REVIEW  Early Greek Model: (500 B.C., Pythagoreans) The seven objects (sun, 5 planets, and the moon) are attached to seven concentric transparent spheres (at a uniform rate). The early Greek Model predicted a uniform motion of the planets. What observation contradicted this prediction? Retrograde Motion A new theory was required to account for retrograde motion:  Aristachus’ Theory: (~ 300 B.C.) Planets follow circular orbits around the sun. This theory was shot down because (a) Aristarchus did not have scientific “status” and (b) people had a hard time believing that the earth could move at all since it is so large. It was noticed that during the retrograde motion of a planet, the planet seemed BRIGHTER. What would cause that? The planet would be brighter if it were CLOSER TO EARTH during its retrograde motion! A new theory was required ….  Simple Epicycle Theory: (~ 100 B.C.) The simple epicycle theory  could not account for the finer details of planetary motion. It had to be modified, and this was done by Ptolemy…  Ptolemy’s Epicycle Theory: (~ 100 A.D.) In order to describe these finer details, more than 80 epicycles were required. Also, Earth had to be slightly off center.. This theory lasted 1500 years!!! In the year A.D. 1543, on his deathbed, Copernicus Signed his book, On the Revolutions of Heavenly Spheres The year A.D. 1543 is often taken as the “birth of modern science”. Copernicus agreed with the Pythagoreans: a theory of the physical world should be elegant—not complicated like Ptolemy’s epicycle theory. The Copernicus’ theory was not new (first was Aristarchus), but he was able to describe retrograde motion …  Copernican Heliocentric theory: sun centered, everything tracked on circular orbits. The heliocentric theory correctly described retrograde motion! We now have TWO theories that were capable of describing all of the currently observable phenomena: Ptolemy’s Epicycle Theory Copernicus’ Heliocentric Theory   Which one is correct??? A better question might be: Which theory is WRONG? We need an experiment (in the form of an observation) that would show contrast between the theories. The test was the observation of the phases of the planet Venus. To give you an understanding of the meaning of phase, let’s look at the phases of the moon... If Venus followed the epicycle path as formulated by Ptolemy, we would never see the “full Venus” but we would see a “new Venus” twice: Remember the location of the various planets vis-à-vis Earth in Ptolemy’s and Pre-Ptolemy’s theories Venus Sun But if Venus went around the Sun instead of the Earth, we would see a “full Venus” during its epicycle: Remember the location of the various planets vis-à-vis the Sun in Copernicus’ theory Venus Earth Why didn’t they just check this immediately to check which theory was correct?? Ans: They couldn’t see the phases of Venus with the bare eye -- they needed experimentalists: they needed a TELESCOPE! Galileo Observed a “Full Venus” in the 1600’s, thereby eliminating the geocentric epicycle theory. Copernicus himself admitted that his theory did not agree with all of the known data/measurements. DEFINITIONS: Qualitative: general behavior not directly compared to actual measurements (numbers). Quantitative: quantitative measurements compare numbers calculated from a theory to numbers measured through experiment. So the Copernican theory could describe qualitative features such as retrograde motion and the phases of Venus, but did NOT compare well with quantitative measurements of orbits. Quantitative measurements: Tycho Brahe He developed very accurate instruments to measure the angular positions of the stars and planets. Not with a telescope but sighting along sticks (see figures 1.18 – 1.20 on p. 21). He cataloged the positions of the planets for over 20 years! Johannes Kepler joined Brahe in 1600, about a year before Brahe’s death. Kepler could not be an observational astronomer due to bad eyesight, but he was a good mathematician. He analyzed Brahe’s data in detail. At the time (still before the observations of Venus by Galileo), Kepler was stuck on the Epicycle and Copernican theories. He favored the Copernican theory, but could not make the theory match the observations! After much work, Kepler came up with a new theory: Circle: the set of all points equidistant from a center point. Ellipse: Kepler’s Theory : Kepler’s Laws Kepler’s 1st Law: Each planet move in an elliptical orbit around the sun with the sun occupying one foci of the ellipse (the other one is empty). Kepler’s 2nd Law: The imaginary line connecting the planet to the sun sweeps out equal areas in equal times Keplers 3rd Law: The square of any planet’s period of revolution is proportional to the cube of its mean distance from the sun. Kepler’s 1st Law: Each planet move in an elliptical orbit around the sun with the sun occupying one foci of the ellipse (the other one is empty). Kepler’s 2nd Law: The imaginary line connecting the planet to the sun sweeps out equal areas in equal times Keplers 3rd Law: The square of any planet’s period of revolution is proportional to the cube of its mean distance from the sun. P2(in Earth years) = a3(in astronomical units) An astronomical unit the average distance between Earth and the Sun: 149,600,00 km.
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