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Astronomers have very little access to the velocity component perpendicular
to the line of sight. They will thus assign the observed Doppler shift to
the line-of-sight motion, i.e., they will neglect the transverse Doppler
effect.
The formula 2 indicates that the dependency on
is
of second order in
, while the dependency on
is only of
first order in
. Hence, neglecting the transverse Doppler effect
is correct as long as
 |
(3) |
In this case, the Doppler equation can be approximated to first order to
 |
(4) |
In other words, the frequency change under a change of frame is attributed
only to the radial velocity between the rest and observation frame. We note
that condition 3 is enforced if the velocities are
non-relativistic, i.e.
 |
(5) |
Next: Approximation 2: First order
Up: Various approximations of the
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2015-03-19