# Aberration of light

aberrationstellar aberrationconstant of aberrationaberration of starlightastronomical aberrationaberratedaberration effectaberration of star lightannual aberrationannual solar aberration
The aberration of light (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of the observer.wikipedia
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In 1727, James Bradley provided a classical explanation for it in terms of the finite speed of light relative to the motion of the Earth in its orbit around the Sun,
He is best known for two fundamental discoveries in astronomy, the aberration of light (1725–1728), and the nutation of the Earth's axis (1728–1748).

### Light-time correction

light time correctionlight time delaylight-time effect
Aberration is also related to light-time correction and relativistic beaming, although it is often considered separately from these effects.
It should be contrasted with the aberration of light, which depends upon the instantaneous velocity of the observer at the time of observation, and is independent of the motion or distance of the object.

### Apparent place

apparent positionsapparent motionapparent places
The aberration of light (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of the observer.
Annual aberration — a deflection caused by the velocity of the Earth's motion around the Sun, relative to an inertial frame. This is independent of the distance of the star from the Earth.

The reasoning in the relativistic case is the same except that the relativistic velocity addition formulas must be used, which can be derived from Lorentz transformations between different frames of reference.
Standard applications of velocity-addition formulas include the Doppler shift, Doppler navigation, the aberration of light, and the dragging of light in moving water observed in the 1851 Fizeau experiment.

### Moving magnet and conductor problem

conductor moving in the field of a magnetelectric conductor moving with respect to a magnet
The aberration of light, together with Lorentz's elaboration of Maxwell's electrodynamics, the moving magnet and conductor problem, the negative aether drift experiments, as well as the Fizeau experiment, led Albert Einstein to develop the theory of special relativity in 1905, which presents a general form of the equation for aberration in terms of such theory.
This problem, along with the Fizeau experiment, the aberration of light, and more indirectly the negative aether drift tests such as the Michelson–Morley experiment, formed the basis of Einstein's development of the theory of relativity.

### Aether drag hypothesis

aether-draggingaether-dragging theoriesFresnel drag coefficient
However, Bradley's theory was incompatible with 19th century theories of light, and aberration became a major motivation for the aether drag theories of Augustin Fresnel (in 1818) and G. G. Stokes (in 1845), and for Hendrik Lorentz's aether theory of electromagnetism in 1892.
All Arago observed was ordinary stellar aberration.

### Michelson–Morley experiment

Michelson and MorleyMichelson–MorleyMichelson–Morley interferometer experiment
The aberration of light, together with Lorentz's elaboration of Maxwell's electrodynamics, the moving magnet and conductor problem, the negative aether drift experiments, as well as the Fizeau experiment, led Albert Einstein to develop the theory of special relativity in 1905, which presents a general form of the equation for aberration in terms of such theory.
Eventually, Fresnel's idea of an (almost) stationary aether was preferred because it appeared to be confirmed by the Fizeau experiment (1851) and the aberration of star light.

### Special relativity

special theory of relativityrelativisticspecial
Aberration is historically significant because of its role in the development of the theories of light, electromagnetism and, ultimately, the theory of special relativity.
(1) If the receiver is in motion, the displacement would be the consequence of the aberration of light.

### Hendrik Lorentz

LorentzH. A. LorentzH.A. Lorentz
However, Bradley's theory was incompatible with 19th century theories of light, and aberration became a major motivation for the aether drag theories of Augustin Fresnel (in 1818) and G. G. Stokes (in 1845), and for Hendrik Lorentz's aether theory of electromagnetism in 1892.
Although Lorentz did not give a detailed interpretation of the physical significance of local time, with it, he could explain the aberration of light and the result of the Fizeau experiment.

### Stellar parallax

parallax shiftparallaxparallax method
Aberration should not be confused with parallax.
The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of Earth's axis, and catalogued 3222 stars.

### Lorentz ether theory

aether theoryether theorya theory of electrodynamics
However, Bradley's theory was incompatible with 19th century theories of light, and aberration became a major motivation for the aether drag theories of Augustin Fresnel (in 1818) and G. G. Stokes (in 1845), and for Hendrik Lorentz's aether theory of electromagnetism in 1892.
(Woldemar Voigt had previously used the same expression for local time in 1887 in connection with the Doppler effect and an incompressible medium.) With the help of this concept Lorentz could explain the aberration of light, the Doppler effect and the Fizeau experiment (i.e. measurements of the Fresnel drag coefficient) by Hippolyte Fizeau in moving and also resting liquids.

### Speed of light

clight speedvelocity of light
The change in angle is typically very small — of the order of v/c where c is the speed of light and v the velocity of the observer. It may be calculated using the relation substituting the Earth's average speed in the Sun's frame for v and the speed of light c. Its accepted value is 20.49552 arcseconds (at J2000).
Another method is to use the aberration of light, discovered and explained by James Bradley in the 18th century.

### Relativistic beaming

beambeamingbeaming effect
Aberration is also related to light-time correction and relativistic beaming, although it is often considered separately from these effects.
Aberration is the change in an object's apparent direction caused by the relative transverse motion of the observer.

### Lorentz transformation

boostboostsLorentz boosts
The reasoning in the relativistic case is the same except that the relativistic velocity addition formulas must be used, which can be derived from Lorentz transformations between different frames of reference.
The transformation of velocity is useful in stellar aberration, the Fizeau experiment, and the relativistic Doppler effect.

### Fizeau experiment

dragging of lightexperiment in 1851Fizeau experiment (1851)
The aberration of light, together with Lorentz's elaboration of Maxwell's electrodynamics, the moving magnet and conductor problem, the negative aether drift experiments, as well as the Fizeau experiment, led Albert Einstein to develop the theory of special relativity in 1905, which presents a general form of the equation for aberration in terms of such theory.
Thus from the viewpoint of the aether models at that time, the experimental situation was contradictory: On one hand, the aberration of light, the Fizeau experiment and the repetition by Michelson and Morley in 1886 appeared to support partial aether-dragging.

### Epoch (astronomy)

J2000epoch2000.0
It may be calculated using the relation substituting the Earth's average speed in the Sun's frame for v and the speed of light c. Its accepted value is 20.49552 arcseconds (at J2000).
Meeus defines the beginning of a Besselian year to be the moment at which the mean longitude of the Sun, including the effect of aberration and measured from the mean equinox of the date, is exactly 280 degrees.

### Samuel Molyneux

Consequently, when Bradley and Samuel Molyneux entered this sphere of research in 1725, there was still considerable uncertainty as to whether stellar parallaxes had been observed or not, and it was with the intention of definitely answering this question that they erected a large telescope at Molyneux's house at Kew.
His work with James Bradley attempting to measure stellar parallax led to the discovery of the aberration of light.

### Ecliptic

ecliptical orbitsecliptic planeplane of the ecliptic
Assuming a circular orbit, annual aberration causes stars exactly on the ecliptic (the plane of Earth's orbit) to appear to move back and forth along a straight line, varying by \kappa on either side of their position in the Sun's frame.
The exact instants of equinoxes and solstices are the times when the apparent ecliptic longitude (including the effects of aberration and nutation) of the Sun is 0°, 90°, 180°, and 270°.

### Luminiferous aether

aetherluminiferous etherether
However, this explanation proved inaccurate once the wave nature of light was better understood, and correcting it became a major goal of the 19th century theories of luminiferous aether.
This effect is now known as stellar aberration.

### Gamma Draconis

γ DraEltaninγ Draconis
Robert Hooke, in 1674, published his observations of γ Draconis, a star of magnitude 2 m which passes practically overhead at the latitude of London (hence its observations are largely free from the complex corrections due to atmospheric refraction), and concluded that this star was 23″ more northerly in July than in October.
In 1728, while unsuccessfully attempting to measure the parallax of this star, James Bradley discovered the aberration of light resulting from the movement of the Earth.

On August 19, 1727, Bradley embarked upon a further series of observations using a telescope of his own erected at the Rectory, Wanstead.
Combined with observations from his friend Samuel Molyneux's house at Kew in Surrey, this established the existence of the phenomenon of aberration of light, and also allowed Bradley to formulate a set of rules that would allow the calculation of the effect on any given star at a specified date.

### Stellar aberration (derivation from Lorentz transformation)

Stellar aberration (derivation from Lorentz transformation)
Stellar aberration is an astronomical phenomenon "which produces an apparent motion of celestial objects".

### Jean Picard

PicardJean-Felix PicardPicard, Jean
However, in 1680 Jean Picard, in his Voyage d’Uranibourg, stated, as a result of ten years' observations, that Polaris, the Pole Star, exhibited variations in its position amounting to 40″ annually.
These correspondences led to Picard's contributions to areas of science outside the field of geodesy, such as the aberration of light he observed while in Uraniborg, or his discovery of mercurial phosphorescence upon his observance of the faint glowing of a barometer.

### Augustin-Jean Fresnel

FresnelAugustin FresnelA Fresnel
However, Bradley's theory was incompatible with 19th century theories of light, and aberration became a major motivation for the aether drag theories of Augustin Fresnel (in 1818) and G. G. Stokes (in 1845), and for Hendrik Lorentz's aether theory of electromagnetism in 1892.
Similarly inconclusive was stellar aberration — that is, the apparent change in the position of a star due to the velocity of the earth across the line of sight (not to be confused with stellar parallax, which is due to the displacement of the earth across the line of sight).

### Robert Hooke

HookeDr Robert HookeHooke, Robert
Robert Hooke, in 1674, published his observations of γ Draconis, a star of magnitude 2 m which passes practically overhead at the latitude of London (hence its observations are largely free from the complex corrections due to atmospheric refraction), and concluded that this star was 23″ more northerly in July than in October.
Gamma Draconis was the same star James Bradley used in 1725 in discovering the aberration of light.