## The Scientific Revolution

What the ancients knew. Aristotle; Eratosthenes, librarian of Alexandria 3rd century BC
measured the angle of a perpendicular gnomon at Alexandria on a day when a similar gnomon
at Syrene, 5000 stades south, cast no shadow. The angle is 7 1/5˚ or 1/50 a circle. So the
distance between Alexandria and Syrene is 1/50 the earth's surface of 250,000 stades
(24,000 miles).

In the 3rd century BC Aristarchus of Samos estimated the relative size of sun, moon, and
earth by measuring shadows during the half moon and a full eclipse. He estimated that the
moon wa 40 earth diameters distant--the actual figure is about 30. But he thought the
sun's distance was 12,000 earth diameters, which is much too small. Consequences.

Galileo's experiments of motion. He discovered that d/t[squared] is a constant. In other
words, if a car moves at 10 m in the first second, in twice that time it will move 4 times as
fast or 40m during the first two seconds. In the first 3 seconds it would move 9 times as
fast or 90m.

The Geocentric World View. Dante's view: gravity and levity, the 4 elements in the
sublunary sphere, perfect circular motion. Earth at center surrounded by 10 spheres: moon,
Mercury, Venus, Son, Mars, Jupiter, Saturn, in turn surrounded by the sphere of the fixed
stars. 10th sphere is the empyrean heaven, 9th the *primum mobile*. Problems with
Aristarchus' heliocentric theory: appearances, clouds and birds, and parallax. The
*Almagest* of Ptolemy 150 AD. epicycles and eccentrics--eventually over 80!

Copernicus born 1473 in Poland. His theory reduced the 80 ugly spheres of Ptolemy to 34.
Held off publication for fear of ridicule but the Pope actually approved of his ideas. Who
so radical a century later? Unity of medieval thought--theology, astrology, astronomy
connected--even people made up of 4 humors phlegmatic, choleric, sanguine, or melancholic.
Copernicus inadvertently shows this unity to be an illusion.

Tycho Brahe refines naked eye measurement and acquires data in his observatory; his
assistant Johannes Kepler realizes that the orbits are elliptical.

Galileo and his telescope: sunspots, the surface of the moon. The "Medicean Stars" of
Jupiter.

It was Newton who explained *why* the orbits are elliptical. 1687 his *Principia
Mathematica* pulled all the themes of motion and gravity together to explain how orbits
work.