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marcus
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Since we get this kind of discussion fairly often as newcomers join the forum maybe I'll try to boil it down to something easier to remember. As a rough rule of thumb to get the recession rate (in units of c) from redshifts like z = 3 and 4, divide by 2. Or if you like decimal numbers multiply z by 0.5.
This gives the approximate recession rate when light was emitted. For instance for z = 3 the recession was a bit over 1.5 c, so that's right.
For z = 4 the recession rate was a bit over 2.0 c, so right again.
For z =5 this rule gives 2.5c and the right answer is 2.4 c, so still close.
As a crude approx therefore, you get the recession (when light was emitted) by multiplying redshift by a factor of 0.5. This works roughly in the range z = 3 to 5.
For larger redshifts up to z = 10 the factor to use is more like 0.4, which is usually a bit on the conservative side.
For z = 6 this gives 2.4c (the right answer is 2.75)
For z = 7 this gives 2.8c (the right answer is 3.0)
For z = 8 it gives 3.2c (the right answer is 3.4)
For z = 9 it gives 3.6c (the right answer is 3.7)
For z = 10 it gives 4.0c (the right answer!)
And the earliest protogalaxies are around z = 10. In a sense we don't have to go any farther with our approximation. At z=10 they were just beginning to form. Beyond that we can SEE stuff (e.g. CMB at z = 1100) but we don't normally see galaxies because they mostly haven't formed yet. So that factor of 0.4 works over a useful range.
check this by googling "cosmocalc 2010"
This gives the approximate recession rate when light was emitted. For instance for z = 3 the recession was a bit over 1.5 c, so that's right.
For z = 4 the recession rate was a bit over 2.0 c, so right again.
For z =5 this rule gives 2.5c and the right answer is 2.4 c, so still close.
As a crude approx therefore, you get the recession (when light was emitted) by multiplying redshift by a factor of 0.5. This works roughly in the range z = 3 to 5.
For larger redshifts up to z = 10 the factor to use is more like 0.4, which is usually a bit on the conservative side.
For z = 6 this gives 2.4c (the right answer is 2.75)
For z = 7 this gives 2.8c (the right answer is 3.0)
For z = 8 it gives 3.2c (the right answer is 3.4)
For z = 9 it gives 3.6c (the right answer is 3.7)
For z = 10 it gives 4.0c (the right answer!)
And the earliest protogalaxies are around z = 10. In a sense we don't have to go any farther with our approximation. At z=10 they were just beginning to form. Beyond that we can SEE stuff (e.g. CMB at z = 1100) but we don't normally see galaxies because they mostly haven't formed yet. So that factor of 0.4 works over a useful range.
check this by googling "cosmocalc 2010"
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