# Hubble's law and redshift

1. Nov 13, 2005

### SN1987a

How would one use hubble's law to find the redshift of a galaxy$10^10$ light years away? (in other words $3*10^9 pc$)

All I know however is the version of hubble's where $v=H_o d$, with $H_o=71 \frac{m}{s*pc}$, which tells me that $v= 2.2*10^11 m/s$. But this violates the second principle of special relativity!!!!:surprised

How do I get around this problem?

Last edited: Nov 13, 2005
2. Nov 13, 2005

### big man

3. Nov 13, 2005

### SN1987a

Yeah, but km/sMpc is the same as m/spc, is it not? So that doesn't change my problem a whole lot.

4. Nov 13, 2005

### big man

well if you plug in the numbers you will find that you should get a reasonable answer. And no they aren't the same. m/skpc would be the same as km/sMpc.

5. Nov 14, 2005

### SpaceTiger

Staff Emeritus
Well, big man is right about your value of Hubble's constant, but one really shouldn't use Hubble's law to find the distance or speed of an object at 3 Gpc. Hubble's Law is just a first order approximation approximation to whatever cosmological model describes the universe that we live in. This approximation is only valid if the object's recession speed is much less than the speed of light (for your purposes, this corresponds to redshifts <~ 0.1).

Even when you put in the correct value of Hubble's constant, you'll get v ~ 0.7c, so Hubble's Law will give a pretty inaccurate result. However, if this is a homework assignment and you've just learned basic cosmology, I suspect that your teacher wants you to use Hubble's Law anyway.

By the way, objects can recede from us at rates greater than the speed of light. This is because the object isn't moving through space, the space itself is expanding. The expansion of space is not restricted by the speed of light.