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Document Preview: 1.To what redshift/blueshift could we observe HI if our spectrometer covered a 64.00 MHz band centred on 1.410 GHz. [What velocities do these correspond to? [Would this be a sensible place to place the centre frequency of your receiver?2. You have detected HI (21cm) emission from a nearby galaxy at three locations: -at the galaxy center (C), -10 arcmin to the east of the galaxy center along the galaxy's major axis (E), and -10 arcmin to the west of the galaxy center (W). The HI emission peaks at XXXXXXXXXXcm at (C), XXXXXXXXXXcm at (W), and XXXXXXXXXXcm at (E).(a) For a Hubble constant of 70 km/sec/Mpc, how far away is this galaxy (in Mpc)? (b) How fast is the galaxy rotating? Assume that the galaxy is seen edge-on. (c) Assuming the gas is on circular orbits, use Newton's law of gravity to determine the amount of mass in the galaxy interior to 10 arcmin radius. (d) The peak brightness temperature at location (C) is 12K - what is the peak column density of this galaxy at this location?

Robert · Accepted Answer

Problem 1 
It’s given that spectrometer covers a band of 64MHz and is entered it 1.410 GHz . To the maximum Shift in the 
frequency that we can predict with the spectrometer is 64MHz . 
We have the frequency band from 
64 64
1.41GHz MHz 1.442GHz to 1.41GHz MHz 1.378GHz
2 2
     
So,  so if we treat that the emitted frequency  is 1.378 GHz  then the observed  frequency should be less than 
1.442 GHz  in order to predict by our spectroscope. This corresponds to the maximum red shift  “z” . 
which is given by  o
e
1.442
z 1 1 0.0464 (redshift)
1.378

    

 
and the maximum blue shift is given by  o
e
1.378
z 1 1 0.0443 (blueshift)
1.442

     

 
What velocities do these correspond to? 
This maximum red shift corresponds to a velocity “v” given by 
8 1 1
v z x c where cisspeed of light
0.0464x3x10 13920000ms 13920kms 

  
 
and  the maximum  blue shift corresponds to a velocity “v” given by 
8 1 1
v z x c where cisspeed of light
0.0443x3x10 13290000ms 13290kms 

  
 
Problem 2
Doppler Shift 
When a source of light is moving toward or away from an observer, the measured wavelength of the received 
light (λobserved) will be different than the wavelength of the light if the source were at rest (λrest). The measured 
wavelength of the observed light and the line-of-sight velocity (VLOS) of the source are related through the 
Doppler equation: 
los observed rest
rest
v
where cis speedof light
c
 



Rotation Velocity 
The line-of-sight velocity  (ie the point O, E,

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I will submit questions as an attachment Document Preview: 1.To what redshift/blueshift could we observe HI if our spectrometer covered a 64.00 MHz band centred on 1.410 GHz. [What velocities do...