1. The problem statement, all variables and given/known data 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 106 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 1.6×1020 W. (c). Assume the cloud lies at a distance of 4 kpc in a direction l = 0o 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 = 10−26W/m2/Hz. 2. Relevant equations Question 1 - I'm not sure how to get Vt 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, Vt. Which means I might have to decompose Vo into components Vt and Vr 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 8.3x10-22W/m2). Any help is greatly appreciated.