Editing Hubble's law (section)

==== Redshift velocity ====
The redshift {{mvar|z}} is often described as a ''redshift velocity'', which is the recessional velocity that would produce the same redshift {{em|if}} it were caused by a linear [[Doppler effect]] (which, however, is not the case, as the velocities involved are too large to use a non-relativistic formula for Doppler shift). This redshift velocity can easily exceed the speed of light.<ref name="Madsen">{{cite book |last=Madsen |first=M. S. |date=1995 |title=The Dynamic Cosmos |url=https://books.google.com/books?id=_2GeJxVvyFMC&pg=PA35 |page=35 |publisher=[[CRC Press]] |isbn=978-0-412-62300-4 }}</ref> In other words, to determine the redshift velocity {{math|''v''<sub>rs</sub>}}, the relation:

<math display="block"> v_\text{rs} \equiv cz,</math>

is used.<ref name="Dekel">{{cite book |last1=Dekel |first1=A. |last2=Ostriker |first2=J. P. |date=1999 |title=Formation of Structure in the Universe |url=https://books.google.com/books?id=yAroX6tx-l0C&pg=PA164 |page=164 |publisher=[[Cambridge University Press]] |isbn=978-0-521-58632-0 }}</ref><ref name="Padmanabhan">{{cite book |last=Padmanabhan |first=T. |date=1993 |title=Structure formation in the universe | url=https://books.google.com/books?id=AJlOVBRZJtIC&pg=PA58 |page=58 |publisher=[[Cambridge University Press]] |isbn=978-0-521-42486-8 }}</ref> That is, there is {{em|no fundamental difference}} between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called [[Relativistic Doppler effect|Fizeau–Doppler formula]]<ref name="Sartori">{{cite book |last=Sartori |first=L. |date=1996 |title=Understanding Relativity |page=163, Appendix 5B |publisher=[[University of California Press]] |isbn=978-0-520-20029-6 }}</ref>

<math display="block">z = \frac{\lambda_\text{o}}{\lambda_\text{e}}-1 = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}-1 \approx \frac{v}{c}.</math>

Here, {{math|''λ''<sub>o</sub>}}, {{math|''λ''<sub>e</sub>}} are the observed and emitted wavelengths respectively. The "redshift velocity" {{math|''v''<sub>rs</sub>}} is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity. Next, the connection between redshift or redshift velocity and recessional velocity is discussed.<ref name="L_Sartori">{{cite book|last=Sartori |first=L. |date=1996 |title=Understanding Relativity |pages=304–305 |publisher=[[University of California Press]] |isbn=978-0-520-20029-6 }}</ref>