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Relativistic Velocity

  1. Oct 26, 2004 #1
    Which velocity can be said to be relativistic velocity? I mean is there any range beyond which velocities can be called as relativistic velocities?
  2. jcsd
  3. Oct 26, 2004 #2


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    All velocities are relativistic, but relativistic effects will not be easily noticeable until the speed is large enough to make


    (where v is the speed, and c is the speed of light)

    significantly larger than 1.

    An example: suppose that v=0.1c, i.e. 10% of the speed of light. Then gamma is about 1.005. Is that significantly larger than 1? That depends on that you're doing. Sometimes a 0.5% correction to the non-relativistic result isn't important, and sometimes it is.
  4. Oct 27, 2004 #3
    Is same true for relativistic energies also?
  5. Oct 27, 2004 #4
    The kinetic energy of a particle is [itex]E_{kin.}=(\gamma -1)mc^2 [/itex] if this deviates substantially from classical kinetic energy you should use the relativistic result.

    So you could use as a criterium: if [itex]2 (\gamma -1)c^2/v^2[/itex] is significantly larger than 1 you deal with relativistic velocities...
  6. Oct 27, 2004 #5


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    Consider the orbital speed of a satellite or spacecraft: ~17,000mph. For an astronaut, this is not a relativistic velocity, meaning he won't notice the time dilation on his watch from takeoff to landing. For a GPS satellite, however, this is a relativistic velocity and must be accounted for in its functioning in order for GPS positions to be accurate.
  7. Oct 28, 2004 #6


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    To see the answer to your question it helps to use the series expansion


    The kinetic energy is


    Note that the first term after the last equality sign is just the non-relativistic kinetic energy. The other terms are relativistic corrections to the non-relativistic result. If the speed is large enough these terms can't be ignored.
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