. Big in angular size when nearly new, small when nearly full. Impact of Galileo s Observations The impact was immediate and forceful: Kepler was delighted, and soon acquired his own telescope, as did many others. Many scholars began to take the Copernican system seriously as a physical description. Further works laid the foundations of classical physics. With the telescope, everyone could literally see for themselves. Broad acceptance of the heliocentric model (v.5.1) during the 17 th century. 4
Empirical Laws Kepler s Laws are Empirical Laws: They describe how the planets move. They don t explain why they move that way. Not yet Physical Laws: Kepler made a start, but he had incorrect ideas about forces. Kepler s thinking was strongly motivated by his notions of universal harmony. Correct explanation had to wait until the work of Isaac Newton. Eppur si muove (and still, it moves) Galileo spent his final 4 years in blindness, and died under house arrest, on January 8, 1642. In December of that same year, Isaac Newton was born in Woolsthorpe England. In 1992, 350 years later, Pope John Paul II officially declared Galileo innocent. 5