A distant galaxy is at a distance D D\,D from Earth. A spectral line of electromagnetic radiation has a rest frequency f0 f_0\,f0 when measured in a laboratory on Earth. Under non-relativistic assumptions, with a Hubble constant H0 H_0\,H0 and the speed of light in a vacuum ccc, which of the following is the correct expression for the observed frequency f f\,f of this spectral line in the light received from the galaxy?
f=cf0c+H0Df = \frac{c f_0}{c + H_0 D}f=c+H0Dcf0
f=f0(1−H0Dc)f = f_0 \left(1 - \frac{H_0 D}{c}\right)f=f0(1−cH0D)
f=cf0c−H0Df = \frac{c f_0}{c - H_0 D}f=c−H0Dcf0
f=f0(1+H0Dc)f = f_0 \left(1 + \frac{H_0 D}{c}\right)f=f0(1+cH0D)