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Ancient Cosmology Monday, September 29 For 2000 years, geocentric model for the universe was widely assumed. Stars affixed to celestial sphere Moon, Sun, planets, between Earth & stars Spherical Earth at center of universe Most famous advocate of geocentric model: the astronomer nd Ptolemy (2 century AD). Developed elaborate model to describe motion of stars, Sun, Moon, & planets. Stars: Circular motion around north celestial pole (near the North Star, Polaris) Time to complete circle = 23 hours, 56 min. = 1 sidereal day Stars look as if they were glued to rigid spherical shell rotating once every 23 hr, 56 min. (You can’t tell, without a telescope, that some stars are closer than others.) Sun: Circular motion around celestial pole: part of circle is below horizon, so we say Sun “rises” and “sets”. Time to complete circle = 24 hours. Observed motions of the Sun: humanity’s first clock. Noon Sunrise Sunset 1 solar day = time from one noon to the next = 24 hours IF the Sun orbited the Earth once per day: Midnight Sunset × Observer Noon Sunrise SINCE the Earth rotates once per day: × × Midnight Sunrise Sunset Noon × × Observed motions of the Sun can be described if either 1) The Sun goes around the Earth once per day, or 2) The Earth rotates about its axis. Describing motions of stars and Sun (and also Moon) was fairly simple in the geocentric model. Describing motion of planets was difficult. Planet = “Wanderer” in Greek To naked eye, a planet looks like a star a tiny blob of light. Planets are distinguished by their motion relative to stars. ↑ NORTH Planets usually move west to east, but sometimes east to west (retrograde), relative to stars. Ptolemy’s explanation of retrograde motion: Planet (P) moves in a small circle called the epicycle. Earth Center of epicycle (A) moves in a large circle called the deferent. Combination of small and large circles creates “loop-the-loop” retrograde motion. Detailed structure of Ptolemy’s geocentric model: Earth Complicated! A bold minority opinion: Aristarchus (3rd cent. BC) proposed that the Earth rotates on its axis & goes around the Sun. First heliocentric (Sun-centered) model. Heliocentric model was rejected by the contemporaries of Aristarchus. Aristarchus was accused of impiety. Why did Aristarchus bother with a heliocentric model, given the grief he received? Questions posed by Aristarchus: How far away is the Sun? How large is the Sun? A sphere (like the Sun) will be 1/2° across when its distance is 115 times its diameter. How far away is the Sun? Farther away than the Moon! Moon comes between Sun and Earth during a solar eclipse. Moon, like Earth, is an opaque sphere, capable of blocking light. Phases of the Moon: The Moon is an opaque sphere illuminated by the Sun. s Half close to Sun is illuminated. M E Half away from Sun is dark. Gibbous, crescent shapes: result of perspective. How Aristarchus found the relative distances of Sun and Moon. “First quarter” or “last quarter” Moon: we see bright portion of Moon as a perfect half-circle. When we see the Moon as a half-circle, Earth-Moon-Sun angle must be 90°. 90° 87° When Aristarchus saw the Moon as a half-circle, he measured the Moon-Earth-Sun angle to be 87°. A more accurate diagram: M E 90° 87° S 3° Get out your rulers: Earth – Sun distance (E-S) is 19 times Earth – Moon distance (E-M). Aristarchus: Sun is 19 times farther away (and thus 19 times bigger) than Moon. (This is actually an underestimate of the Sun’s immense size.) Aristarchus: Earth is 3 times size of Moon (from size of Earth’s shadow on Moon). Despite the arguments of Aristarchus (“Why should big Sun orbit tiny Earth?”), heliocentric model ignored for 18 centuries. Reviver of “heliocentrism”: Nicolaus Copernicus (Polish: 1473 – 1543) Wednesday’s Lecture: Renaissance Cosmology Reading: Chapter 2