The speed of light is constant in a vacuum. It was assumed that this speed was the fastest that a photon could travel and was used as a standard against photon propagation occurring in other environments.
If our solar system is being drawn toward a black hole in the middle of our galaxy and far away other solar systems are collapsing toward the center of their galaxies, then indeed there would be a red shift even if there is no relative movements between the center of the galaxies.
Our planet is moving through space around 67,000 mph but nowhere near the speed of other objects as they travel in ellipical orbits around the sun. Imagine the speeds that might be obtained around larger stars. Imagine the speed that particles could obtain falling toward a black holes.
Your question is very valid. I await a measuring device other than the Dopler effect.
The Doppler Effect is usually thought of as a source moving and its effect on the wavelength received at a frame of reference that is stationary. The same happens when the reference is moving and the source is stationary. The apparent wavelength elongates under both scenarios.
Assuming that the galaxies are stationary, the stars in a distant galaxy revolving toward us would have their light shifted with shorter wavelengths. But any radial velocity of the stars caused by attraction toward the center of their galaxy (black hole or not) would diminish the effect. On the other hand, stars moving away from us would have the wavelength elongated further by the same radial velocity.
When we measure the wavelength of light from a galaxy, you measure the summation of all the light we are receiving from the galaxy and we are not stationary. You receive more light from the near side of the galaxy than you do from the far side since the density of photons is decreasing the further they travel from a point source and the sources on the near side are closer. The further we are from a galaxy the more pronounced this effect would be. Thus the light from the near side would produce more waves and a more apparent elongated state at our stationary receiver. If the receiver is our planet and is moving toward the center of our galaxy, the effect would be intensified even if the galaxies were stationary.
To answer your last question, I donâ€™t have a reference to cite since Iâ€™ve been unable to find any reference that discusses the situation. So I simply question the use of Doppler and put forth a hypothesis that the results may be biased. Iâ€™d enjoy reading any reference that you know which discusses the situation as I described.
Gravity causes all revolving bodies to experience radial acceleration. Without it an object would simply fly off into space instead of orbiting. Orbiting requires maintaining enough tangential speed that a vertical component continuously offsets the gravitational attraction. If adequate tangential velocity is not obtained, the object falls back to earth.
For galaxies its more complicated than orbiting earth since each object in the galaxy generates its own gravitational field. If a galaxy is collapsing, hypotheically from any point outside a galaxy that has a uniform distribution of luminous objects (except from above its axis), the objects nearest the observer will be traveling in an inward spiral - away from the observer.
If galaxies are shrinking then the space between them would be expanding.
We can't see the center of our galaxy which would imply that we most probably can't see the far side of another galaxy. This would prevent us from seeing if the far side is moving away or toward the observer. It would seem that this is the real test of whether the universe is expanding and its rate of expansion.
I've researched this matter but can't find a reference where this situation has been explored.