Aberration of light

Aberration of light (also referred to as astronomical aberration or stellar aberration) is an astronomical phenomenon defined as an apparent motion of the heavenly bodies; stars describing more or less elliptic annual orbits, according to the latitude of the star; consequently at any moment the star appears to be displaced from its true position. This apparent motion is due to the finite speed of light relative to the velocity of an observer on the Earth. It has three components: diurnal aberration, annual aberration, and secular aberration. Secular aberration is due to the motion of the Sun through space, whose rectilinear motion when combined with a star's rectilinear motion cannot be distinguished from the deflection due to light-time and is thus ignored. Diurnal aberration is due to Earth's rotation on its axis and does not exceed 0.32" (it is most pronounced for equatorial observers). The rest of this article concerns annual aberration due to the velocity of the Earth in its annual orbit about the Sun.

Contents

1 Phenomenon observations 2 Mechanics 3 Discovery and development 4 Generalization 5 References 6 See also

Phenomenon observations

When observed from the Earth, light from the Sun or any other astronomical object shows an aberration. Aberration is the deflection of the position of a celestial object toward the direction of motion of the observer on Earth due to Earth's velocity relative to inertial space. This effect does not require displacement through space of either the celestial object or of Earth, only the velocity of Earth at some instant. The orbital velocity of the Earth is about 1/10,000 the speed of light, so the annual aberration of the Sun is 1/10,000 radian toward the west (-20.5"), directly opposite to its apparent motion along the ecliptic. This aberration must not be confused with light-time correction. Indeed, the vectorial sum of a planet's aberration of light and that planet's light-time correction is called planetary aberration.

The aberration of light also causes the positions of other stars to be displaced from their average position by up to 20.5" —the variation is dependent upon the Earth's velocity around the Sun and the star's relative direction from our vantage point.

To familiarize ourselves with this phenomenon, the umbrella analogy is possibly the best known figure. When stationary, the most efficient position in which to hold an umbrella is obviously vertical; when walking, the umbrella must be held more and more inclined from the vertical as the walker quickens his pace. Another familiar figure, pointed out by Pierre Louis Maupertuis, is that a sportsman, when aiming at a bird on the wing, sights his gun some distance ahead of the bird, the distance being proportional to the velocity of the bird.

Mechanics

The mechanical idea, named the parallelogram of velocities, permits a ready and easy graphical representation of these facts. Reverting to the analogy of the umbrella, let AB (fig. 1) represent the velocity of the rain, and AC the relative velocity of the person holding the umbrella. The diagonal AD of the parallelogram, of which AB and AC are adjacent sides, will represent, both in direction and magnitude, the motion of the rain as apparent to the observer. Hence for the best protection from the rain, the stick must point along the resultant AD meaning the umbrella must be inclined at an angle BAD to the vertical. This angle is conveniently termed the aberration: due to these two motions.

Discovery and development

The discovery of the aberration of light in 1725 by James Bradley is one of the most important in the whole domain of astronomy. That it was unexpected there can be no doubt; and it was only by extraordinary perseverance and perspicuity that Bradley was able to explain it in 1727. Its origin is seated in attempts made to free from doubt the prevailing discordances as to 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.

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 occasion.

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 2^m which passes practically overhead at the latitude of London, and whose observations are therefore singularly free from the complex corrections due to astronomical refraction, and concluded that this star was 23" more northerly in July than in October.

When James Bradley and Samuel Molyneux entered this sphere of astronomical research in 1725, there consequently prevailed much uncertainty as to 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, in fact, inexplicable by existing theories; and 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.

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. The question as to 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:

1. only stars near the solstitial colure had their maximum north and south positions when the Sun was near the equinoxes,
2. 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),
3. the apparent motions of all stars at about the same time was in the same direction.

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 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.

Generalization

To generalize this, let S (fig. 3) be the Sun, ABCD the Earth's orbit, and s the true position of a star. When the Earth is at A, in consequence of aberration, the star is displaced to a point a, its displacement sa being parallel to the Earth's motion at A; when the Earth is at B, the star appears at b; and so on throughout an orbital revolution of the Earth. Every star, therefore, describes an apparent orbit, which, if the line joining the Sun and the star be perpendicular to the plane ABCD, will be exactly similar to that of the Earth, i.e. almost a circle. As the star decreases in latitude, this circle will be viewed more and more obliquely, becoming a flatter and flatter ellipse until, with zero latitude, it degenerates into a straight line (fig. 4).

The major axis of any such aberrational ellipse is always parallel to AC, i.e. the ecliptic, and since it is equal to the ratio of the velocity of light to the velocity of the Earth, it is necessarily constant. This constant length subtends an angle of about 40" at the Earth; the constant of aberration is half this angle. The J2000.0 value is 20.49552". The minor axis, on the other hand, is not constant, but, as we have already seen, depends on the latitude, being the product of the major axis into the sine of the latitude.

Assured that his explanation was true, Bradley corrected his observations for aberration, but he found that there still remained a residuum which was evidently not a parallax, for it did not exhibit an annual cycle. He reverted to his early idea of a nutation of the Earth's axis, and was rewarded by the discovery that the Earth did possess such an oscillation. Bradley recognized the fact that the experimental determination of the aberration constant gave the ratio of the velocities of light and of the Earth; hence, if the velocity of the Earth be known, the velocity of light is determined.

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
• List of astronomical topics
• Augustin-Jean Fresnel
• George Gabriel Stokes
• James Bradley
• Proper motion
• Timeline of electromagnetism and classical opticsde:Aberration (Astronomie)

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