Question

Another known cause of red shift in light is the source being in a high gravitational field. Discuss how this can be eliminated as the source of galactic red shifts, given that the shifts are proportional to distance and not to the size of the galaxy.

Short answer

The observed galaxy's gravitational redshift cancels out most of the Milky Way's blue shift. Because travelling through empty space does not cause a gravitational redshift/blueshift, any residual shift would not be proportional to distance.

Step-by-step solution

 Definition of red shifts.

The Red shift occurs due to the difference effect of gravitational field acting on the observer and source. The gravitational red shift is observed when the source is in high gravitational field.

How the gravitational field can be eliminated as the source of galactic red shifts?

Gravitational redshift occurs when light is emitted from a higher gravitational potential and travels towards a lower gravitational potential. When we observe light from a distance, it first escapes from the gravitational field of the star and then enters the gravitational field of the Earth. During its escape, redshift occurs (because it is travelling from a higher gravitational potential, closer to the star, to a lower gravitational potential, further from the star), and during observation, blue shift occurs (lower potential further from the Earth, higher closer to the Earth). Because the mass-to-radius ratio of galaxies is nearly the same, gravitational red shift is almost eliminated.

Furthermore, any residual shift would not be proportional to distance because gravitational redshift occurs when travelling through gravitational fields, so travelling through empty space (with negligible gravity) should have no effect on the shift.