Let's assume that the measured spectrum is made of a line centered around
in the observatory frame. The associated rest frame frequency,
i.e., the frequency of the line at rest, will be
. The
observation is naturally set up so that the source frame is also the rest
frame. This implies that
,
and
are linked through
The modeller will use the Doppler effect to interpret the observed
frequency difference
as a local velocity
difference (projected along the line of sight direction) around the
systemic velocity of the source. Let's write
(
) the velocity
associated to
(
). The velocity difference will be noted