“Finally we shall place the Sun himself at the center of the Universe “Finally we shall place the Sun himself at the center of the Universe. All this is suggested by the systematic procession of events and the harmony of the whole Universe, if only we face the facts, as they say, ‘with both eyes open’ ” - Nicolaus Copernicus De Revolutionibus orbium coelestium “There was music in the cafes at night and revolution in the air. ” - Bob Dylan

Copernicus (1473-1543) was the sun of a successful merchant in central Poland. Copernicus studied to be a physician, which, at the time included the study of astronomy, because doctors used astrology to decide on treatments. Copernicus worked as a deacon in the Church and spent his time studying Astronomy. He wrote the first draft of De Revoluitonibus in 1513, but, because of worries about how it would be received, he delayed publication until 1543, when he was on his death bed.

What else was going on at the Beginning of the 16th Century? Europe was coming out of the dark ages, rediscovering Greek and Roman learning and exploring the world. Explorers were sailing to Africa and Asia. Columbus discovered America while Copernicus was studying at the University. Malgalhães (Magellan) circumnavigated the globe. All this relied heavily on Astronomy. Printing was becoming common. A man of modest means, like Copernicus, could own books. He had 2 copies of the Almagest. There was an explosion in artistic activity.

Michelangelo’s “David” 1501-1504 da Vinci’s “Mona Lisa” 1503-1506

Copernicus’ Solar System The Sun is in the center Simpler than Ptolemy’s Model (No need for epicycles) Circular Orbits are assumed. This will be proved wrong. More accurate? No, it had about the same accuracy. Why would we prefer this model to Ptolemy’s? From De Revolutionibus

Ptolemy’s Geocentric System, codified in the Almagest Figures from Astronomy Today by Chaisson and McMillan This is getting complicated. Link to movie

The conviction of simplicity persists. Occam’s Razor William of Ockham (1285-1349) was a Franciscan monk and philosopher who espoused the virtues of simplicity and poverty in science and in life. Suggesting that the Pope conform to the latter got him excommunicated. “One should not increase, beyond what is necessary, the number of entities required to explain anything.” If you have two theories that are equally successful in explaining a phenomenon, the simpler one is better. The conviction of simplicity persists.

Tycho Brahe (1546 – 1601) The discovery of a new star

Stellar Parallax Tycho argued that the new star must be in the celestial sphere because it exhibited no parallax. This discovery showed that the heavens were not perfect and unchanging.

25 Years of Planetary Observations Tycho caught the attention of King Frederick II of Denmark With royal funds, he built the ultimate observatory. He designed, & tested instruments, compiling the most comprehensive planetary observations ever, with accuracy of 1°, about 5x better than before. Uraniborg, Hven complete with wine cellar and prison

Johannes Kepler (1571-1630) Kepler joined Tycho a year before Tycho’s death (1600). Assuming Tycho’s position, Kepler inherited the records of Tycho’s observations. From this Kepler knew that planets did not travel on circles and devised a new way to describe planetary motion. Kepler searched for a single physical explanation to planetary motion – a force between planets and the Sun.

A force must therefore act. Kepler thought it was magnetic* Kepler aimed to explain Tycho’s observations which showed that planets do not move in circles He noted that planets closer to the Sun in Copernicus’ model moved faster than those further out. A force must therefore act. Kepler thought it was magnetic* Thus he believed that a simple set of laws existed by which all planets move. *Influenced by William Gilbert’s De Magnete

Kepler’s Three Laws Planets move about the Sun in elliptical orbits with the Sun at one focus. The line joining a planet to the Sun sweeps over equal areas in equal intervals of time. The square of the time of one revolution of a planet about the Sun is proportional to the cube of the orbit’s semimajor axis.

1. Planets move in elliptical orbits with the Sun at one focus.

2. The line joining the Sun to the planet sweeps equal areas in equal intervals of time. Link to movie

3. The square of a planet’s period equals the cube of its semi-major axis P2 = k · a3 P is the period, a is the semi-major axis, k is a constant which depends on the units of P & a. (For P in years and a in Astronomical Units, k=1.) The farther a planet is from the Sun, the longer it’s year

Simple Example of P2=a3 Consider a hypothetical planet orbiting the sun with a semi-major axis of 4 A.U. Let a = 4 A.U. (Astronomical Units) Then a3 = 43 A.U.3 = 64 A.U.3 P2 = 64 years2 P = SQRT(P2)=SQRT(64) years = 8 years The period of the planet is 8 years.

Kepler’s Third Law P a P2 a3 Mercury 0.24 0.39 0.058 Venus 0.61 0.72 0.378 Earth 1.00 Mars 1.88 1.52 3.53 Jupiter 11.86 5.20 140.6 140.8 Saturn 29.42 9.54 865.8 867.4 Uranus 83.75 19.19 7014. 7067. Neptune 163.7 30.07 26804. 27186. Pluto 248.0 39.48 61514. 61540.

Summary In the 16th century Europeans began exploring the planet, navigating by the stars, and renewed their interest in science and the arts. In Astronomy this led to the first new theory describing celestial motions in 1400 years. The Copernican revolution was a tentative, first step towards the establishment of the modern scientific method.