Aberration of the light - SpeedyLook encyclopedia

The aberration of the light was discovered by the astronomer James Bradley in 1725, but only published in 1727. It results in the fact that the direction connects of a source of light depends on the Speed of that which observes it, in the same way that the rain seems to fall since a direction located forwards vehicle and not at the vertical from this one when this one moves. Bradley discovered the phenomenon in 1725 by studying the variations of the apparent position of the star γ Draconis. It been necessary for him nearly two years before including/understanding this phenomenon and publishing it.

Historical aspects

The possibility of an apparent displacement of stars as consequence of the model copernician had been emitted as of the end of XVIe century, but it is with a movement of Parallaxe that the majority of the writings referred. Until the end of the XVIIe century, any reliable measurement of apparent star movement. It is the Astronome French Jean Picard which seems it was the first to observe the phenomenon of aberration in 1680, but that it in vain tried to explain in term of parallax.

The phenomenon of aberration of the light had been the subject of several studies after Rømer had measured for the first time the Speed of light in 1676. Several attempts at description, in particular by the British Astronome John Flamsteed in 1689 took place. It was observed in a convincing way by Bradley in the month of December 1725 with the star γ Draconis confirmed by its additional observations in March 1726. Several other stars were observed in 1727.

Bradley had many difficulties of including/understanding his observations. An assumption that it considered initially was that the apparent movement of stars was a consequence of a variation of the axis of rotation of the Ground. However this interpretation did not make it possible to explain the observations. The anecdote tells that it is by observing the variation of the apparent direction of the wind according to speed and the direction taken by a sailing ship that Bradley had the idea to apply this reasoning finally rather simple to the light. After being itself assured the validity of the assumption according to which it was the aberration which was responsible for the apparent movement of stars, it realized that by withdrawing this phenomenon from the apparent movements observed there still remained an apparent movement of stars. Remembering its initial assumption, it could then show the existence of a small variation of the axis of rotation of the Earth: it is the phenomenon of Nutation, until it waited a score of years before publishing it in 1748.

Description of the phenomenon

In practice, the phenomenon of aberration can be observed for the star S. One observes an elliptic movement apparent of those during one year. This phenomenon is due at the relative speed of the Ground on its Orbite compared to stars, and does not depend on the distance from star to the Earth, but only from its angle compared to the ecliptic . It should not be confused with the Parallaxe which is only due for a purpose of Perspective, significant only for rather close stars. Moreover, the two phenomena do not have the same order of magnitude, approximately 20 seconds of arc for the aberration, against one second of arc for the parallax of the closest stars. It is besides this difference in order of magnitude which allowed the discovery of the aberration of stars nearly one century before that of their parallax. Because of rotation of the Earth, there exists also a phenomenon of diurnal aberration, all the more marked as the observer is located near to the Ecuador. The amplitude of this phenomenon is however much lower, about a fraction of a second of arc.

The phenomenon of aberration brought an additional confirmation to the model copernician. It also made it possible to estimate speed of light, in a coherent way with a first estimate made by Rømer one fifty of years before. At the time, uncertainties on the size of the Solar system did not make it possible to know with precision the size of the orbit of the Earth and consequently its speed along its orbit, which prevented a precise measurement speed of light.

A surprising consequence of the phenomenon of aberration is that a strongly accelerated observer reaching a speed close to that of the light would see it quasi totality of the objects located in front of him projected towards a direction connect very near to the direction towards which it moves, giving the erroneous impression to him which it is moving away from the direction towards which it moves. This phenomenon thus makes it possible an observer with the very fast movement to see forwards objects in fact located behind him.

Traditional calculation

One considers two reference frames

R

and

R'

in translation one compared to the other, with a speed v . It is supposed that the axes of the two reference frames remain parallel. If the light arrives in the

Oxy

plan of the reference frame

R

, by forming an angle θ with the axis

Ox

. Speed of light has then as components

\ begin {pmatrix} - C \ cos \ theta \ \ - C \ sin \ theta \ end {pmatrix}

. In the reference frame

R'

, these components become

\ begin {pmatrix} - C \ cos \ theta - v \ \ - C \ sin \ theta \ end {pmatrix}

, formant thus an angle

\ theta'

such as:

\ tan \ theta' = {\ sin \ theta \ over \ cos \ theta + v/c}

If the star is with the zenith ( $\ theta = \ pi/2$ ), then $\ tan \ theta' = {C \ over v}$ or $\ tan (\ pi/2 - \ theta') = {v \ over C}$ . The variation of angle is thus of approximately v / C . Observation of same star in six months of interval (during which the speed of the Earth passes from v to - v ) allows to measure the double of this angle. Knowing v , one can deduce C from it. For the phenomenon of aberration of stars, it is the $v/c$ report/ratio which one measures, where $v$ is the orbital velocity of the Earth, about constant during time because the orbit of the Earth is quasi circular. The amplitude of the movement of aberration of $v/c$ , is expressed in term of angle, that is to say 20.49552" . It is what one calls aberration the constant .

Relativistic calculation

Preceding calculation is valid if

c

represents a low speed in front of that of the light. It is the traditional phenomenon of aberration, such as for example the variation of the apparent direction of the wind according to the speed and the direction of a sailing ship. For the light, preceding calculation is not completely exact, since the vector

\ begin {pmatrix} - C \ cos \ theta-v \ \ - C \ sin \ theta \ end {pmatrix}

has a standard higher than C . That would mean that speed of light is higher than C in the reference frame

R'

. It is thus necessary to use the formulas of relativistic transformation speeds. In the reference frame

R'

, the direction of light propagation is done in fact according to the direction

{1 \ over 1 + {v \ over C} \ cos \ theta} \ begin {pmatrix} - C \ cos \ theta-v \ \ - C \ sin \ theta \ sqrt {1 - {v^2 \ over c^2}} \ end {pmatrix}

, so that

\ tan \ theta' = {\ sin \ theta \ over \ cos \ theta + v/c} \ sqrt {1 - {v^2 \ over c^2}}

The difference with the traditional formula is unperceivable in the case of the Earth.

See too

the Effect Doppler: the change of reference frame also results in a modification of the frequency of the received wave. The aberration of the light is with the effect Doppler the experimental translation of the transformation of the quadri-vector of wave during a change of reference frame, within the framework of the restricted Relativité.
the relativistic Calculations

External bonds

Seeing Relativity a teaching site explaining various effects of restricted relativity of which aberration.

Random links:

Thaliacea | Proto87 | Union of the écrivaines and the Québécois writers | Simon Ward (British actor) | The Day of the judgment of Pluto