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How is the age of a light wave coming from a distant object determined?

• When light coming from a distant object in the universe is received, how is the time when it left that object determined? In other words, how is the distance of a spatial object determined just by looking at the light received from it?

• Answer:

  For stars... You have to find the red shifts of the corresponding absorption lines. Most stars have fairly similar absorption lines - so some practice should identify which lines are shifted the most (and by which wavelengths). We know the wavelengths of most of these absorption lines through theory and our laboratories. We can pretty much choose any absorption line we want - all of them will produce the same value of z. So for our equation below, plug our known value of the absorption line into [math]\lambda_{obsv}[/math] and the measured value of the absorption line into [math]\lambda_{emit}[/math]. (see http://en.wikipedia.org/wiki/Redshift#Redshift_formulae) Then we get a value of z, or the value of the redshift. Now, the next step is slightly tricky. Anyways, see http://en.wikipedia.org/wiki/Hubble_constant#Recessional_velocity. You get the equation here: The age of the light should be roughly equal to [math]t_0-t_e[/math], after substitution for z and our Hubble Constant of 71.0 ± 2.5 (km/s)/Mpc. Note that the Hubble Constant is not necessarily a constant, but has varied over time. In any case, though, it's often used. As an additional exercise, we can also plug this value of z into the below equation to get a scale factor of a (or how large the universe was at the time the object emitted light, with our current universe having a scale factor of 1) (http://en.wikipedia.org/wiki/Scale_factor_(Universe)) Then plug this value of a(t) into the below equation And from that, we get the proper distance of our object at epoch t.