When Hubble first looked at redshifts of light from distant galaxies, and calculated the speed at which they were 'retreating from us' (or, the speed at which the space between them and us is increasing), did he consider gravitational redshift of light escaping from the gravity well of stars?
If not did that throw his calculations out, and by how much?
How much is light from a Sun-sized star redshifted as it escapes the Sun's gravity well? For example, from 589nm** to ... what, exactly? (I think very small for our Sun?)
How much is light from a galaxy in the middle of Hubble's data* redshifted? (*say, one of the 46 galaxies approx $10^6$ parsecs away, so, moving at 500 km/sec?). Again, from 589nm to what, exactly?
I'd love to know the two (sets of) equations to use here, or a link to them.
Apologies if this is answered elsewhere. I couldn't find one that compared the two effects quantitatively.
I'm also interested in this from a historical point of view - ie, whether this is something Hubble factored in. I know General Relativity was published more than a decade before Hubble's redshift-expansion work, but was gravitational redshift published/known/accepted by 1927?
Is it an effect that's now taken into account? Can we measure it in light from objects distant enough to be subject to cosmological redshift? Eg, if there are lots of white dwarfs in a galaxy, would we have to tweak estimate of distance to that galaxy?)
** I chose 589nm as one of the Na lines. I think that Hubble used these to quantify redshift.