1. The problem statement, all variables and given/known data Light from distant stars is Compton scattered many times by free electronsin the outer space before reaching us.This shifts the light toward the red.How can this shift be distinguished from the Doppler red shift due to the motion of receding stars??? 2. Relevant equations 3. The attempt at a solution When visible light [of colour other than red---like blue/yellow/green etc] is scattered off free electrons,the Compton shift is negligible...and what we observe is very nearly the original wavelength, somewhat reduced in intensity... But when the Doppler Effect is the concern,the colour (wavelength) is increased with respect to us due to relative motion.If we were flying at the same rate with the star, there would be no red-shift...In this case,light that reaches us, has long wavelength (red). Compton scattering does nothing but to change red to red itslef...So, from colour observation, we get the idea... Please let me know if you support this idea.