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Pulsar Radius from its rotational period

  1. Feb 11, 2009 #1

    TFM

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    1. The problem statement, all variables and given/known data

    A pulsar emits bursts of radio waves with a period of 10 ms. Find an upper limit to the radius of the pulsar.

    2. Relevant equations

    Not Sure

    3. The attempt at a solution

    Can anyone help with this, I cannot see how the period will help tell you the upper limit to the radius. I know that pulsars are basically neutron stars, and they have high densities (10^15 kg/m^3), but I ams lightly unsure how to get the radius of the pulsar from its period.

    Any helpful suggestions would be most helpful,

    Thanks in advanced,

    TFM
     
  2. jcsd
  3. Feb 11, 2009 #2

    mgb_phys

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    What happens when the rotation rate is fast enough that centrifugal force on a point on the surface as is stronger than gravity?
     
  4. Feb 11, 2009 #3

    TFM

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    Well, Gravity is pulling down, the centrifugal force is pushing outwards, so items on the surface would be "pushed" off of the surface.
     
  5. Feb 11, 2009 #4

    mgb_phys

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    Correct - so at a certain speed the surface would break off, doesn't this set a maximum radius for a given rotation rate?
     
  6. Feb 11, 2009 #5

    TFM

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    Indeed it would,

    So:

    [tex] mg = m\omega^2r [/tex]

    [tex] g = \omega^2r [/tex]


    And since:

    [tex] Omega = \frac{2\pi}{Period} [/tex]

    Thus:

    [tex] g = \frac{4\pi^2}{Period^2}r [/tex]

    Does this look okay?
     
  7. Feb 11, 2009 #6

    mgb_phys

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    You will need to write 'g' for the star in terms of it's mass (or density) and radius.
     
  8. Feb 12, 2009 #7

    TFM

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    True, but we aren't given a mass for the star? Would we use the density as being 10^15?
     
  9. Feb 12, 2009 #8

    TFM

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    Okay, so if we use:

    [tex] g = -\frac{MG}{r^2} [/tex]

    and

    [tex] M = density*volume [/tex]

    [tex] M = density*(\frac{4}{3}\pi r^3) [/tex]

    [tex] g = -\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2} [/tex]


    Thus:

    [tex] -\frac{(density*(\frac{4}{3}\pi r^3))G}{r^2} = \frac{4\pi^2}{Period^2}r [/tex]

    Since we need the magnitude only for g:

    [tex] \frac{(density*(\frac{4}{3}\pi r^3))G}{r^2} = \frac{4\pi^2}{Period^2}r [/tex]

    [tex] (density*(\frac{4}{3}\pi ))G = \frac{4\pi^2}{Period^2} [/tex]

    Does this look better?

    TFM
     
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