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Homework Help: Astrophysics - tricky unit conversions?

  1. Aug 24, 2010 #1
    1. The problem statement, all variables and given/known data

    I've got a radius of 22.69kpc, and a velocity of 180km/s. I wish to find the angular rotation speed in units of arcsec/year.

    I'm stuck at the moment

    3. The attempt at a solution

    Starting with the basic v=r[tex]\omega[/tex], I transpose to get [tex]\omega[/tex]=v/r.

    For now, I'm going to convert all length units to parsec, and all time units to years.

    velocity = 180km/s = (5.83*10^-12)pc/s = (1.84*10^-4)pc/year
    radius = 22.69kpc = 22690pc

    [tex]\omega[/tex] = [(1.84*10^-4)pc/year]/[22690pc] = (8.11*10^-9) yr^-1
    since the units of parsec cancel

    This is where I'm stuck, how do I ge the arcsec units in?
  2. jcsd
  3. Aug 24, 2010 #2
    You have to convert from radians to degrees, and then to arcseconds (which is 1/3600 of a degree---1 arcminute is 1/60 of a degree, and 1 arcsecond is 1/60 of an arcminute)
  4. Aug 24, 2010 #3
    Thanks for the reply.

    So I'm guessing what I've done up to that point is correct?

    i.e., after the parsecs cancel I actually have:

    w = (8.11*10^-9) rad/yr

    then I should convert to:

    w = (xxxx) degrees/yr
    w = (yyyy) arcsec/yr

    Sound good?
  5. Aug 25, 2010 #4
    I did the above and got an answer of:

    w=0.0016712178 arcsec/year,

    meaning it would take approx 600 years to rotate through 1".

    I couldn't find any reference values, so just wondering if the answer sounds right (or is in the correct magnitude of some other known angular velocities)
  6. Aug 25, 2010 #5


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    I agree with the calculation. The answer makes sense if it is talking about a star orbiting in a galaxy. For comparison, our sun's revolution rate is the same order of magnitude, about 0.006 arcsec/year (based on an orbital period of 200 million years).
  7. Aug 25, 2010 #6
    thanks for the reply.

    for your information, it was a star orbiting around the m101 (pinwheel galaxy) at:
    R25 (isophotal radius at 25 B-mag arcsec^-2) = 22.69kpc
    Vmax (rotational velocity @ R25) = 180km/s
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