CC105Handout - Handout on Motions on Earth & in Space...

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( 2008 by A. Marscher) Kepler’s Laws – page 1 Box 1. The properties of an ellipse – page 2 Two Views of Falling Bodies: Galileo vs. Aristotle – page 3 Newton’s Mathematical Description of Motion – page 3 Motion: Basic Definitions – page 4 The Basic Equation Relating Distance to Velocity and Acceleration – page 4 Two-dimensional Trajectories – page 4 Example of a Two-dimensional Trajectory – page 5 Newton’s Laws of Motion – page 7 Momentum: A Conserved Quantity – page 8 Newton’s Law of Universal Gravitation – page 8 Newton’s Laws and Falling Bodies – page 9 The Equivalence Principle – page 9 Is Newton’s Law of Universal Gravitation Beautiful? – page 9 Application of Newton’s Laws to Planetary Motions – page 10 Energy – page 11 Escape Velocity – page 12 General Characteristics of Orbits – page 13 Philosophical Implications of Newton’s Laws: Determinism and the “Clockwork Universe” – page 14 Chaos – page 15 Einstein’s Relativity – page 15 Motion near the Speed of Light – page 15 Relation between Energy and Mass – page 16 General Relativity: Effect of Mass on the Geometry of Space-Time – page 17 Summary – page 17 Glossary – page 18 Questions for Discussion – page 20 Examples of How to Solve Problems in the Physics of Motion – page 21
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1 Motions on Earth and in Space Supplement to CC105 Lectures 3 & 4 ©2008 by Prof. Alan P. Marscher Kepler’s Laws At the beginning of the 17 th century, Johannes Kepler worked doggedly with Danish astronomer Tycho Brahe’s data on Mars, trying to make sense out of the planet’s complicated changes in apparent speed as well as its pronounced retrograde motion when it was on the opposite side of the sky from the Sun. After an exhaustive number of attempts to create a successful model, he decided to use geometry to determine the shape of Mars’ orbit as it would be viewed from the Sun. This followed Copernicus’s heliocentric hypothesis. Once he traced out Mars’s orbit, he saw that it was an ellipse. At last, Kepler had found the grand pattern of the heavens: The planetary orbits are ellipses, not circles ! In the process of calculating Mars’s orbit, Kepler found that the speed of Mars changes such that it moves faster when it is closer to the Sun. Upon further study, he was able to determine a mathematical law to describe the behavior of the velocity. In 1609, Kepler published his 1st and 2nd laws of planetary motion: 1. A planet’s orbit is an ellipse with the Sun at one focus . (See Box 1 for the properties of an ellipse.) 2. An imaginary line between the Sun and a planet sweeps out equal areas in equal time intervals (see Figure 1). What remained was a mathematical description of how the
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CC105Handout - Handout on Motions on Earth & in Space...

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