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## Homework Statement

Two questions here, but it's mainly terminology I don't understand;

1(a). Calculate the proper motion of the Galactic Centre (GC) with respect

to the sun (and measured relative to the ‘stationary’ distant galaxies

and quasars) in units of arcsec/yr, assuming that the Galaxy rotation

speed at the solar circle is Vo = 220 km/s and the distance to the GC

is Ro = 8.5 kpc.

2. A spherical HI cloud has a density of 10

^{6}atoms m

^{-3}and a gas mass of

50 M⊙

(a). What is the cloud radius in pc?

(b). Show that the luminosity of the cloud in its 1.42 GHz (21 cm) emission

line is 1.6×10

^{20}W.

(c). Assume the cloud lies at a distance of 4 kpc in a direction l = 0

^{o}and is

observed with a radio telescope of field of view (beam-size) 20 arcmin.

What flux would you measure from the cloud in its 1.42 GHz (21 cm)

emission line?

(d). Random bulk motions in the cloud of ±10 km/s along the line of

sight Doppler-broaden the observed line. What is the full width in

frequency of the broadened line? From this and your answer in part

(c) write down the average flux per unit frequency, and express your

answer in units of Janskys (Jy), where 1 Jy = 10

^{−26}W/m

^{2}/Hz.

**2. Homework Equations**

Question 1 -

I'm not sure how to get V

_{t}

**3. The Attempt at a Solution**

1.

*Galaxy rotation speed at the solar circle is Vo = 220 km/s*

I'm confused at what this speed actually represents. For the equation of proper motion, I need the transverse velocity, V

_{t}. Which means I might have to decompose V

_{o}into components V

_{t}and V

_{r}using an angle... which I don't know

2. c)

*and is observed with a radio telescope of field of view (beam-size) 20 arcmin.*

I'm not sure how to relate the beam-size into measuring the flux, other than I assume it will be related to the proportion of the flux it can measure compared to amount received at Earth (Which I've found to be 8.3x10

^{-22}W/m

^{2}).

Any help is greatly appreciated.