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Lecture3 Momentum&amp;Gravity

# Lecture3 Momentum&amp;Gravity - Momentum and Gravity...

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Momentum and Gravity 2/2/09 Astronomy 309R - Spring 2009 1

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2/2/09 Astronomy 309R - Spring 2009 2 Motivation: A Review of Kepler’s Laws (that Kepler inferred by studying Tycho Brahe’s measured orbit of Mars) 1. The orbit of a planet is an ellipse with the sun at one of the foci. 2. A line joining a planet and the sun sweeps out equal areas in during equal intervals in time. 3. (orbital period) 2 is proportional to (radius of the orbit) 3 http://xkcd.com
Implications of Kepler’s Laws An implication of the 2 nd Law: any single planet moves faster when it is closer to the sun, and lower than when it is farther from the sun. (Please convince yourselves that you can reach this conclusion simply by contemplating what is stated in the 2 nd Law!) An implication of the 3 rd Law: planets farther from the sun move slower than planets closer to the sun. Let the symbol “ ” mean “proportional to”. So the 3 rd Law can be written to state that: period 2 radius 3 . You can take a square root of both sides, to obtain the proportionality: period radius 1.5 . The velocity of a planet is equal to the circumference, which is 2 × π × radius, divided by the orbital period. So the velocity is proportional to radius/period, which is in turn proportional to radius/radius 1.5 , which nothing other than radius 0.5 (note the minus sign!) that we can recognize as one divided by the square root of the radius. In mathematical notation, Clearly, the larger the radius, the smaller the velocity! 2/2/09 Astronomy 309R - Spring 2009 3

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Some Questions Left Unanswered by Kepler • Why do the planets remain in perpetual motion? (Perhaps there is a deeper, more general physical law that guarantees perpetual motion for planets orbiting the sun.) • What is the physical origin of the neat relation period 2 radius 3 ? (Perhaps there is a deeper, more general physical law that implies Kepler’s 3 rd Law, and from which many other conclusions, distinct from Kepler’s laws, can be drawn.) 2/2/09 Astronomy 309R - Spring 2009 4
Concepts to Lean • Momentum • Isolated systems • Conservation of momentum • Newton’s laws of motion • Newton’s law of gravitation • Angular momentum 2/2/09 Astronomy 309R - Spring 2009 5

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2/2/09 Astronomy 309R - Spring 2009 6 Momentum • Every body carries momentum associated with the motion of the body. The momentum of stationary bodies is equal to zero. • Momentum has magnitude (strength) and direction.
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Lecture3 Momentum&amp;Gravity - Momentum and Gravity...

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