# Aberration of starlight

Aberration of starlight is the difference between the observed position of a star and its true direction; this is a combined result of the observer’s motion across the path of the incoming starlight and the finite speed of light. In other words, the aberration of starlight is an apparent shift of the position of a celestial object during the year because at the speed of light with which the photons travel we have to sum the speed of the Earth along its orbit.

$\vec{v}_{LE}=\vec{v}_{LS}+\vec{v}_{SE}$

We have: $$\sin\theta =\dfrac{v}{c}$$, where $$c$$ is the speed of light and $$v=3\times 10^4$$ m/s is the speed of Earth. $$\vec{v}_{LE}$$ is the velocity of light with respect to the Earth. $$\vec{v}_{SE}$$ is the velocity of the star with respect to the Earth. $$\vec{v}_{LS}$$ is the velocity of light with respect to the star.

The typical example is that of a man running in the rain, and he must point the umbrella forward to avoid getting wet. Replacing the umbrella with a telescope and photons to the raindrops, and we will have an almost perfect analogy: but there is a difference, and it is not trivial. Photons travel at the speed of light in any frame of reference, but this does not apply to raindrops!

There are three components of the aberration of starlight: annual aberration (up to 20.47″) caused by the Earth’s revolution around the Sun, diurnal aberration (up to 0.3″) caused by the Earth’s axial rotation, and the very small secular aberration caused by the motion of the solar system through space. Stars on the ecliptic appear to move and fro along a line of 41″; stars 90° from the ecliptic appear to trace out a circle of radius 20.5″; and stars in intermediate positions ellipses of major axis 41″.