Imagine we have two space ships moving each with a speed of $\frac{3}{4}c$ as shown below. What is the speed that either the red or yellow space ships sees for the other space ship speed?
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Due to the very long life time, the emission line is very sharp, i.e. it has a small natural spectral broadening. This can be seen from <a href="https://en.wikipedia.org/wiki/Uncertainty_principle">Heisenberg's uncertainty principle</a> $\Delta E \Delta t \sim \hbar$. If $\Delta t$ is very large, then $\Delta E$ is small and the spectral line is very sharp. Therefore shifts to this line must come from Doppler shifts which can be used to measure speeds accurately.
