Astrophysics - tricky unit conversions?

[t_n_p]

Homework Statement

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

The Attempt at a Solution

Starting with the basic v=r$$\omega$$, I transpose to get $$\omega$$=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

$$\omega$$ = [(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?

 

[zhermes]

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)

 

[t_n_p]

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?

 

[t_n_p]

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)

 

[Redbelly98]

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).

 

[t_n_p]

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