lecture-03

lecture-03 - These lecture notes were prepared for Rutgers...

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Unformatted text preview: These lecture notes were prepared for Rutgers Physics 341/342: Principles of Astrophysics by Prof. Chuck Keeton, and modified by Profs. Saurabh Jha and Eric Gawiser. All rights reserved. c 2011 Lecture 3: Celestial Mechanics This discussion is drawn from Chapters 1–2 of Carroll & Ostlie. I. Some History There are many things in the sky that change: • Sun: day, seasons. • Moon: phases. • Stars: move across the sky every night; also vary with the season. • Planets: points of light that “wander” among the stars. Five are visible to the naked eye — Mercury, Venus, Mars, Jupiter, and Saturn. It sure looks like they all move around the Earth. This idea (the “geocentric” universe) could fairly easily explain the motions of the Sun, Moon, and stars. However, there was one serious puzzle: retrograde motion . From time to time, one of the planets would stop, turn around and go backwards, then stop and go forwards again (relative to the stars). This is particularly apparent with Mars: These observations date at least to the Greeks. The Greeks were obsessed with geometry, so they believed that motion had to be perfect circles. To explain retrograde motion with circular orbits, Hipparchus (c. 150 BC) first proposed “epicycles.” His model could explain the effect qualitatively, but could not reproduce ever more accurate observations. To fit the data, Ptolemy (c. 100 AD) was forced to offset the circle from Earth and allow it to wobble slightly. (A common misconception is that Ptolemy and his successors added more and more epicycles. They couldn’t — even one was hard enough to compute. See The Book Nobody Read by Owen Gingerich for details.) Nicholas Copernicus (1472-1543) developed the Sun-centered (or “heliocentric”) model. His model could easily explain retrograde motion, as shown in Figure 3a. He published his ideas in De Revolutionibus Orbium Coelestium (“On the Revolution of the Celestial Sphere”). 1 Figure 1: From http://www.umich.edu/˜geo113/113/outl1.html. Figure 2: From http://www.mi.sanu.ac.yu/vismath/liao/introduction.html. Copernicus’s model could also nicely explain why the planets fall into two categories (see Figure 3b): • Inferior planets: Mercury and Venus. Never seen far from Sun. • Superior planets: Mars, Jupiter, and Saturn. Could be near Sun, or on opposite side of sky, or in between. (It is commonly believed that Copernicus greatly simplified the picture of planetary motion. In fact, he still insisted on circular orbits, so he still had to introduce some fudge factors not all that different from Ptolemy’s model. In other words, Copernicus traded epicycles for a moving Earth, and given that he did not drastically simplify the model, that is not a trade 2 Figure 3: (a, left) Illustration of retrograde motion in the heliocentric model. From http://www.umich.edu/ ˜geo113/113/outl1.html. (b, right) Inferior versus superior plan- ets. From http://library.thinkquest.org/29033/begin/elongation.htm....
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This note was uploaded on 10/20/2011 for the course PH 341 taught by Professor Gawiser during the Fall '11 term at Rutgers.

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lecture-03 - These lecture notes were prepared for Rutgers...

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