# What Is the Aberration of Light?

Phil Riddel

In astronomy, the aberration of light is a shift in the apparent position of an object caused by the relative motion of the object and the observer. Aberration of light is only significant at very large scales and affects the perceived positions of stars and planets for observers on the Earth. The apparent displacement of stars results from the Earth’s motion around the Sun, and from its rotation.

Aberration of light was discovered in the 17th century, when attempts were made to measure the distances from the Earth to various stars using parallax — a concept that describes how an object's position appears to shift when observed from different locations. The idea was that the apparent position of a star should change throughout the year as the Earth orbits the Sun. If the star’s exact position in the sky was checked on a given date, then checked again six months later, when the Earth was opposite its position from when the first measurement was taken, this gave two measurements separated by the diameter of the Earth’s orbit — a distance of approximately 186,000,000 miles (300,000,000 km). This was thought sufficient to obtain a parallax value and thus calculate the star’s distance using trigonometry.

A number of measurements were made, but the results were puzzling. The greatest apparent displacement of the star being observed should have been found between observations six months apart, when the locations of the observations were furthest apart. The actual displacements, however, followed a completely different pattern and were clearly not due to parallax. The Pole Star, Polaris, for example, was found to follow a roughly circular path, with a diameter of about 40 arc seconds (40”), an arc second being 1/3,600 of a degree. Parallax displacement does occur, but it is very small, even for the nearest stars, and would not have been measureable using the instruments available at that time.

The mystery was solved by James Bradley, the British Astronomer Royal, in 1729. He discovered that the observed shifts in the position of a star were due to the Earth’s velocity, and not to its position, relative to the star. The light from the star takes time to reach the Earth and because the Earth is moving, the starlight appears to come from a point that is displaced slightly from the star’s true position, in the direction of motion. The biggest displacements are observed when the Earth’s motion is perpendicular to the direction of the starlight. The same phenomenon can be seen with rain falling vertically; to a moving observer — for example, in a train or bus — the rain seems to fall diagonally from a point of origin ahead of the observer in the direction of motion.

Bradley’s calculation, using the speed of light and the speed of the Earth’s motion around the Sun, indicated a maximum displacement of about 20” to either side of the true position for Polaris. This gave an overall variation of about 40” over the year, in agreement with observations. In calculating the aberration of light, modern astronomers need to take into account the effects of relativity, but in most cases, the classical calculation is adequate.

The seasonal shifts in star positions are known as annual aberration or stellar aberration, and the star’s true position is called its geometric position. Smaller displacements result from the Earth’s rotation; this is known as diurnal aberration. Secular aberration is the term used to describe the astronomical aberration caused by the solar system’s motion within the galaxy; although it has an effect on the apparent positions of very distant stars and other galaxies, it is very small and is not usually taken into account. In calculating stellar aberration, only the Earth’s motion need be considered; however, planetary aberration — which affects the apparent positions of the planets — results from the motion of both the Earth and the planets, so both need to be included to calculate the correct value.