How can I calculate red shift for intragalactic bodies

[Frank Einstein]

Hello everyone. I am doing an studi on Be stars, all of which are inside the Milky Way, I want to show that the red shift won't be a big deal here, but I am confused about how to prove it; what I have done is combining the equations
λr=λe(1+z) and cz=Hd to get λr=λe(1+Hd/c) where z=v/c.

I get extremely minor changes in my red shift if I introduce the Galaxy's diametre in d, but I am not sure that aplying the equation cz=Hd is legitimate here or if it can only be used to measure distances between galaxies.

Can someone please tell me if I am using a good methode to calculate the red shift?

Thanks for reading.

 

[mfb]

The milky way doesn't follow the Hubble flow, you cannot use the overall expansion of the universe here. You might have to consider the local motion, however, which is of the order of 20-200 km/s (depending on where the stars are in the galactic disk), with some stars moving at up to 1000 km/s.

 

[Frank Einstein]

I was afraid that would be the anwser. Thank you very much for telling me.