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<H2><A NAME="SECTION00059000000000000000">
Aberration</A>
</H2>
The finite speed of light combined with the motion of the observer
around the Sun during the year causes apparent displacements of
the positions of the stars. The effect is called
the <I>annual aberration</I> (or ``stellar''
aberration). Its maximum size, about
<IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img265.gif"
ALT="$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$"> ,
occurs for stars <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img22.gif"
ALT="$90^{\circ}$"> from the point towards which
the Earth is headed as it orbits the Sun; a star exactly in line with
the Earth's motion is not displaced. To receive the light of
a star, the telescope has to be offset slightly in the direction of
the Earth's motion. A familiar analogy is the need to tilt your
umbrella forward when on the move, to avoid getting wet. This
Newtonian model is,
in fact, highly misleading in the context of light as opposed
to rain, but happens to give the same answer as a relativistic
treatment to first order (better than 1 milliarcsecond).
<P>
Before the IAU 1976 resolutions, different
values for the approximately
<P> <IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img265.gif"
ALT="$20\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$"> <I>aberration constant</I> were employed
at different times, and this can complicate comparisons
between different catalogues. Another complication comes from
the so-called <I>E-terms of aberration</I>,
that small part of the annual aberration correction that is a
function of the eccentricity of the Earth's orbit. The E-terms,
maximum amplitude about
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img32.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$"> ,
happen to be approximately constant for a given star, and so they
used to be incorporated in the catalogue <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$">to reduce the labour of converting to and from apparent place.
The E-terms can be removed from a catalogue <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> by
calling
sla_SUBET
or applied (for example to allow a pulsar
timing-position to be plotted on a B1950 finding chart)
by calling
sla_ADDET;
the E-terms vector itself can be obtained by calling
sla_ETRMS.
Star positions post IAU 1976 are free of these distortions, and to
apply corrections for annual aberration involves the actual
barycentric velocity of the Earth rather than the use of
canonical circular-orbit models.
<P>
The annual aberration is the aberration correction for
an imaginary observer at the Earth's centre.
The motion of a real observer around the Earth's rotation axis in
the course of the day makes a small extra contribution to the total
aberration effect called the <I>diurnal aberration</I>. Its
maximum amplitude is about
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img76.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$"> .
<P>
No SLALIB routine is provided for calculating the aberration on
its own, though the required velocity vectors can be
generated using
sla_EVP
and
sla_GEOC.
Annual and diurnal aberration are allowed for where required, for example in
sla_MAP
<I>etc</I>. and
sla_AOP
<I>etc</I>. Note that this sort
of aberration is different from the <I>planetary
aberration</I>, which is the apparent displacement of a solar-system
body, with respect to the ephemeris position, as a consequence
of the motion of <I>both</I> the Earth and the source. The
planetary aberration can be computed either by correcting the
position of the solar-system body for light-time, followed by
the ordinary stellar aberration correction, or more
directly by expressing the position and velocity of the source
in the observer's frame and correcting for light-time alone.
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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