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PH 201 Dr. Cecilia Vogel Lecture 23

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REVIEW equilibrium stable vs. unstable static OUTLINE eqlb universal gravitation

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Universal Gravity Newton’s Universal Law of Gravity: applies universally Applies to surface of planet Applies to orbiting satellites Applies to projectiles etc…

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Satellites A satellite is planet around Sun moon around planet artificial satellite around planet Keppler’s Laws were stated in terms of planets around Sun but apply to others, too

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Keppler’s Laws Keppler’s 1 st Law planets travel in elliptical orbit, link to image link to image with Sun at one focus ellipse has 2 foci nothing at other focus larger orbit larger semi-major axis more circular smaller eccentricity perfect circle e=0, a=r

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Keppler’s Laws Keppler’s 2 nd Law planet sweeps out equal areas in equal times, when closer PE is ________, so KE is ___ so goes faster when close when farther PE is ________, so KE is ___ so goes slower when far The same planet goes slower when it is far from the sun than when it is close to the sun

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Satellite Energy Generally within one planet’s orbit: larger r, slower speed Circular Orbit uniform circ motion, with F g =F c

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Keppler’s Laws Keppler’s 3 rd Law=“Law of Periods” T 2 is proportional to a 3, perfect circle: F=ma closer planets go

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How to Weigh the Sun Observe planet the period and or Calculate the mass of the Sun

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Geosynchronous Orbits Artificial satellite if it is to keep over same point, T = also M = so All circular geosynchronous orbits are at r = 42000 km h = 36,000 km

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Planet’s Gravity What is the gravitational pull of a planet on something on its surface ? let M = planet’s mass, m = object’s mass R = radius of planet

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Planet’s Gravity What is the gravitational acceleration on a planet’s surface? let a g = free-fall acceleration on planet free-fall —> F = ma on Earth: M = 5.98X10 24 kg, R = 6.37X10 6 m

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Earth’s Gravity What is the gravitational acceleration on a Earth’s surface? a g = 9.83 m/s 2 g = 9.80 m/s 2 ???? Force of gravity provides force for centripetal and a g = g + h

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