How Does Hubble's Law Calculate Redshift for Distant Galaxies?

[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!

How do I get around this problem?

 

[big man]

hey man

http://scienceworld.wolfram.com/physics/HubbleConstant.html

Here's a link to a website that gives the Hubble constant as 83/81 km/sMpc

So maybe that value you had was in Mpc and not just pc.
It comes out will a reasonable value in the end so it should work.

 

[SN1987a]

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

 

[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.

 

[SpaceTiger]

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

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.