## The Doppler effect

The Doppler effect is used to interpret the frequency axis of the measured spectrum. Using the radio convention, the non-relativistic Doppler effect in the observatory frame can be written as

(2)
where is the velocity of the source in the observatory frame, and are the frequency of the measured photon in the observatory and rest frame respectively. is positive if the source recesses and the rest frame is defined as the frame where the velocity of the emitting gas cell is zero. Introducing the doppler parameter , we obtain
(3)