# Factor of how much linear size scale has changed

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Question: By what factor has the linear size-scale of the Universe changed between when the light was emitted from the galaxy and now?

The question gives the red shift z and I have the equation linear size scale = 1 / 1 + z and I know how to calculate the linear size scale. But I'm a little confused as to what the question is saying. It is asking about the factor of how much the linear size scale has changed right? So if I just give the linear size scale, the answer won't be fully correct. So I'm assuming to calculate the factor, I would need to find the initial red shift z and calculate the exponent which will give me the new linear size scale that I calculated previously? Thanks for your help.

## Answers and Replies

phyzguy
Science Advisor
I don't quite understand what you are asking. By definition, 'now' means z=0 and the scale factor a = 1. So when you calculate the size scale a = 1/(1+z) at the time of emission that tells you the factor by which the size scale has changed from then to now. If you are 6 feet tall today and were 3 feet tall when you were 8 years old, you were 0.5X as tall then as you are now.

Ok I understand. The linear size scale itself is the factor by which the size of the universe changed. I thought the question is more complex than what it really is asking. Thanks.