Aberration of light
Encyclopedia
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations. It was discovered in 1725 and later explained by the third Astronomer Royal
Astronomer Royal
Astronomer Royal is a senior post in the Royal Household of the Sovereign of the United Kingdom. There are two officers, the senior being the Astronomer Royal dating from 22 June 1675; the second is the Astronomer Royal for Scotland dating from 1834....

James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...

, who attributed it to the finite speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

and the motion of Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

in its orbit around the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

.

At the instant of any observation of an object, the apparent position of the object is displaced from its true position by an amount which depends solely upon the transverse component of the velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

of the observer, with respect to the vector of the incoming beam of light (i.e., the line actually taken by the light on its path to the observer). The result is a tilting of the direction of the incoming light which is independent of the distance between object and observer.

In the case of an observer on Earth, the direction of a star's velocity varies during the year as Earth revolves around the Sun (or strictly speaking, the barycenter of the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

), and this in turn causes the apparent position of the star to vary. This particular effect is known as annual aberration or stellar aberration, because it causes the apparent position of a star to vary periodically over the course of a year. The maximum amount of the aberrational displacement of a star is approximately 20 arcseconds in right ascension
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...

or declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...

. Although this is a relatively small value, it was well within the observational capability of the instruments available in the early eighteenth century.

Aberration should not be confused with stellar parallax, although it was an initially fruitless search for parallax that first led to its discovery. Parallax is caused by a change in the position of the observer looking at a relatively nearby object, as measured against more distant objects, and is therefore dependent upon the distance between the observer and the object.

In contrast, stellar aberration is independent of the distance of a celestial object from the observer, and depends only on the observer's instantaneous transverse velocity with respect to the incoming light beam, at the moment of observation. The light beam from a distant object cannot itself have any transverse velocity component, or it could not (by definition) be seen by the observer, since it would miss the observer. Thus, any transverse velocity of the emitting source plays no part in aberration. Another way to state this is that the emitting object may have a transverse velocity with respect to the observer, but any light beam emitted from it which reaches the observer, cannot, for it must have been previously emitted in such a direction that its transverse component has been "corrected" for. Such a beam must come "straight" to the observer along a line which connects the observer with the position of the object when it emitted the light.

Aberration should also be distinguished from light-time correction
Light-time correction
Light-time correction is a displacement in the apparent position of a celestial object from its true position caused by the object's motion during the time it takes its light to reach an observer....

, which is due to the motion of the observed object, like a planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

, through space during the time taken by its light to reach an observer on Earth. Light-time correction depends upon the velocity and distance of the emitting object during the time it takes for its light to travel to Earth. Light-time correction does not depend on the motion of the Earth—it only depends on Earth's position at the instant when the light is observed. Aberration is usually larger than a planet's light-time correction except when the planet is near quadrature
In astronomy, quadrature is that aspect of a heavenly body in which it makes a right angle with the direction of the Sun. It is applied especially to the apparent position of a superior planet, or of the Moon at first and last quarters....

(90° from the Sun), where aberration drops to zero because then the Earth is directly approaching or receding from the planet. At opposition
Opposition (astronomy)
In positional astronomy, two celestial bodies are said to be in opposition when they are on opposite sides of the sky, viewed from a given place . In particular, two planets are in opposition to each other when their ecliptic longitudes differ by 180°.The astronomical symbol for opposition is ☍...

to or conjunction with the Sun, aberration is 20.5" while light-time correction varies from 4" for Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

to 0.37" for Neptune
Neptune
Neptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times...

(the Sun's light-time correction is less than 0.03").

## Explanation

It has been stated above that aberration causes a displacement of the apparent position of an object from its true position. However, it is important to understand the precise technical definition of these terms.

### Apparent and true positions

The apparent position of a star or other very distant object is the direction in which it is seen by an observer on the moving Earth. The true position (or geometric position) is the direction of the straight line between the observer and star at the instant of observation. The difference between these two positions is caused by parallax
Parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...

and by aberration. When the star is a distant object, parallax is negligible and the difference is due mostly to aberration.

Aberration occurs when the observer's velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

has a component that is perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

to the line traveled by the light incoming from the star. Let us suppose (as is the practical case) that the star is sufficiently distant that all light from the star travels in parallel paths to the Earth observer, regardless of where the Earth is in its orbit. That is, there is zero parallax. On the left side of Figure 1, the case of infinite light speed is shown. S represents the spot where the star light enters the telescope, and E the position of the eye piece. If light moves instantaneously, the telescope does not move, and the true direction of the star relative to the observer can be found by following the line ES. However, if light travels at finite speed, the Earth, and therefore the eye piece of the telescope, moves from E to E’ during the time it takes light to travel from S to E. Consequently, the star will no longer appear in the center of the eye piece. The telescope must therefore be adjusted. When the telescope is at position E it must be oriented toward spot S’ so that the star light enters the telescope at spot S’. Now the star light will travel along the line S’E’ (parallel to SE) and reach E’ exactly when the moving eye piece also reaches E’. Since the telescope has been adjusted by the angle SES’, the star's apparent position is hence displaced by the same angle.

For the simple case where the direction of the light beam along the line SE is perpendicular to the motion of the observer then only light emitted at an angle equal to the arc cosine of the ratio of the observer's speed to the speed of light will reach the telescope. Consequently, the telescope too must be oriented at this same angle away from the light beam's trajectoery in the direction of the motion to capture this emitted light.

### Moving in the rain

Many find aberration to be counter-intuitive, and a simple thought experiment based on everyday experience can help in its understanding. Imagine you are standing in the rain. There is no wind, so the rain is falling vertically. To protect yourself from the rain you hold an umbrella directly above you.

Now imagine that you start to walk. Although the rain is still falling vertically (relative to a stationary observer), you find that you have to hold the umbrella slightly in front of you to keep off the rain. Because of your forward motion relative to the falling rain, the rain now appears to be falling not from directly above you, but from a point in the sky somewhat in front of you.

The deflection of the falling rain is greatly increased at higher speeds. When you drive a car
Čar
Čar is a village in the municipality of Bujanovac, Serbia. According to the 2002 census, the town has a population of 296 people.-References:...

at night through falling rain, the rain drops illuminated by your car's headlights appear to (and actually do) fall from a position in the sky well in front of your car.

### Relative frame of reference

According to the special theory of relativity, the aberration only depends on the relative velocity v between the observer and the light from the star. The formula from relativistic aberration
Relativistic aberration
Relativistic aberration is described by Einstein's special theory of relativity, and in other relativistic models such as Newtonian emission theory. It results in aberration of light when the relative motion of observer and light source changes the position of the light source in the field of view...

can be simplified to

where θ is the true angle SEE’, θ’ is the apparent angle S’EE’, and v is the relative speed between the starlight and the observer. Thus, the aberration of light does not imply an absolute frame of reference, as when one moves in the rain. The speed of the rain perceived in a running car is increased as it hits the windscreen more heavily. Instead, according to the special theory of relativity, the speed of light is constant and only its direction changes. The above formula accounts for that while the simpler tan(θ-θ’)=v/c does not.

In most cases the transverse velocity of the star is unknown. However, for some binary systems where a high rotating speed can be inferred, it doesn't cause an aberration as apparently implied by the relativity principle. As discussed above, aberration occurs because the observer moves relative to parallel beams of light coming from the star. In contrast to the case of the observer, the star moves with the divergent beams of light that it emits in all directions, and its motion just selects which one is destined to hit the observer. Indeed, dependency on the source is paradoxical: Consider a second source of light that on a given instant coincides with the star, but is not at rest with it. Suppose that two rays of light reach the observer, one emitted by the star and the other by the second source in the instant when they coincide. If rays are straight, since they share two points (the coinciding sources and the observer) then they must coincide. However, since the velocities of the sources differ, the observer would see those rays coming from different directions, if aberration depended on the source's motion.

Although the velocity of the star may be unknown, from the above formula one can derive the relation between the angles θ1 and θ2 seen by two arbitrary observers moving with velocities v1 and v2, and then use the velocity addition theorem to subtract the unknown velocity w of the star in order to express v1 and v2 relative to an arbitrary frame:

Provided that the observers were actually looking at the same star and its velocity didn't change between their observations, the formula shows how w cancels out. Then, using again the velocity addition theorem to express the relative velocity of the two observers as one finds the relative aberration. It only uses the latter relative velocity and c to equate the angles observed in different frames of reference.

## Types of aberration

There are a number of types of aberration, caused by the differing components of the Earth's motion:
• Annual aberration is due to the revolution of the Earth around the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

.
• Planetary aberration is the combination of aberration and light-time correction.
• Diurnal aberration is due to the rotation
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

of the Earth about its own axis.
• Secular aberration is due to the motion of the Sun and solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

relative to other stars in the galaxy
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

.

### Annual aberration

Suppose a star is observed with a telescope idealized as a narrow tube. The light enters the tube from a star at angle θ and travels at speed c taking a time h/c to reach the bottom of the tube, where our eye detects the light. Suppose observations are made from Earth, which is moving with a speed v. During the transit of the light, the tube moves a distance vh/c. Consequently, for the photon to reach the bottom of the tube, the tube must be inclined at an angle φ different from θ, resulting in an apparent position of the star at angle φ. As the Earth proceeds in its orbit, the velocity changes direction, so φ changes with the time of year the observation is made, allowing the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

to be determined. The two angles are related by the speed of light and the speed of the tube, but actually do not depend upon the length of the tube, as explained next. The apparent angle and true angle are related using trigonometry as:

independent of the path length h traversed by the light.
It may be more useful to express the correction (θ−φ) to the observed angle φ in terms of the observed angle itself:

which, because small v/c leads to small corrections, becomes:

where use is made of the small-angle approximation to the sine function sin x ≈ x.

As an example, if v is the component of the Earth's velocity along the direction of the light rays, this velocity changes month-to-month as the Earth traverses its orbit, making v a periodic function of the time of year, and consequently the aberration also varies periodically. This effect was used in 1727 by J Bradley
James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...

to determine the speed of light as approximately 183,000 miles/s. A facsimile of his observations on the star γ-Draconis is shown in Figure 3. More detail is provided below.

As the Earth revolves around the Sun, it is moving at a velocity of approximately 30 km/s. The speed of light is approximately 300,000 km/s. In the special case where the Earth is moving perpendicularly to the direction of the star (that is, if angle θ in Figure 2 is 90 degrees), the angle of displacement, θ − φ, would therefore be (in radian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

s) the ratio of the two velocities, or 1/10000, or about 20.5 arcseconds.

This quantity is known as the constant of aberration, and is conventionally represented by κ. Its precise accepted value is 20".49552 (at J2000).

The plane of the Earth's orbit is known as the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...

. Annual aberration causes stars exactly on the ecliptic to appear to move back and forth along a straight line, varying by κ on either side of their true position. A star that is precisely at one of the ecliptic's poles will appear to move in a circle of radius κ about its true position, and stars at intermediate ecliptic latitudes will appear to move along a small ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

(see Figure 4).

Aberration can be resolved into east-west and north-south components on the celestial sphere
Celestial sphere
In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...

, which therefore produce an apparent displacement of a star's right ascension
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...

and declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...

, respectively. The former is larger (except at the ecliptic poles), but the latter was the first to be detected. This is because very accurate clocks are needed to measure such a small variation in right ascension, but a transit telescope calibrated with a plumb line
Plumb-bob
A plumb-bob or a plummet is a weight, usually with a pointed tip on the bottom, that is suspended from a string and used as a vertical reference line, or plumb-line....

can detect very small changes in declination.

Figure 5 shows how aberration affects the apparent declination of a star at the north ecliptic pole, as seen by an imaginary observer who sees the star transit at the zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

(this observer would have to be positioned at latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

66.6 degrees north – i.e. on the arctic circle
Arctic Circle
The Arctic Circle is one of the five major circles of latitude that mark maps of the Earth. For Epoch 2011, it is the parallel of latitude that runs north of the Equator....

). At the time of the March equinox
Equinox
An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...

, the Earth's orbital velocity is carrying the observer directly south as he or she observes the star at the zenith. The star's apparent declination is therefore displaced to the south by a value equal to κ. Conversely, at the September equinox, the Earth's orbital velocity is carrying the observer northwards, and the star's position is displaced to the north by an equal and opposite amount. At the June and December solstice
Solstice
A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes...

s, the displacement in declination is zero. Likewise, the amount of displacement in right ascension
Right ascension
Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:...

is zero at either equinox
Equinox
An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...

and maximum at the solstice
Solstice
A solstice is an astronomical event that happens twice each year when the Sun's apparent position in the sky, as viewed from Earth, reaches its northernmost or southernmost extremes...

s.

Note that the effect of aberration is out of phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

with any displacement due to parallax. If the latter effect were present, the maximum displacement to the south would occur in December, and the maximum displacement to the north in June. It is this apparently anomalous motion that so mystified Bradley and his contemporaries.

#### Solar annual aberration

A special case of annual aberration is the nearly constant deflection of the Sun from its true position by κ 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 actual position on the ecliptic by a position or angle κ. This constant deflection is often explained as due to the motion of the Earth during the 8.3 minutes that it takes light to travel from the Sun to Earth. This is a valid explanation provided it is given in the Earth's reference frame (where it becomes purely a light-time correction
Light-time correction
Light-time correction is a displacement in the apparent position of a celestial object from its true position caused by the object's motion during the time it takes its light to reach an observer....

for the position of the eastward-moving Sun as seen from a stationary Earth), whereas in the Sun's reference frame the same phenomenon must be described as aberration of light when seen by the westward-moving Earth, which involves having Earth's telescopes pointed "forward" (westward, in a direction toward the Earth's motion relative to the Sun) by a slight amount.

Since this is the same physical phenomenon, simply described from two different reference frames, it is not a coincidence that the angle of annual aberration of the Sun is equal to the path swept by the Sun along the ecliptic, in the time it takes for light to travel from it to the Earth (8.316746 minutes divided by one sidereal year (365.25636 days) is 20.49265", very nearly κ). Similarly, one could explain the Sun's apparent motion over the background of fixed stars as a (very large) parallax effect.

### Planetary aberration

Planetary aberration is the combination of the aberration of light (due to Earth's velocity) and light-time correction
Light-time correction
Light-time correction is a displacement in the apparent position of a celestial object from its true position caused by the object's motion during the time it takes its light to reach an observer....

(due to the object's motion and distance). Both are determined at the instant when the moving object's light reaches the moving observer on Earth. It is so called because it is usually applied to planets and other objects in the solar system whose motion and distance are accurately known.

### Diurnal aberration

Diurnal aberration is caused by the velocity of the observer on the surface of the rotating Earth. It is therefore dependent not only on the time of the observation, but also the latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

of the observer. Its effect is much smaller than that of annual aberration, and is only 0".32 in the case of an observer at the equator, where the rotational velocity is greatest.

### Secular aberration

The Sun and solar system are revolving around the center of the Galaxy, as are other nearby stars. Therefore the aberrational effect affects the apparent positions of other stars and on extragalactic
Extragalactic astronomy
Extragalactic astronomy is the branch of astronomy concerned with objects outside our own Milky Way Galaxy. In other words, it is the study of all astronomical objects which are not covered by galactic astronomy, the next level of galactic astronomy....

objects: if a star is two thousand light years from Earth, we don't see it where it is now, but where it was two thousand years ago (in a reference frame moving with the solar system).

However, the change in the solar system's velocity relative to the center of the Galaxy varies over a very long timescale, and the consequent change in aberration would be extremely difficult to observe. Therefore, this so-called secular aberration is usually ignored when considering the positions of stars. In other words, star maps show the observed apparent positions of the stars, not their calculated true positions.

To estimate the true position of a star whose distance and proper motion are known, just multiply the proper motion (in arcseconds per year) by the distance (in light years). The apparent position lags behind the true position by that many arcseconds. Newcomb gives the example of Groombridge 1830
Groombridge 1830
Groombridge 1830 is a star in the constellation Ursa Major.-Description:It is a yellowish class G8 subdwarf catalogued by Stephen Groombridge with the Groombridge Transit Circle between 1806 and the 1830s and published posthumously in his star catalog, Catalogue of Circumpolar Stars...

, where he estimates that the true position is displaced by approximately 3 arcminutes from the direction in which we observe it. Modern figures give a proper motion of 7 arcseconds/year, distance 30 light years, so the displacement is 3 arcminutes and a half. This calculation also includes an allowance for light-time correction, and is therefore analogous to the concept of planetary aberration.

## Historical background

The discovery of the aberration of light in 1725 by James Bradley
James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...

was one of the most important in astronomy. It was totally unexpected, and it was only by extraordinary perseverance and perspicacity that Bradley was able to explain it in 1727. Its origin is based on attempts made to discover whether the stars possessed appreciable parallax
Parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...

es. The Copernican
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....

theory of the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

– that the Earth revolved annually about the Sun – had received confirmation by the observations of Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

and Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

(who, however, never accepted heliocentrism
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...

), and the mathematical investigations of Kepler
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...

and Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

.

### Search for stellar parallax

As early as 1573, Thomas Digges
Thomas Digges
Sir Thomas Digges was an English mathematician and astronomer. He was the first to expound the Copernican system in English but discarded the notion of a fixed shell of immoveable stars to postulate infinitely many stars at varying distances; he was also first to postulate the "dark night sky...

had suggested that this theory should necessitate a parallactic shifting of the stars, and, consequently, if such stellar parallaxes existed, then the Copernican theory would receive additional confirmation. Many observers claimed to have determined such parallaxes, but Tycho Brahe and Giovanni Battista Riccioli
Giovanni Battista Riccioli
Giovanni Battista Riccioli was an Italian astronomer and a Catholic priest in the Jesuit order...

concluded that they existed only in the minds of the observers, and were due to instrumental and personal errors. In 1680 Jean Picard
Jean Picard
Jean-Felix Picard was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He was the first person to measure the size of the Earth to a reasonable degree of accuracy in a survey conducted in 1669–70, for which he is honored with a...

, in his Voyage d’Uranibourg
Uraniborg
Uranienborg was a Danish astronomical observatory operated by Tycho Brahe; built circa 1576-1580 on Hven, an island in the Øresund between Zealand and Scania, which at that time was part of Denmark. The observatory was shortly after its construction expanded with an underground facility,...

,
stated, as a result of ten year
Year
A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic....

s' observations, that Polaris
Polaris
Polaris |Alpha]] Ursae Minoris, commonly North Star or Pole Star, also Lodestar) is the brightest star in the constellation Ursa Minor. It is very close to the north celestial pole, making it the current northern pole star....

, or the Pole Star
Pole star
The term "Pole Star" usually refers to Polaris, which is the current northern pole star, also known as the North Star.In general, however, a pole star is a visible star, especially a prominent one, that is approximately aligned with the Earth's axis of rotation; that is, a star whose apparent...

, exhibited variations in its position amounting to 40" annually. Some astronomers endeavoured to explain this by parallax, but these attempts were futile, for the motion was at variance with that which parallax would produce.

John Flamsteed
John Flamsteed
Sir John Flamsteed FRS was an English astronomer and the first Astronomer Royal. He catalogued over 3000 stars.- Life :Flamsteed was born in Denby, Derbyshire, England, the only son of Stephen Flamsteed...

, from measurements made in 1689 and succeeding years with his mural quadrant, similarly concluded that the declination of the Pole Star was 40" less in July than in September. Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...

, in 1674, published his observations of γ Draconis, a star of magnitude
Apparent magnitude
The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...

2m which passes practically overhead at the latitude of London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...

, and whose observations are therefore free from the complex corrections due to astronomical refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

, and concluded that this star was 23" more northerly in July than in October.

When James Bradley and Samuel Molyneux
Samuel Molyneux
Samuel Molyneux FRS , son of William Molyneux, was an 18th-century member of the British parliament from Kew and an amateur astronomer whose work with James Bradley attempting to measure stellar parallax led to the discovery of the aberration of light...

entered this sphere of astronomical research in 1725, there consequently prevailed much uncertainty whether stellar parallaxes had been observed or not; and it was with the intention of definitely answering this question that these astronomers erected a large telescope at the house of the latter at Kew
Kew
Kew is a place in the London Borough of Richmond upon Thames in South West London. Kew is best known for being the location of the Royal Botanic Gardens, now a World Heritage Site, which includes Kew Palace...

. They determined to reinvestigate the motion of γ Draconis; the telescope, constructed by George Graham
George Graham (clockmaker)
George Graham was an English clockmaker, inventor, and geophysicist, and a Fellow of the Royal Society.He was born to George Graham in Kirklinton, Cumberland. A Friend like his mentor Thomas Tompion, Graham left Cumberland in 1688 for London to work with Tompion...

(1675–1751), a celebrated instrument-maker, was affixed to a vertical chimney stack, in such manner as to permit a small oscillation of the eyepiece, the amount of which (i.e. the deviation from the vertical) was regulated and measured by the introduction of a screw and a plumb line.

The instrument was set up in November 1725, and observations on γ Draconis were made on the 3rd, 5th, 11th, and 12 December. There was apparently no shifting of the star, which was therefore thought to be at its most southerly point. On December 17, however, Bradley observed that the star was moving southwards, a motion further shown by observations on the 20th. These results were unexpected and inexplicable by existing theories. However, an examination of the telescope showed that the observed anomalies were not due to instrumental errors.

The observations were continued, and the star was seen to continue its southerly course until March, when it took up a position some 20" more southerly than its December position. After March it began to pass northwards, a motion quite apparent by the middle of April; in June it passed at the same distance from the zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

as it did in December; and in September it passed through its most northerly position, the extreme range from north to south, i.e. the angle between the March and September positions, being 40".

### Aberration vs nutation

This motion was evidently not due to parallax, for the reasons given in the discussion of Figure 2, and neither was it due to observational errors. Bradley and Molyneux discussed several hypotheses in the hope of finding the solution. The idea that immediately suggested itself was that the star's declination varied because of short-term changes in the orientation of the Earth's axis relative to the celestial sphere – a phenomenon known as nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

. Because this is a change to the observer's frame of reference (i.e. the Earth itself), it would therefore affect all stars equally. For instance, a change in the declination of γ Draconis would be mirrored by an equal and opposite change to the declination of a star 180 degrees opposite in right ascension.

Observations of such a star were made difficult by the limited field of view of Bradley and Molyneux's telescope, and the lack of suitable stars of sufficient brightness. One such star, however, with a right ascension nearly equal to that of γ Draconis, but in the opposite sense, was selected and kept under observation. This star was seen to possess an apparent motion similar to that which would be a consequence of the nutation of the Earth's axis; but since its declination varied only one half as much as in the case of γ Draconis, it was obvious that nutation did not supply the requisite solution. Whether the motion was due to an irregular distribution of the Earth's atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

, thus involving abnormal variations in the refractive index, was also investigated; here, again, negative results were obtained.

On August 19, 1727, Bradley then embarked upon a further series of observations using a telescope of his own erected at the Rectory, Wanstead
Wanstead is a suburban area in the London Borough of Redbridge, North-East London. The main road going through Wanstead is the A12. The name is from the Anglo-Saxon words wænn and stede, meaning "settlement on a small hill"....

. This instrument had the advantage of a larger field of view and he was able to obtain precise positions of a large number of stars that transited close to the zenith over the course of about two years. This established the existence of the phenomenon of aberration beyond all doubt, 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. However, he was no closer to finding an explanation of why aberration occurred.

### Development of the theory of aberration

Bradley eventually developed the explanation of aberration in about September 1728 and his theory was presented to the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

in mid January the next year. One well-known story (quoted in Berry, page 261) was that he saw the change of direction of a wind vane on a boat on the Thames, caused not by an alteration of the wind itself, but by a change of course of the boat relative to the wind direction. However, there is no record of this incident in Bradley's own account of the discovery, and it may therefore be apocrypha
Apocrypha
The term apocrypha is used with various meanings, including "hidden", "esoteric", "spurious", "of questionable authenticity", ancient Chinese "revealed texts and objects" and "Christian texts that are not canonical"....

l.

The discovery and elucidation of aberration is now regarded as a classic case of the application of scientific method
Scientific method
Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...

, in which observations are made to test a theory, but unexpected results are sometimes obtained that in turn lead to new discoveries. It is also worth noting that part of the original motivation of the search for stellar parallax was to test the Copernican theory that the Earth revolves around the Sun, but of course the existence of aberration also establishes the truth of that theory.

In a final twist, Bradley later went on to discover the existence of the nutation of the Earth's axis – the effect that he had originally considered to be the cause of aberration.

• Aberration
Aberration in optical systems
Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge...

• Nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

• Proper motion
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...

James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...

• Fresnel, Augustin-Jean
Augustin-Jean Fresnel
Augustin-Jean Fresnel , was a French engineer who contributed significantly to the establishment of the theory of wave optics. Fresnel studied the behaviour of light both theoretically and experimentally....

• List of astronomical topics
• Stokes, George Gabriel
George Gabriel Stokes
Sir George Gabriel Stokes, 1st Baronet FRS , was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics , optics, and mathematical physics...

• Timeline of electromagnetism and classical optics
Timeline of electromagnetism and classical optics
Timeline of electromagnetism and classical optics*424 BC Aristophanes "lens" is a glass globe filled with water....