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This question already has an answer here:

How do scientists know the age of the CMB? And how does it correlate to the age of universe?

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marked as duplicate by AccidentalFourierTransform, user191954, stafusa, Qmechanic Sep 8 '18 at 5:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ I'm voting to close this question as off-topic because it shows insufficient prior research. $\endgroup$ – AccidentalFourierTransform Sep 8 '18 at 1:53
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    $\begingroup$ Why? Isn't this place meant to ask questions? $\endgroup$ – ObsessionWithElectricity Sep 8 '18 at 2:08
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    $\begingroup$ My comment above contains a link (apologies if it wasn't clear enough: the link is admittedly not as emphasised as I would like). Please read it to familiarise yourself with what we expect about questions here. Thank you for your collaboration. $\endgroup$ – AccidentalFourierTransform Sep 8 '18 at 2:37
  • $\begingroup$ Possible duplicate of Age of the CMB: How do we know? $\endgroup$ – stafusa Sep 8 '18 at 5:01
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By combining what is presently well-understood about the interaction between particles and radiation at extremely high temperatures with what is also known about the thermal history of the universe, mathematical analysis of the characteristics of the CMB allows astrophysicists to accurately estimate both the age of the universe and the age of the CMB itself.

In this sense, the characteristics of the CMB tell us the age of the universe.

An excellent exposition of this topic is contained in Stephen Weinberg's book, The First Three Minutes, and in a variety of more current papers in the literature specifically about the CMB.

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The wiki article here describes the discovery of the cmb. To get at the age of the universe one needs a particular model, as the big bang model.

The motion of stars galaxies and clusters of galaxies is measured by observing changes in the spectrum of light arriving on earth of specific atoms existing on the celestial bodies which emit light.

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    $\begingroup$ to the down voter, I observe that the policy is that we should be nice to new users . just pointing out rules is not "nice" $\endgroup$ – anna v Sep 8 '18 at 3:43

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