Thommo wrote:

zaybu wrote:

Greyman wrote:You obtain equation (6) by approximating under the assumption: d_1 << R_{source}

That is, you assert that the distance from earth's surface to the emitter galaxy is much less than the radius of the earth.

Assume the universe is infinite, Rsource → ∞.

Then for any galaxy at a distance d1,

d1 << Rsource

This is always true.

eh? Rsource is described as the radius of the Earth in the text, isn't it?

Indeed the first case, we have emiters above the earth, the R is the earth's radius. When the calculation is generalized, R is the radius of the source of gravity. So when we apply this to a galaxy a certain distance d, R is now the radius of the universe. Just take fig 1, replace a single emitter with a single galaxy and the earth with the rest of the universe.

campermon wrote:

Thommo wrote:

campermon wrote:This bit has confused me too.

I'm also not following whether g1 is the acceleration due to gravity or the gravitational potential, are you?

hmmm..has to be acceleration to be dimensionally correct.

It is the gravitational potential at d1, as defined in equation 2.

zaybu wrote:

Thommo wrote:

zaybu wrote:

Greyman wrote:You obtain equation (6) by approximating under the assumption: d_1 << R_{source}

That is, you assert that the distance from earth's surface to the emitter galaxy is much less than the radius of the earth.

Assume the universe is infinite, Rsource → ∞.

Then for any galaxy at a distance d1,

d1 << Rsource

This is always true.

eh? Rsource is described as the radius of the Earth in the text, isn't it?

Indeed the first case, we have emiters above the earth, the R is the earth's radius. When the calculation is generalized, R is the radius of the source of gravity. So when we apply this to a galaxy a certain distance d, R is now the radius of the universe. Just take fig 1, replace a single emitter with a single galaxy and the earth with the rest of the universe.

As far as I can tell that makes no sense. If R is the radius of the source of gravity and that source is the universe then the blueshift occurs in an undefined radial direction, unless you additionally assume that the Earth is the centre of a spherical universe, which isn't right, in particular the gravitational acceleration inside that sphere isn't given by the same equation as it is outside . Further if Rsource is now infinite (justifying d1 <<< Rsource) then your division by Rsource in (6) is a nonsense.

Thommo wrote:
If R is the radius of the source of gravity and that source is the universe then the blueshift occurs in an undefined radial direction,

You have to look from the POV of an observer. Light coming from a far distance is emitted in all direction, but we only observe that portion that comes our way. It's that light that we see redshifted.

unless you additionally assume that the Earth is the centre of a spherical universe, which isn't right, in particular the gravitational acceleration inside that sphere isn't given by the same equation as it is outside .

We're not looking inside the earth. In fig 1, the emitter is outside the earth. Now replace the emitter with a galaxy, and the earth represents the source which comprises a gazillion number of galaxies.