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

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Hubble's Law, expressed as v = H₀d, can be used to estimate the redshift of distant galaxies, but its accuracy diminishes at large distances, such as 10^10 light years or 3 Gpc. The law is a first-order approximation that is only valid for recession speeds much less than the speed of light, typically corresponding to redshifts less than approximately 0.1. Using the Hubble constant correctly is crucial, as a misinterpretation of units can lead to erroneous results. Even with the correct constant, calculations for such distant objects can yield speeds approaching 0.7c, indicating significant inaccuracies. It's important to note that galaxies can recede faster than light due to the expansion of space, which is not limited by relativistic constraints.
SN1987a
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How would one use hubble's law to find the redshift of a galaxy10^10 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?
 
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Yeah, but km/sMpc is the same as m/spc, is it not? So that doesn't change my problem a whole lot.
 
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.
 
SN1987a said:
How would one use hubble's law to find the redshift of a galaxy10^10 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.
 
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