Editing Aberration (astronomy) (section)

====Solar annual aberration====
A special case of annual aberration is the nearly constant deflection of the Sun from its position in the Sun's rest frame by <math>\kappa</math> towards the ''west'' (as viewed from Earth), opposite to the apparent motion of the Sun along the ecliptic (which is from west to east, as seen from Earth). The deflection thus makes the Sun appear to be behind (or retarded) from its rest-frame position on the ecliptic by a position or angle <math>\kappa</math>.

This deflection may equivalently be described as a light-time effect due to motion of the Earth during the 8.3&nbsp;minutes that it takes light to travel from the Sun to Earth. The relation with <math>\kappa</math> is : [0.000099365&nbsp;rad / 2&nbsp;π&nbsp;rad] x [365.25&nbsp;d x 24&nbsp;h/d x 60&nbsp;min/h] = 8.3167&nbsp;min ≈ 8&nbsp;min&nbsp;19&nbsp;sec = 499&nbsp;sec. This is possible since the transit time of sunlight is short relative to the orbital period of the Earth, so the Earth's frame may be approximated as inertial. In the Earth's frame, the Sun moves, at a mean velocity v = 29.789&nbsp;km/s, by a distance <math>\Delta x = vt</math> ≈ 14,864.7&nbsp;km in the time it takes light to reach Earth, <math>t=R/c</math> ≈ 499&nbsp;sec for the orbit of mean radius <math>R</math> = 1&nbsp;AU = 149,597,870.7&nbsp;km. This gives an angular correction <math>\tan(\theta) \approx \theta = \Delta x/R</math> ≈ 0.000099364&nbsp;rad = 20.49539&nbsp;sec, which can be solved to give <math>\theta = v/c = \kappa</math> ≈ 0.000099365&nbsp;rad = 20.49559&nbsp;sec, very nearly the same as the aberrational correction (here <math>\kappa</math> is in radian and not in arcsecond).