The Doppler effect expresses that a source emitting in its rest frame at a
frequency
will appear to emit at a frequency
in the
observation frame, which depends on the velocity of the source in the
observation frame,
. The relation between
and
is
given by
For objects far from the observer,
because of the
universe expansion. For close-by objects, Eq.
shows that
the dependency on
is of second order in
, while the
dependency on
is only of first order in
. Hence, for
all cases, the Doppler equation is simplified to