Lecture 9 - Later Greek Astronomy (2/2/96)

Seeds: Chapter 4

1. Problem Set #1 (Question 6)
   • The single observation that constrains the minimum and maximum distance of an inner planet in a nearly circular orbit is the greatest elongation.
   • The greatest elongation of Venus was measured by the Greeks, including Ptolemy, to be about 47 degrees.
   • Therefore, the ratio of max dist / min dist = 6.4, regardless of whether you adopt a Ptolemean or Copernican system!
   • Ptolemy had this right, and it is the Figure 4-7 in Seeds that is an inaccurate representation of the Ptolemaic system!
2. Later Greek Astronomy - The Alexandrian School
   • Centered in Alexandria, Egypt, which was conquered by Alexander the Great
   • The Great Library at Alexandria was a center for learning and knowledge for the Greeks, Romans, and Moslems until it was burned.
3. Aristarchus of Samos (310 - 230 BC)
   • Developed heliocentric model
   • Only one manuscript survives, "On the Sizes and Distances of the Sun and Moon"
   • Calculated relative sizes and distances of Moon and Sun (and Earth)
     • Assumption #1: Moon receives light from Sun -> phases
     • Assumption #2: 1st and 3rd quarter are separated by 87 degrees from Earth - Sun line in orbit
     • Assumption #3: Diameter of Earth's Umbral shadow during Lunar eclipse is twice the diameter of the Moon
     • Assumption #4: The angular diameter of the Moon and the Sun from the Earth are the same, and equal to 2 degrees
     • Deduction #1: the ratio of the distance to the Moon, and the distance to the Sun from the Earth is 19
     • Deduction #2: the ratio of the diameter of the Sun to the diameter of the Earth is about 7
     • The correct values are 400 and 109 respectively
     • Aristarchus used incorrect values, since the angular diameters of the Sun and Moon are 1/2 degree, and the 1st and 3rd quarters are immeasurably different from 90 degrees from the new moon
   • When he found that the Sun was larger than the Earth, this probably induced him to adopt a heliocentric cosmology
4. Eratosthenes (276 - 190 BC)
   • Measured accurately the diameter of the Earth
   • Like other Greeks, believed the Earth was spherical
   • Used fact that Sun was overhead (at zenith) in Syrene, Egypt, at noon on midsummer.
   • At same time, in Alexandria, 5000 stadia North of Syrene, the Sun was found to be not at the zenith, but 7.2 degrees South of the zenith ( 1/50 of a circle ).
   • Therefore, the circumference of the Earth is 50 x 5000 stadia or 250,000 stadia
   • Thus, the radius of the Earth is 40,000 stadia ( C = 2*PI*R )
   • If one stadium = 1/6 km (we dont know exactly!) then radius of Earth is 6667 km (correct value is 6378 km).
5. Hipparchus and the Zenith of Greek Astronomy
   • In Alexandria (probably) from 160-120 BC
   • Built observatory at Rhodes
   • made instruments and remarkable measurements for that time
   • devised celestial coordinate system for designating positions of stars and planets (RA and Dec)
   • devised magnitude system (see Lecture 3) for apparent brightness of objects
   • compared his measured positions of stars to those from earlier records and found change in the position of the North Celestial Pole over 150 years -> precession!
   • refined Aristarchus' method to get good estimate of the Moon's relative size and distance -> distance = 59 Earth diameters
   • The early Greeks (Eudoxus about 400 BC) measured the Sun's motion across the sky and found its speed along the Ecliptic varied during the year (now we know this is due to its elliptic orbit), and tried to explain it using a series of pivoting spheres.
   • Hipparchus used off-center circular orbit called an eccentric for the Sun, which worked very well (the Earth's orbit about the Sun is very nearly an off-center circle as we will see).
   • measured small differences in length of seasons (equinoxes to solstices, etc.) and determined correctly that the Sun was closest to the Earth in December at that time (it is now in January)
   • pointed out that nested circular orbits (epicycle and deferent) could also reproduce Sun's orbit, but preferred simpler eccentric model
   • could not reproduce Moon's motion with eccentric (we know now that the Moon's orbit is quite elliptical with precessing nodes!)
   • planets and their retrograde motions (see Lecture 10 were not able to be modeled with the eccentric

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