From the Earth-centered to the Sun-centered Model Tuesday, January 8

geocentric For 2000 years, geocentric model for the universe was widely assumed. Spherical Earth at center of universe Moon, Sun, planets, between Earth & stars Stars affixed to celestial sphere Dante, AD 1300

Ptolemy Most famous advocate of geocentric model: the astronomer Ptolemy (2 nd century AD). motion Developed elaborate model to describe motion of stars, Sun, Moon, & planets.

Stars: Circular motion around north celestial pole (near the North Star, Polaris) sidereal day Time to complete circle = 23 hours, 56 min. = 1 sidereal day

as if 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.)

Andromeda Galaxy: 2 million light-years away Comet Hale-Bopp: 10 light-minutes away No sense of depth!

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 Observed motions of the Sun: humanity’s first clock. solar day 1 solar day = time from one noon to the next = 24 hours Sunrise Noon Sunset

IF IF the Sun orbited the Earth once per day:Sunrise Noon Sunset Midnight ×Observer

× × × SINCE SINCE the Earth rotates once per day:NoonSunsetMidnightSunrise ×

either Observed motions of the Sun can be described if either or 1) The Sun goes around the Earth once per day, or 2) The Earth rotates about its axis.

Q: Why did ancient astronomers believe the Earth is not moving? A: Well, do you feel any motion? Rotation speed at Earth’s equator = circumference / rotation period = 40,000 kilometers / 24 hours = 1667 kilometers/hour

stars Sun Moon Describing motions of stars and Sun (and also Moon) was fairly simple in the geocentric model. planets Describing motion of planets was very difficult.

Planet = “Wanderer” To naked eye, a planet looks like a star - a tiny blob of light.

motion 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: epicycle Planet (P) moves in a small circle called the epicycle. deferent 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 (3 rd cent. BC) proposed that the Earth rotates on its axis & goes around the Sun. heliocentric First heliocentric (Sun-centered) model.

rejected 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? 110 times A sphere (like the Sun) will be 1/2° across when its distance is 110 times its diameter.

How far away is the Sun? Farther away than the Moon! between 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 E M Half close to Sun is illuminated. 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.

must be When we see the Moon as a half-circle, Earth-Moon-Sun angle must be 90°. measured When Aristarchus saw the Moon as a half- circle, he measured the Moon-Earth-Sun angle to be 87°. 90° 87°

Trigonometry Alert! x y θ

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 huge Sun orbit tiny Earth?”), heliocentric model ignored for 18 centuries. Reviver of “heliocentrism”: Nicolaus Copernicus (Polish: 1473 – 1543)

Basic structure of Copernicus’ model: Earth Sun

Geocentric model (Ptolemy): ◦ Earth in central location ◦ Celestial sphere rotating about axis ◦ Sun orbiting around Earth Heliocentric model (Copernicus): ◦ Sun in central location ◦ Earth rotating about axis ◦ Earth orbiting around Sun

Thursday’s Lecture: Reading: Chapter 1 Planets and Stars and Galaxies (Oh my!)