Polaris is a particular star. It is almost exactly over the North Pole. This position makes this star perfect to do some calculation in relation to the Earth.
|1) On the North Pole the star is to the zenith of the observer. For a globular Earth astronomers say that the North Pole has latitude 90°; also the height angle of the Polaris is exactly 90° .|
|2) The equator on a globe has 0° in latitude and the Polaris should be seen on the horizon that is 0° on the horizon.|
Pictures taken from the site astrodidattica.vialattea.net.
|3) We can understand that in each point of the northern hemisphere the height (angle) of the Polaris always is the same of the latitude of the place .|
A good exercise could be to measure these angles and check them because it is evident that on a flat Earth these angles should be greater, and for example at the equator the angle shouldn’t be zero but a little more. Let’s do it.
Measuring Polaris angle
- First we have to pinpoint Polaris in the sky ;
- Second we have to measure the angle.
This star is motionless in the sky so we have no problem to find it at different hours or season: it is always there indicating the North direction. Polaris, that by Arabs was called Alruccabah , is easy to find because looks quite isolated from other stars and it is brilliant enough to be seen also in a gloomy night or in the presence of the moon.
A big help comes from stars of the Big Dipper. Polaris can be identified thanks to two stars of the Big Dipper called in fact “pointers” or “Pole guards”. These stars are β and α known also with Arab name Merak and Dubhe. Polaris can be found at 4,5 times the extension of β to α.
Measuring the angle
How can we measure the angle? We could use a sextant, but have you got one? We need something useful, handsome and cheap because we need a lot of measures in different places in the world. (Please dear friends, do them and report me the results)
I’ve found the existence of this instrument, the Kamal that you can see in the picture.
You need to produce it with a piece of wood (40-60 cm) and a piece of tiny rope (1 meter is good). Tie the rope to the wood exactly in the middle, maybe doing a little incision in the wood so that the rope will not move from the middle.
Once you have produced your Kamal you can go outside and measure!
As you can see in the picture the rope should be kept tight till the eye. The lowest point of the wood must stay horizontal with your eye and should be kept perpendicular to the rope. The highest point of the wood must “touch” the star.
To reach the correct position you have to bring nearer or maybe farther the wood. When you are in position keep a sign of the length of the rope and measure it. Now guys we have to do a little of trigonometry.
Call a the length of the wood. Call b the length of the rope that you have measured. α is the angle of the star we are searching.
From trigonometry we find:
Last year I made this experiment and I found a result 9° bigger than the latitude. I thought that this was proving that the Earth is not a globe. Anyway, by now, since I understand a bit better the optic rules which are in control of the skies, I have to review my considerations. Earth is flat but my measurement were not perfect.
I have repeated the experiment, each time with some more precision . So, I have to acknowledge that the angle I found was only quite near, but only approximate, to the latitude. Of course, the Kamal instrument can give just approximated results. I still can’t believe that, everywhere on the Earth, Polaris measures an angle equal to the local latitude. But, I’m sure that, for all physical phenomena, there should be an explanation.
Knowing the altitude of the stars
An important consideration I have to do is that, by now, we already know the altitude of the stars. They are in the moving part of the dome that is a hemisphere with a radius measuring 26640km. But, when measuring the altitude of Polaris, it appears to stay at a much lower height. This is an evidence of the fact that we cannot be able to determine the height of Polaris by just doing some simple trigonometric calculation.
Why does Polaris appear to be nearer then in reality?
The problem is to find an answer to this question: why does Polaris seem to be so near to us when we know that it is high at least 26640 km over the North pole?
The answer is in something we now already know. It is something in connection to the Van Allen belt. The plasma in it produces an inversion in the refractive index. This is the same phenomenon making it possible for us to see the same face of the moon from everywhere all over the Earth.
See also this article:
The northern magnetic column
We must remember that, starting from the lower north pole up to the top of the dome there is a huge magnetic column. It produces a thick layer of plasma at a 4000-6000 kms of height, that is the Van Allen belt. The magnetic column generates an inversion of the refractive angle. Moreover, the atmosphere can produce many refraction phenomena. Thus a celestial body may appear higher than in reality. At the higher altitudes, above the limits of the van Allen belt, the magnetic column produces the inverse phenomenon and stars appear to be lower than they are in reality.
Seeing Polaris up to 20° beyond the equator
This change in the refractive index is not uniform and makes it possible seeing Polaris with an angle that is about the same of the latitude angle. As we know, this is not something which is true in an absolute sense. In fact there are evidences proving that it is possible to see Polaris up to 20° beyond the equator.
So the Earth is flat and our data, in the course of time, are getting more and more precise.
|In alternative to the Kamal you can build by yourself a small and simple astrolabium like that in the picture.
Now it’s your turn. Please do the experiment and tell me the results, in the comment space of this post, or maybe on facebook or send me a mail (firstname.lastname@example.org). I’m very curious of results from the equator…from my friends in Brazil for example. If results will be interesting I will write a post exposing them.
Bye, and thank you for reading.