Satellites in Circular Orbits and Apparent Weightlessness

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Satellites in Circular Orbits and Apparent
Weightlessness

• Sections 5.5 and 5.6

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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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Why only 1 speed?

• r is measured from the center of the earth

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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

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Example

• Calculate the speed of a satellite 500 km above
  the earths surface.
• v 7.30 x 103 m/s
• 16,335 mph

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GPS

• Read pages 133 and 134 about the GPS satellites

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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)

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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

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Find the Period of Orbit

• Period Time taken for one orbit
• From previous equation
• Also v dist / time

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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 earths surface.
• Altitude 3.59x107 m
• 22300 mi

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5.6 Apparent Weightlessness

• Astronauts in the space shuttles and
  international space station seem to float
• They appear weightless
• They are really falling

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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

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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

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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

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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

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Practice Work

• Try these weighty problems
• 144 P27-30
• Total of 4 problems