What distance is used in Hubble's Law.

[Javier Chornet]

Hello,

I was thinking about the Hubble's law and I know that it's determined as $$H(t)=\frac{1}{a(t)}\frac{da(t)}{dt}$$ and then, thinking in the derivate of the scale factor as the speed, we've de usual formula $$v(t)=H(t)D$$
But my question is: the distance is the distance we observe the object (so now it's in farther because of the time that takes the light to go across these distance) or the real distance of the object?
In other worlds: is the distance of the galaxy when the light was emmited or the real distance at the moment of observation (despite we observe it nearest)?

I was thinking on it and trying to solve it using the derivation of the formula but I'm not convinced on any option.

Thanks,
Javier Chornet.

 

[Chalnoth]

The distance that's used for this purpose is known as the "proper distance". This is the distance that would be measured by a ruler at the time of observation.

If you want an in-depth view of distance measures in cosmology, see here:
http://arxiv.org/abs/astro-ph/9905116

 

[Javier Chornet]

The distance that's used for this purpose is known as the "proper distance". This is the distance that would be measured by a ruler at the time of observation.

If you want an in-depth view of distance measures in cosmology, see here:
http://arxiv.org/abs/astro-ph/9905116

So the used disance is the real distance of the galaxy at the moment of the observation (further than the distance we observe because the finite spee light).
Thank you! Your answer was so iluminating, and the paper you've referred is great!
Thanks again!

 

[Javier Chornet]

The distance that's used for this purpose is known as the "proper distance". This is the distance that would be measured by a ruler at the time of observation.

If you want an in-depth view of distance measures in cosmology, see here:
http://arxiv.org/abs/astro-ph/9905116

Sorry again,
But then, if I measure the redshift, I'm measuring the speed that the galaxy had when she emmited the light. So for knowing the speed at the proper distance for know the value of Hubble's constant, you must calculate it theoretically based on the data collected from when the ligth was emmited, musn't you?

 

[Chalnoth]

Sorry again,
But then, if I measure the redshift, I'm measuring the speed that the galaxy had when she emmited the light. So for knowing the speed at the proper distance for know the value of Hubble's constant, you must calculate it theoretically based on the data collected from when the ligth was emmited, musn't you?

Actually, the redshift measures the amount of expansion between the time the light was emitted and the current time.

There is some change in the redshift due to the movement of us and the far-away galaxy relative to the background expansion. But for the most part the redshift can't really be understood as a doppler shift at all. Rather, as the universe expands, the wavelength of the photon also increases along with the expansion.