Aberration of light
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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 is caused by the twin facts that the speed of light is finite, and that an observer on Earth is moving relative to any inertial frame. It does not require Earth to carry an observer to some other position after some period of time—only that Earth changes velocity. A change in the position of an observer causes parallax, which must not be confused with the aberration of light.
Stellar aberration is independent of the distance of a celestial object from the observer. It should also be distinguished from light-time correction, which is due to the displacement of a solar system object, like a planet, through space during the time taken by its light to reach an observer on Earth. Light-time correction is independent of the motion of Earth. Planetary aberration (of solar system objects) is the combination of the aberration of light (due to Earth's velocity) and light-time correction (due to a planet's displacement). Both are determined at the instant when the object's light reaches Earth.
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Explanation
Image:Aberration1.gif Stellar aberration causes the apparent position of a star to be displaced, and occurs when the observer's motion has a component that is perpendicular to a line between the star and observer. In the diagram to the right, S represents the position of the star, and E the position of the observer on Earth. The true direction of the star relative to the observer is thus ES, whose length represents the speed of light. However, Earth has a velocity in the direction represented by the line EE’, whose length represents that velocity. The Law of Aberration states that the star will therefore appear to lie in the direction ES’, instead of ES, where SS’ is parallel and equal in length to EE’. The star's apparent position is hence displaced from its true position by the angle SES’.
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 stellar aberration, caused by the differing components of the Earth's motion:
- Annual Aberration is due to the revolution of the Earth around the Sun.
- 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 and diurnal aberration cause stars to appear to vary in position on a periodic basis, and their effect must be included when computing the apparent position of a star at any given time. Secular aberration can be regarded as constant for all practical purposes, and so is usually ignored.
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).
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 either side of their true position. A star that is precisely at one of the ecliptic 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.
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 (center 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 an east-west and north-south component on the celestial sphere. The former is larger, but the latter, present because of the 23.4° tilt of the Earth's axis (obliquity of the ecliptic), was the first to be detected. This is because accurate clocks are needed to measure the East-West component, but only a good plumb line is needed for the north-south component.
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 location 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.
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 with of magnitude 2m 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".
This motion is evidently not due to parallax, for, in this case, the maximum range should be between the June and December positions; neither was it due to observational errors. Bradley and Molyneux discussed several hypotheses in the hope of fixing the solution. One hypothesis was: while γ Draconis was stationary, the plumb-line, from which the angular measurements were made, varied; this would follow if the axis of the Earth varied.
Aberration vs nutation
The oscillation of the Earth's axis may arise in two distinct ways; distinguished as nutation of the axis and variation of latitude. Nutation, the only form of oscillation imagined by Bradley, postulates that while the Earth's axis is fixed with respect to the Earth (i.e. the north and south poles occupy permanent geographical positions), yet the axis is not directed towards a fixed point in the heavens; variation of latitude, however, is associated with the shifting of the axis within the Earth, i.e. the geographical position of the north pole varies.
Nutation of the axis would determine a similar apparent motion for all stars: thus, all stars having the same polar distance as γ Draconis should exhibit the same apparent motion after or before this star by a constant interval. Many stars satisfy the condition of equality of polar distance with that of γ Draconis, but few were bright enough to be observed in Molyneux's telescope.
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.
Bradley had already perceived, in the case of the two stars previously scrutinized, that the apparent difference of declination from the maximum positions was nearly proportional to the Sun's distance from the equinoctial points; and he realized the necessity for more observations before any generalization could be attempted. For this purpose he repaired to the Rectory, Wanstead, then the residence of Mrs. Pound, the widow of his uncle James Pound, with whom he had made many observations of the heavenly bodies.
Here he had set up, on August 19, 1727, a more convenient telescope than that at Kew, its range extending over 6 1/4 degrees on each side of the zenith, thus covering a far larger area of the sky. Two hundred stars in the British Catalogue of Flamsteed traversed its field of view; and, of these, about fifty were kept under close observation. His conclusions may be thus summarized:
- only stars near the solstitial colure had their maximum north and south positions when the Sun was near the equinoxes,
- each star was at its maximum position when it passed the zenith at six o'clock morning and evening (this he afterwards showed to be inaccurate, and found the greatest change in declination to be proportional to the latitude of the star),
- the apparent motions of all stars at about the same time was in the same direction.
Development of the theory of aberration
A re-examination of his previously considered hypotheses as to the cause of these phenomena was fruitless; the true theory was ultimately discovered by pure accident, comparable in simplicity and importance with the association of a falling apple with the discovery of the principle of universal gravitation. Sailing on the river Thames, Bradley repeatedly observed the shifting of a vane on the mast as the boat altered its course and, having been assured that the motion of the vane meant that the boat, and not the wind, had altered its direction, he realized that the position taken up by the vane was determined by both the motion of the boat and the direction of the wind.
The application of this observation to the phenomenon which had so long perplexed him was not difficult, and, in 1727, he published his theory of the aberration of light —a corner-stone of the edifice of astronomical science. Let S (fig. 2) be a star and the observer be carried along the line AB; let SB be perpendicular to AB. If the observer be stationary at B, the star will appear in the direction BS; if, however, he traverses the distance BA in the same time as light passes from the star to his eye, the star will appear in the direction AS. Since, however, the observer is not conscious of his own translatory motion with the Earth in its orbit, the star appears to have a displacement which is at all times parallel to the motion of the observer.
References
- A detailed account of Bradley's work is given in S. Rigaud, Memoirs of Bradley (1832), and in Charles Hutton, Mathematical and Philosophical Dictionary (1795).
- A particularly clear and lucid account is given in H. H. Turner, Astronomical Discovery (1904).
- "Aberration", Explanatory Supplement to the Astronomical Almanac (1992), 127-135, 700.
See also
- Aberration
- Bradley, James
- Fresnel, Augustin-Jean
- List of astronomical topics
- Stokes, George Gabriel
- Proper motion
- Timeline of electromagnetism and classical optics
This article incorporates text from the Encyclopædia Britannica Eleventh Edition{{#if:{{{article|}}}| article {{#if:{{{url|}}}|[{{{url|}}}}} "{{{article}}}"{{#if:{{{url|}}}|]}}{{#if:{{{author|}}}| by {{{author}}}}}}}, a publication now in the public domain.de:Aberration (Astronomie) es:Aberración de la luz fr:Aberration de la lumière ko:광행차 hr:Aberacija svjetlosti ja:光行差 pl:Aberracja światła ru:Аберрация света sk:Aberácia (astronómia)