- #1

ChrisVer

Gold Member

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## Main Question or Discussion Point

It is known that the dipole anisotropies of the CMB radiation, can give the relative velocity of the Earth with respect to the CMB "rest" frame...

In first order, this is given by [itex] \beta \approx 1.2 \times 10^{-3}[/itex] or [itex]u_{CMB} \approx 360 km/s [/itex].

I have one question here:

Why is the velocity given as such?

In first approximation we have [itex]T' (\theta)_{observed} \approx T_{cmb} (1 + \beta \cos \theta)[/itex]

and this depends on [itex]\theta[/itex], the direction in which we are looking at CMB. So I'd say that the velocity of the earth wrt to the CMB rest frame, should also depend on [itex]\theta[/itex]:

[itex]1.2 \times 10^{-3} = |\frac{\Delta T}{T}| = |\frac{T - T'}{T}| = |1- T'/T| = |\beta \cos \theta|[/itex]

Also, I'm not sure how can this affect the measurements of distances with the Hubble's law:

[itex] u = H_0 D[/itex]

Is it because the [itex]u[/itex] will have to get the contribution from [itex]u_{CMB}[/itex]? but this is crazy, because the far-away galaxy we are observing, will also have to move with some velocity wrt CMB... How is Hubble's law then affected?

In first order, this is given by [itex] \beta \approx 1.2 \times 10^{-3}[/itex] or [itex]u_{CMB} \approx 360 km/s [/itex].

I have one question here:

Why is the velocity given as such?

In first approximation we have [itex]T' (\theta)_{observed} \approx T_{cmb} (1 + \beta \cos \theta)[/itex]

and this depends on [itex]\theta[/itex], the direction in which we are looking at CMB. So I'd say that the velocity of the earth wrt to the CMB rest frame, should also depend on [itex]\theta[/itex]:

[itex]1.2 \times 10^{-3} = |\frac{\Delta T}{T}| = |\frac{T - T'}{T}| = |1- T'/T| = |\beta \cos \theta|[/itex]

Also, I'm not sure how can this affect the measurements of distances with the Hubble's law:

[itex] u = H_0 D[/itex]

Is it because the [itex]u[/itex] will have to get the contribution from [itex]u_{CMB}[/itex]? but this is crazy, because the far-away galaxy we are observing, will also have to move with some velocity wrt CMB... How is Hubble's law then affected?