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Aberration of light

2007 Schools Wikipedia Selection. Related subjects: General Physics

   The aberration of light (also referred to as astronomical aberration or
   stellar aberration) is an astronomical phenomenon which produces an
   apparent motion of celestial objects. It was discovered and later
   explained by the third Astronomer Royal, James Bradley, in 1725, who
   attributed it to the finite speed of light and the motion of Earth in
   its orbit around the Sun.

   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 upon the transverse component of the velocity 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). In the
   case of an observer on Earth, the direction of its velocity varies
   during the year as Earth revolves around the Sun (or strictly speaking,
   the barycenter of the solar system), and this in turn causes the
   apparent position of the object 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 or declination. 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,
   which is due to the motion of the observed object, like a planet,
   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 (90° from the
   Sun), where aberration drops to zero because then the Earth is directly
   approaching or receding from the planet. At opposition to or
   conjunction with the Sun, aberration is 20.5" while light-time
   correction varies from 4" for Mercury to 0.37" for Neptune (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

   Figure 1. Diagram illustrating stellar aberration
   Figure 1. Diagram illustrating stellar aberration

   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 mostly by aberration.

   Aberration occurs when the observer's velocity has a component that is
   perpendicular to the line traveled by light between the star and
   observer. In Figure 1 to the right, S represents the spot where the
   star light enters the telescope, and E the position of the eye piece.
   If the telescope does not move, the true direction of the star relative
   to the observer can be found by following the line ES. However, if
   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, the star will no
   longer appear in the centre of the eye piece. The telescope must
   therefore be adjusted so that the star light enters the telescope at
   spot S’. Now the star light will travel along the line S’E’ 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.

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

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.
     * Planetary aberration is the combination of aberration and
       light-time correction.
     * Diurnal aberration is due to the rotation of the Earth about its
       own axis.
     * Secular aberration is due to the motion of the Sun and solar system
       relative to other stars in the galaxy.

Annual aberration

   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 (i.e. if SEE’ in the diagram is 90 degrees),
   the angle of displacement, SES’, would therefore be (in radians) the
   ratio of the two velocities, i.e. 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).
   Figure 2. Diagram illustrating the effect of annual aberration on the
   apparent position of three stars at ecliptic longitude 270 degrees, and
   ecliptic latitude 90, 45 and 0 degrees, respectively
   Figure 2. Diagram illustrating the effect of annual aberration on the
   apparent position of three stars at ecliptic longitude 270 degrees, and
   ecliptic latitude 90, 45 and 0 degrees, respectively

   The plane of the Earth's orbit is known as the ecliptic. 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 (see figure 2).

   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.
   This constant deflection is often erroneously 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. The latter is a type of parallax, and
   actually causes the apparent motion of the Sun along the ecliptic
   towards the east relative to the fixed stars. (8.316746 minutes divided
   by one sidereal year (365.25636 days) is 20.49265", very close to κ,
   but of opposite sign, east vs. west.) Nor is this the Sun's light-time
   correction because the Sun is almost motionless, moving around the
   barycenter (centre of mass) of the solar system by usually much less
   than 0".03 (as viewed from Earth) during 8.3 minutes.

   Aberration can be resolved into east-west and north-south components on
   the celestial sphere, which therefore produce an apparent displacement
   of a star's right ascension and declination, 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 can detect very small changes in
   declination.
   Figure 3. Diagram illustrating aberration of a star at the north
   ecliptic pole
   Figure 3. Diagram illustrating aberration of a star at the north
   ecliptic pole

   Figure 3, above, 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 (this observer would have to be
   positioned at latitude 66.6 degrees north – i.e. on the arctic circle).
   At the time of the March equinox, 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 solstices, the displacement is zero.

   Note that the effect of aberration is out of phase 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.

Planetary aberration

   Planetary aberration is the combination of the aberration of light (due
   to Earth's velocity) and light-time correction (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 and longitude 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 centre of the Galaxy,
   as are other nearby stars. It is therefore possible to conceive of an
   aberrational effect on the apparent positions of other stars and on
   extragalactic objects. However, the change in the solar system's
   velocity relative to the centre 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.

   However, it is possible to estimate the displacement between the
   apparent and true position of a nearby star whose distance and motion
   are known. Newcomb gives the example of Groombridge 1830, where he
   estimates that the true position is displaced by approximately 3
   arcminutes from the direction in which we observe it. 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 was
   one of the most important in astronomy. It was totally unexpected, and
   it was only by extraordinary perseverance and perspicuity that Bradley
   was able to explain it in 1727. Its origin is based on attempts made to
   discover whether the stars possessed appreciable parallaxes. The
   Copernican theory of the solar system – that the Earth revolved
   annually about the Sun – had received confirmation by the observations
   of Galileo and Tycho Brahe (who, however, never accepted
   heliocentrism), and the mathematical investigations of Kepler and
   Newton.

Search for stellar parallax

   As early as 1573, Thomas Digges 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 concluded that they existed only in the minds of the
   observers, and were due to instrumental and personal errors. In 1680
   Jean Picard, in his Voyage d’ Uranibourg, stated, as a result of ten
   years' observations, that Polaris, or the Pole Star, 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, 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, in
   1674, published his observations of γ Draconis, a star of magnitude 2^m
   which passes practically overhead at the latitude of London, and whose
   observations are therefore free from the complex corrections due to
   astronomical refraction, and concluded that this star was 23" more
   northerly in July than in October.

Bradley's observations

   When James Bradley and Samuel Molyneux 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. They determined to reinvestigate the motion of γ Draconis; the
   telescope, constructed by George Graham (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 12th of 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 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. 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, 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. 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 a year
   later. One well-known story (quoted in Berry, p 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 apocryphal.

   The discovery and elucidation of aberration is now regarded as a
   classic case of the application of scientific method, 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.
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