Although I do have a degree in chemical engineering, I am studying relativity/cosmology on a beginning level just as a hobby. I'm currently attempting to wade through Einstein's relativity equations. However I remain troubled by the underpinning of the whole thing - the constancy of the speed of light. It is easy to accept that light always propagates from its source with a constant velocity similarly to how sound propagates from its source with the same velocity given the same atmospheric conditions. My question is this: Is light emitted by a source in motion relative to an observer moving at the same velocity relative to the observer as light emitted by a source that is stationary relative to the observer? For the moment, pretend that Einstein was never born and his theory of relativity does not exist. How do we know that light received from celestial objects is moving at a constant velocity relative to us on earth? How do we know that the observed redshift and blueshift of light received from distant galaxies is not due to varying speeds of light received from galaxies in in rapid motion toward or away from us? What is the experimental evidence? I'm sure it's a dumb question but maybe some patient person would be willing to contribute to my enlightenment.