"Philosophy is written in this grand book -- I mean the universe -- which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth." Galileo, Il Saggiatore

Assignment: Reading: In Explorations, please read the remainder of Chapter 1 (pp. 54-57), Essay 1, "Backyard Astronomy"( pp. 63-72; especially useful for Observing Lab #2!), and the first two sections of Chapter 2 (pp. 75-77). Sign up for a time slot for Observing Lab #2. Problem Set #3 is due on Thursday at 1pm.

In Class: Question to Ponder Galileo's careful telescopic observations of the Moon showed that a) the Moon orbits the Sun. b) the Moon's orbit is not circular. c) the Moon has mountains and other landforms just like the Earth. d) the Moon is made of green cheese. Tycho Brahe (1546-1601) Danish nobleman The "Hipparchus of his time" Discovered he "Nova" of 1572 concluded that the starry backdrop of the celestial sphere was not constant and unchanging Discovered the Comet of 1577 showed that the comet was located beyond the orbit of the Moon started considering the distances to planets and other celestial objects Built the Uraniborg Observatory on the Island of Hveen, Denmark the finest Observatory in Europe at the time Used Quadrants to measure the positions of the planets to 1/100th of a degree accuracy Compiled a rich, accurate, and complete set of planetary observations spanning more than 30 years Constructed a Hybrid geocentric model of the universe Earth is stationary at the center of the universe Sun and Moon revolve around Earth All other planets revolve around the Sun Johannes Kepler (1571-1630) Succeeded Tycho as "Imperial Mathematician" (1601) Inherited Tycho's dataset Conducted the "War on Mars" Published Astronomia Nova, "The New Astronomy" Established three laws for planetary motion The War on Mars Kepler considered two observations of Mars: one when the planet was at opposition and one 687 days, or one martian year, later At both times, Mars was in the same place, but the Earth wasn't By measuring the elongation of Mars at the second time, Kepler was able to fix the position of Mars in its orbit: By doing this at several pairs of times throughout Tycho's dataset, Kepler mapped out the orbit of Mars in 3-D In doing this he showed that the orbit of Mars was not circular, not centered on the Sun, and the speed of Mars in its orbit was not constant. Kepler's Laws of Planetary Motion 1. Planetary orbits are ellipses with the Sun and one focus (the other focus is "empty"). 2. Planets sweep out equal areas in equal times. 3. Period2 = (semi-major axis)3 Kepler's First Law Definitions for an ellipse: The Sun is at one focus of the ellipse, not in the center. Kepler's Second Law Statement is very mideval in tine -- "constant" of the motion. Planets will sweep out equal areas in equal times during their orbits: Really just a statement that the planet travels faster when close to the Sun and slower when farther away. Kepler's Third Law P2 = a3 P = period in years a = semi-major axis in A.U. (Astronomical Units) Example: Venus has a period of 0.615 years P2 = 0.6152 = 0.378 = a3 a = cuberoot(0.378) = 0.72 A.U.