Astronomical aberration is a phenomenon that makes a star, seen in a telescope, appear in a place slightly different from the expected. Aberration has been observed in 1727 by the English astronomer James Bradley who, in the course of his surveys, noticed that stars seemed to be subject to a slight movement within a period of one sidereal year. He thought that this movement depended on the position of the star inside the celestial sphere.
What is the astronomical aberration
Aberration of light has been considered first as a consequence of the motion of the Earth around the sun. We can explain this phenomenon considering that the light of the star enters the telescope and, since the light speed, though really fast, is limited and not infinite, it takes a short time to reach the eye of the observer. During this short lapse of time the Earth is moving around the sun with an average speed of about 30km/s that is 1/1000 of the speed of light.
The speed of light, t
hus, will show to be under the influence of the speed of the Earth, generating the aberration, an apparent change in the position of the star. A star that is perpendicular to the orbital plane of the Earth has an aberrant circular movement inside the periodicity of one year; a star that is seen exactly on the plane of the ecliptic has an apparent rectilinear movement, while in the intermediate positions this movement appears to be elliptical. The maximum aberration value measured during the year is 20”,49 and that is called annual aberration constant.
A classical example u
sed to describe the aberration is the following: consider a man with an umbrella under the rain. When the man stands still in a place he sees the rain falling vertical. But, if he starts running, he will see the rain falling diagonally. This simply will be an apparent phenomenon due to the composition of two velocities: the one of the rain falling and the speed of the man running.
This phenomenon is considered one of the first experimental proofs that the Earth moves around the sun and not the contrary. In fact if the Earth would be motionless we couldn’t observe the aberration.
The astronomical aberration is only refraction
The basic problem with this phenomenon is the periodicity. Actually, when considering the phenomenon, as we have already noticed, there is a periodical movement presenting a cycle of one year. This means that in six months the aberration passes from a minimum to a maximum and this cycle is repeated every year. We have always been taught by scientists that the Earth is moving around the sun. This could explain the aberration, but astronomers also believe that the sun moves in the galaxy toward Vega. The aberration movement thus shouldn’t be an ellipse but a spiral always changing and without a precise periodicity.
However, aberration has really been measured. So, how can this periodical, mysterious, apparent movement be explained?
|Aberration: experimentally measured or simply theoretically calculated?
Aberration angles are very small and it is quite difficult to think that they have been measured avoiding errors due to refraction. Thus the incredible match between measured values and theoretical ones appears astonishing. Let’s see the theory. Consider a telescope 1 meter long. The time light takes to make that distance is :
During this time the Earth covers the following distance:
So we have this situation (see also the figure):
It is noteworthy the fact that Bradley himself recognized that this phenomenon was the same for all the stars. At first Bradley thought that it was caused by the parallax, i.e. an optical error due to the different positions of the Earth during the year. But if the modification of the position is the same for all the stars, this could be caused by the parallax only if stars were all at the same distance from the Earth, thing considered absurd by Bradley himself. He reached, thus, the conclusion that the phenomenon was caused by the aberration of light.
We really know, considering our flat model of the Earth, that this apparent change in the position of the stars can’t be caused by parallax because the earth is motionless, and the stars, month after month, are at the same distance from the Earth, so no parallax is possible.
It is important to consider that this phenomenon is cyclic and manifests the maximum gradient in six months. Could this be explained simply as a refractive optical phenomenon? Let’s see.
A ray of light that, from a star, reaches the Earth, passes through the atmosphere that owns a little, but anyway sensitive, refractive power. Thus, if the ray of light is not perfectly perpendicular to the Earth, it is bent with a small angle called astronomic refraction that can be thus calculated:
where r0 is the refraction angle expressed in minutes of degree and Hc is the height angle of the star.This formula is valid for an atmospheric pressure of 1010mbar and a temperature of 10°C. If temperature and pressure are different this formula should be used:
and refraction will be: R=R0*f.
The true height of the star is H=Hc+R.
The maximum value of aberration measured by Bradley is 20”,49 that is called annual constant of aberration and corresponds to the major semi axis of the aberration ellipse.
The refraction angle can assume a maximum value of 35’,4 on the horizon but it is 3′, only 3’ already at 17,5°. Notice that this value changes with the temperature (as with temperature the air density also changes) and the temperature changes with the seasons, and …mumble mumble…the maximum climatic difference with seasons is cyclic and recurring every six months.
The value of refraction angle changes of about 1% for each 3°C of temperature variation. If we consider a temperature variation from summer to winter of 30°C we have a 10% of variation on the refraction angle.
We arrive thus at 0,3’ i.e. 20” of apparent deviation due to refraction if we consider a star at 17° high, that corresponds quite well to the value of aberration.
We believe that the Earth is motionless and have already proved it in this blog. Thus the aberration cannot exist and this is confirmed by the fact that it has a precise periodicity that doesn’t follow the movement of the sun in the galaxy but the movement of the seasons. Aberration can be, however, easily included among the astronomical refraction phenomena. And, according to the above given calculations, we have proved that the angles calculated (aberration and refraction) are very similar, so refraction is a possible reason for the astronomical aberration.