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Satellites in Circular Orbits and Apparent Weightlessness

Satellites in Circular Orbits and Apparent Weightlessness. Sections 5.5 and 5.6. 5.5 Satellites in Circular Orbits. Uniform Circular Motion Gravity provides centripetal force There is only one speed that a satellite can have if the satellite is to remain in an orbit with a fixed radius.

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Satellites in Circular Orbits and Apparent Weightlessness

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  1. Satellites in Circular Orbits and Apparent Weightlessness Sections 5.5 and 5.6

  2. 5.5 Satellites in Circular Orbits • Uniform Circular Motion • Gravity provides centripetal force • There is only one speed that a satellite can have if the satellite is to remain in an orbit with a fixed radius.

  3. Why only 1 speed? • r is measured from the center of the earth

  4. Consequences • Since 1/r • As r decreases, v increases • Mass of the satellite is not in the equation, so speed of a massive satellite = the speed of a tiny satellite

  5. Example • Calculate the speed of a satellite 500 km above the earth’s surface. • v = 7.30 x 103 m/s 16,335 mph

  6. GPS • Read pages 133 and 134 about the GPS satellites

  7. Satellites about Other Objects • Satellites are anything that orbit some object such as the Earth, Sun, or other massive object • When using the equation, replace mE with the mass of central object (i.e. sun)

  8. Example • Find the mass of a black hole where the matter orbiting it at r = 2.0 x 1020 m move at speed of 7520000 m/s. • M = 1.70x1044 kg

  9. Find the Period of Orbit • Period – Time taken for one orbit • From previous equation • Also v = dist / time

  10. Altitude of TV Satellite • TV Satellite remain in place relative to the earth • This is called Geosynchronous Orbits • Find the altitude of a geosynchronous satellite above the earth’s surface. • Altitude = 3.59x107 m • 22300 mi

  11. 5.6 Apparent Weightlessness • Astronauts in the space shuttles and international space station seem to float • They appear weightless • They are really falling

  12. Apparent Weightlessness • If you are in a fast elevator going down, • You feel lighter • You are apparently lighter • If you are in a broken elevator going down in free fall • You feel very light • You are apparently weightless

  13. Apparent Weightlessness • Satellites are in free fall • Centripetal Acceleration is pointing towards center of earth • Since acceleration points towards earth, the satellite is falling towards the earth

  14. Artificial Gravity • By spinning a cylindrical space station, artificial gravity can be created • On the interior surface, • ac is towards the center • Provided by “floor”

  15. What rotational speed? • What speed should a space station rotate (r = 2000m) so that the astronauts feel their weight as if on earth? • v = 140 m/s

  16. Practice Work • Try these weighty problems • 144 P27-30 • Total of 4 problems

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