# How do you calculate the recession velocity?

\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?

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• $\Delta \lambda$ will not be the same for all changes. – jim May 26 '18 at 20:04

## 1 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 $v$.