[fitswcs] Re: Relativistic transverse Doppler effect

[Mark Calabretta]

On Mon 2004/04/19 10:34:05 +1000, Mark Calabretta wrote
in a message to: fitswcs at nrao.edu

>There are instances where the orientation angle may be inferred by
>geometry (e.g. by the observed tilt of an accretion disk) or by
>modelling.  I therefore propose that the paper be augmented
>
>   1) by the introduction of a new keyword to record the orientation
>      angle, and
>
>   2) by modifying the eight equations involving velocity in Table 3
>      to take account of this orientation angle.

In response to a question I have been asked about this, it should be
stated that Paper III would not consider how theta should be
determined, or what exactly it means for particular relativistic
observers, other than that it resolves the kinematic velocity into
radial and tangential components.  In other words

    v_r = v sin(theta)          ...radial velocity component
    v_t = v cos(theta)          ...transverse velocity component
    v   = sqrt(v_r^2 + v_t^2)

so that Eq. (2) may be written as

                     1 + v sin(theta)/c
    lambda = lambda0 ------------------
                     sqrt(1 - v^2/c^2)

Therefore there would not be a need for additional references to
relativistic physics beyond that already given for Eq. (2).

When theta is unknown, as will most often be the case, it will be
omitted from the header.  This will mean two things:

   a) theta is unknown,

   b) use the default value of +90 deg to compute what the paper
      currently refers to as the "apparent" velocity.

Mark Calabretta
ATNF