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How do you calculate the recession velocity?

Physics Asked by Umber on August 3, 2020

$$
begin{alignat}{7}
&& frac{Delta lambda}{lambda} & = frac{v}{c} \[2.5px]
&therefore & v & approx frac{Delta lambda}{lambda}c
end{alignat}
$$
If you want to find the recession velocity of a galaxy which has an absorption spectrum shown below, the $Delta lambda$ is the same for all the changes (approx from 400 to 430, 410 to 440, 590 to 620, etc.), so when using the equation how do you know which $lambda$ to use as the rest wavelength because they all give different results?

$hspace{150px}$

One Answer

To find the recessional velocity of a galaxy using the formula you referring to, we need to know $lambda$ and $Delta lambda$. What we can actually measure is a red shifted wavelength $lambda_r=lambda+Delta lambda$.

Since the absorption spectrum of elements making up stars and interstellar medium is well known, we can figure out which spectrum lines belong to which elements and, for each $lambda_r$, figure out a corresponding $lambda$ and, from there, $Delta lambda$ and $v$.

Answered by V.F. on August 3, 2020

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