241 – Stars aberration

Astronomical aberration is a phenomenon that makes a star, observed through a telescope, to appear in a place slightly different from the expected. Aberration had 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. There is a diurnal aberration that is usually considered negligible, caused, as they say, by the rotation of the Earth around its axis. There is an annual aberration as well, that is considered to be the
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 30 km/s that is 1/1000 of the speed of light. The speed of light, thus, 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. After six month in fact the speed of the Earth will be in the opposite direction and the star will appear in a slightly different
position.

aberrazione
aberrazione

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” that is called annual aberration constant.

A classical example used 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 were motionless, we couldn’t observe the aberration. Someone, when postulating the Earth to be flat, speculates that there
is an aether wind blowing at a speed of 30 km/s, dragging the light that comes from the stars. It generates, this way, the aberration. I will show through the pages of this book that actually there is a wind of aether on the Earth, but it is much weaker. You could probably remember, in fact, that the Michelson Morley experiment failed in detecting a wind of aether.

aberration

A second different experiment made by Michelson and Gale succeeded in measuring a wind of aether with a speed changing with the latitude. I will postulate this wind keeps the sun and the moon moving on their trajectory. This same wind is responsible for the diurnal aberration but not for the much greater annual aberration. So, if the aberration is not caused by the aether, how should we explain it?

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 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. 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 run that distance is:
t=S/V=0.001[km]/300000[km/sec]=3.33×10–9 sec
During this time, earth covers the distance:
S=30[km/sec]x3.33×10–9 [sec]=1×10–7 [km]
So, you have this situation (see also thefigure):

aberration

The vertical side is the length of the telescope. The horizontal one is the space covered by the Earth in the time the light reaches the observer, α is the aberration angle:
α=tg–1 (1×10–3/1×10–7)=0.005°
0.005°x 3600=20”.62

Exactly the aberration constant. Congratulations! That’s really a great experimental
precision!

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 limited speed 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 (with small differences) from the Earth, so no parallax is possible. It is important to consider that this phenomenon is cyclic and reaches
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:

aberration

where R is the refraction angle expressed in minutes of degree and ha is the height angle of the star. This formula is valid for an atmospheric pressure of 1010 mbar and a temperature of 10°C. If temperature and pressure are different, the refraction should be multiplied by:

The real height of the star is H=ha+R, being R the astronomic refraction previously calculated.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 the refraction angle changes of about 1% for every 3°C in the variation of the temperature. If we consider a temperature variation from summer to winter of 30°C we have a 10% of variation on the refraction angle. That is to say 10% of 3’, which is our average refraction angle of 0,3’. This should correspond to the 20” of apparent deviation due to refraction, (when we consider a star at 17° high, that equals quite well the value of aberration).

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