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Frank L. Preuss

**
What happens after sunset?
**

Today I watched sunset.

Now after sunset I wanted to see, when the first stars start to appear in the sky.

Thirty-one minutes after the sun had disappeared, the first star appeared and it could have been Sirius, in the constellation Canis Major, for Sirius is the brightest star at night and so it could be the first star that is visible and previous observations had shown that at that place it could be Sirius.

Now 6 minutes later the second star appeared and it could be Canopus, in the constellation Carina, for Canopus is the second brightest star at night and it could therefore appear as the second heavenly body.

Now a third heavenly body was seen in the far north. May be it was a planet. May be it was even there, before I saw the other two.

These three objects proved to be the only objects that appeared. The lights of the city did not allow more stars to be seen.

Now from night sky maps I could see that Sirius and Canopus are not visible from my location at that time of the year, but let us carry on and give these two stars these names.

I now wanted to see if there was a way to determine the relationship between two stars and I assumed that the astronomers had sought out a way to determine the position of heavenly objects in the firmament, which then allowed me to calculate the distance between two objects in the sky, for example between Sirius and Canopus, and then compare that calculation with my measurement.

So I measured the angle between the two. I took a sight from the top of my standard lamp on Sirius and marked that point on the windowpane and I did the same with Canopus. I then measured the distance of these two marks on the windowpane. I also measured the distances from these two marks to the top of my standard lamp. These three lengths of that triangle I drew, to scale, on a piece of paper and then measured the angle at that point of the triangle, which represented the top of my standard lamp.

The angle I measured was 33.5^{o}. Now I did not spend much time on this measurement and also did not try to be accurate, because I just wanted to see, if this works.

I now looked up what the astronomers had to say about the position of these two stars.

What I found was this:

Sirius 06^{h} 45^{m} 08.9128^{s} and -16^{o} 42’ 58.0171”.

Canopus 06^{h} 23^{m} 57.1099^{s} and -52^{o} 41’ 44.378”.

When I now convert these to hours and degrees then I get this:

Sirius 6.7525^{h} and -16.7161^{o}

Canopus 6.3992^{h} and -52.6957^{o}

Now from these four figures one can see already that the angle is about 36^{o}, that is the difference between 16.7161 and 52.6957. I had measured 33.5^{o}, which is quite close to 36^{o}, so this is a hint that these two stars could actually be Sirius and Canopus.

This angle can also be calculated. When this investigation is done quite often, then a calculation is faster than making a drawing, because once one calculation has been done, the next ones are easy, particularly when a spread sheet is used.

Here the formula:

a^{2} = b^{2} + c^{2} - 2bc cosα

Or 2bc cosα = b^{2} + c^{2} - a^{2}

Or cosα = (b^{2} + c^{2} - a^{2})/2bc

Now α is the angle of the triangle which is opposite of the length of the triangle that represents the distance between Sirius and Canopus. So

cosα = (1120^{2} + 1275^{2} - 700^{2})/(2*1120*1275) = 0.8368

And that gives an angle α = DEGREES(ACOS(0.8368)) = 33.2^{o}.

So these are two relative simply ways to determine the angle between two stars, to set up a triangle and measure the three lengths of the triangel, and then make a drawing to scale of the triangle or do a calculatation to get the angle. And then one could get the information from the astronomers and calculate from that information the angle, which is little more involved.

One could also of course measure the angle between the two stars directly with a protractor.

This is the end of "Astronomical question and answer 276"

To the German version of this chapter:
Astronomische Frage und Antwort 276

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