Lecture 10 - Ptolemy and Copernicus (2/5/96)

Seeds: Chapter 4

1. The Library at Alexandria
   • Egypt conquered by Alexander the Great (d.323 BC), set up Alexandria as capital
   • Ptolemy I, first satrap (then king) of Egypt after Alexander's death, founds Library. Beginning of Ptolemies as dynasty.
   • The Great Libraray functions as center for Hellenic learning (Aristarchus, Hipparchus, Ptolemy)
   • Library survives fires set by Julius Caesar in 47 BC. End of Ptolemy dynasty with Cleopatra VII (d.30 BC).
   • Ptolemy, the last great Greek astronomer, around AD 140
   • Library destroyed in AD 391
2. Ptolemy
   • Claudius Ptolemaeus (Ptolemy), not one of the Ptolemies that ruled Egypt earlier (note Roman name), around AD 140. Virtually nothing is known of his life.
   • The last great Greek (Roman) astronomer.
   • Compiled 13 volumes of Greco-Roman astronomy, including his own calculations, called Mathematical Syntaxis, later known by its Arabicised name The Almagest
   • Made new measurement of distance to Moon using parallax, found it to be 59 Earth radii (correct value is 60).
   • Mostly known for his geocentric cosmology
   • Also developed mystical principles of Natal Astrology based upon the configuration of the planets in the sky at the time of birth (Zodiac and Houses) still in use today
3. Ptolemy's Cosmology
   • Started from Aristotlean cosmology of crystal spheres centered around the Earth
   • Compiled many previous and his own observations of the positions of the Sun, Moon, and planets. Tried to make a model to fit these measurements.
   • Combination of uniform circular motions around epicycle, orbiting Earth on an eccentric called a deferent
   • Epicycle needed to explain retrograde motion, where planets now known to be outside Earth's orbit are seen to reverse direction of motion across the sky.
   • Retrograde motion due to differing speeds in heliocentric orbits of Earth and outer planets (Earth faster), but needed extra loops (epicycles) in geocentric model.
   • Motion of epicycle on deferent with uniform circular velocity about equant on opposite side of eccentric center from Earth. This was needed to explain the changes in orbital speed observed (now known to be due to elliptic orbits, as we will see from Kepler).
   • Reproduced observed motions of planets fairly accurately, though with very complicated model. A tribute to Ptolemy's mathematical skills that he could make this work!
   • Although this model was able to reproduce the observed motions, it did not reflect the underlying physics --- Ptolemy himself may have thought of it only as a mathematical model, like a computer program
   • Model parameters and constants had to be continually updated by later Arabic and Christian astronomers, as errors accumulated
   • Ptolemy's version of the Aristotlean cosmology was accepted as absolute authority by the Catholic Church until the Copernican Revolution in the 17th century!
4. Copernicus
   • Nicholaus Copernicus (Polish born Mikolaj Kopernik) (b.1473 - d.1543)
   • trained in law and medecine but interests were in astronomy and mathematics
   • developed (redisovered?) heliocentric model
   • He finally published his work in the book "De Revolutionibus" ("On the Revolutions") which came out the year of his death (1543). The rest of the title "of the Heavenly Spheres" was deleted by his publisher for some obscure reason.
   • Previously published his heliocentric ideas anonymously in the so-called "Little Commentary", which largely went un-noticed.
   • Catholic Church knew of his work and was interested, but he escaped persecution that would befall later proponents of his model
   • modeled revolution of Earth about Sun plus rotation of the Earth about its axis
   • had 6 planets orbiting Sun in correct order - Mercury, Venus, Earth, Mars, Jupiter, and Saturn
   • worked out correct relative scale for solar system (see below)
   • but retained idea of uniform motion on circular orbits so his model was less accurate than Ptolemy's
   • the scale of the orbital distances from Sun easily determined by measuring the elongations, the angle between the planet and the Sun as seen from Earth, at various points and times in their orbits
   • The orbits of the inferior planets, the inner planets Mercury and Venus inside the orbit of the Earth, can be measured by the angle of the greatest elongation (see previous lecture).
   • The cardinal points in inferior planetary orbits as seen from the Earth:
     • Inferior Conjunction - between the Earth and the Sun
     • Superior Conjunction - on the other side of the Sun
     • Greatest Western Elongation - largest angle planet makes to West of Sun
     • Greatest Eastern Elongation - largest angle planet makes to East of Sun
   • The superior planets are farther away from the Sun than the Earth (Mars, Jupiter, Saturn)
   • The cardinal points in superior planetary orbits as seen from the Earth:
     • Conjunction - on the other side of (behind) the Sun (0 degrees elongation)
     • Opposition - opposite Sun in sky (180 degrees elongation)
     • Quadrature - the two points where the planet is at right angles to the Sun in the sky (elongation +/- 90 degrees)

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