Topic 1

15/08/2021

In this category we will talk more about constellations and the movement of the Earth, as well as about the orientation after the Sun or stars, etc. All categories are below. 

  1. The celestial vault and the constellations. 
  2. - The celestial vault or as it is also called the celestial sphere is in fact an imaginary sphere. This imaginary sphere surrounds the observer, who in turn, due to it, can observe celestial objects, which are visible. Why is it called that? It is so called because when we observe a celestial body, we see its apparent position as it is given, only by the angles between the right from it to that body and the right to various landmarks. The distance from our eye to our body through an observer does not affect the position of the celestial body on the vault (apparent position). The celestial sphere or the celestial vault is actually a sphere whose radius you cannot measure. It's all that keeps your bodies growing on it, it's like a sky. So its radius is very large, and the Universe is infinite, so we cannot take the middle of a celestial vault, so we will call the "middle of a celestial vault" the point where the observer sees, that is, where we see with our eyes, this point being relative. Of course, there is something between us and that celestial body in the sky. That right thing from which our eyes go to the celestial body is called the half-line between the observer and the celestial object. This half-right starts from our eyes and ends at the point, which represents a celestial body from the apparent position on the celestial vault. Looks like you've heard "apparent position" many times. The apparent position can be detected by some spherical coordinate systems that will be built with the celestial vault or the celestial sphere, of course, we will put everything on paper and we will do so. But for example, when an object is so far from the Earth, that is, larger than the diameter of the earth, how do we do it? It's simple. For example. if one observer is placed in America and another in Germany, they will see the body celestial at the same point, but what differs is the direction in which they look. So the angles from the two observers on Earth to the celestial body are very small. But these objects in the sky that appear appear in the same positions, as we said above, to the two observers, but relative to each other. Thus there is only one growing sphere. And since everything can be seen from Earth, it means that the Earth is the middle of the celestial vault or the crest sphere, so we can consider the Earth: punctiform.  Thus, the only vertical direction in which they look differs from the two observers. Okay, we hope you understand what's above. It's hard to understand at first, but we gave you the simplest explanation. We now turn to the nearest objects. What happens to them? Here it must be specified by which observer the position is indicated (on the celestial sphere / vault of the object). Or if it is considered by a hypothetical observer to be at the center of the Earth. We must think that that celestial vault is a sphere and a sphere is always whole, no matter if no. points below the horizon of the observer are not visible with those above simultaneously.  We continue with the coordinates around the observatory. Think of a man standing up and looking at the sky. Well, above it is a point that is the intersection of the vertical of the place with the celestial sphere. That is, above that man is a point at a certain distance, the half-line coming from the celestial body to a man's eye is perpendicular to the half-line coming from the top point to the eye, the two half-lines form an angle of 90 degrees. That top point is called the zenith. Of course, there is a point that is under the eyes of that man, more precisely under his feet, that point is diametrically opposed to the zenith. The bottom point is called the nadir. Now, we have the data to say that there is a plane passing through the observatory in a straight line. It is perpendicular to the vertical of the observer and intersects the celestial sphere after a large circle. The celestial north pole (boreal or arctic) is above the horizon of the observer in the northern hemisphere and the celestial south pole (austral or antarctic) invisible to an observer is in the northern hemisphere; the visible or upper pole is the pole above the horizon, and the invisible or lower pole is the one below the horizon line. This is called: the observer's horizon. We hope we did not confuse you much, we know that these things are difficult, so below we have prepared some images to better understand everything. 
    So, in a year we see different portions of the celestial vault. 

Nadir and Zenith:

Horizon (The radius of the horizon is more scientific: R = 3.8 √h, where by h we represented the height of the observer's eye above the ground expressed in meters.):

Horizon in plan:

How far do we see an object correctly? - until the end of the atmosphere:

Before talking about the stars, a small and quick introduction should be made. We are talking about the brightness, brightness and magnitude of the stars. We start with magnitude: it depends on the sharp brightness of the object, as well as the distance of the celestial observer-body. You need to know the apparent magnitude for the Olympics. The apparent magnitude is on a logarithmic scale. The first time you need to know a logarithm. A logarithm is the reverse operation of rising to power. So from this we deduce that the logarithm of a number is the exponent at which another fixed number, the base, must be raised to produce that number. Example: log2 (32) means 5, because 2 at power 5 is 32. On that logarithmic scale, the small thousandth value corresponds to the larger brightness. 3 to the power of m. 0. or 3.0 m. In 1200 BC. Astronomer Hipparchus made 6 categories of stars of varying magnitudes, so in 1856, Pogson said that a star of magnitude 1 is a hundred times brighter than one of magnitude 6. He also said that each magnitude has an increase or decrease factor equal to 2,512. Stars emit energy across the spectrum, we can calculate their brightness, but the human eye will always see the spectrum to which it is sensitive. That's all there was to the brightness, we move to brightness that is measured in watts or as a multiple of L ○ (solar brightness). To give you an idea, one watt represents 1 Joule / sec. And the brightness of the Sun is: 3.86 x (10 to the power of 26) W. So L ○ = 3.86 x 10 ^ 26 W (10 ^ 26 = 10 at power 26), which is the amount of energy emitted per second. Take as an example the stars of Centauri A and the star Sun. They have the same brightness, but they look different, that is, Centauri A is less visible, because it is 280,000 AU (astronomical units) from Earth, and the Sun is 1 AU from Earth, so distance matters. The scientific term for apparent brightness is flux, you need to know it to determine intrinsic brightness. Parental brightness is the amount of light that reaches a surface or the Earth. Light from a star is scattered in space over larger and larger regions, subjecting to the law of inverse squares. For example, if the sun were 10 AU from Earth, it would be 10 ^ 2 dimmer, and if it were where the star of Centauri A is, it would be approx. 280,000 ^ 2 more weak. If it were at a distance of 2 AU, then the factor would be 2 ^ 2 = 4. The larger a star, the higher its brightness. And, the amount of energy that reaches our eyes is measured in W / m ^ 2. Below are examples of brightness calculations.


Okay, we're done with the luminosity and brightness exercises. But we haven't done magnitude exercises yet, so do them now, you have explained everything step by step below: 

Please note that a magnitude of a celestial body can be greater than 6 magnitudes, but for a body to be seen from Earth it must have a maximum magnitude of 6. 

3. Constellations. The constellation is one of the 88 different areas of the begging sphere. The constellation can be formed by uniting through several imaginary lines two or more stars, thus forming different things, beings, gods, animals, etc. Constellations are not something that has always been in the sky. No, they formed over time, after the stars formed. So if the stars in a constellation disappear and the constellation disappears. There are 88 constellations that you should learn for the Olympics, these are given below by NASA. After you teach them, we will show you their position in the sky. For see all constellations, please go here: https://starchild.gsfc.nasa.gov/docs/StarChild/questions/88constellations.html

4. The stars. There are extremely many stars throughout the Universe. Don't worry, it won't give you all the stars at the Olympics, it will give you maybe one or two of the most famous ones, so we have prepared a list of the brightest stars for the first 11. 

On one side is the magnitude, on the other is the name Bayer, on the other is the star and on the other is the constellation in which it is located. You don't have to remember the magnitude! You only need to remember the star and the constellation in which it is located. No one will ask you to say the magnitude of a particular star, so learn the star and the constellation it is in.

26.74            Sun                                             -
1.46               Sirius                                    α CMa                Sirius A
0.74              Canopus                               α Car                 Canopus
0.27              Rigil Kentaurus & Toliman    α Cen                Alpha Centauri A
0.05              Arcturus                               α Boo                 Arcturus
0.03              Vega                                     α Lyr                  Vega
0.11                Capella                                 α Aur                  Capella A
0.13               Rigel                                      β Ori                  Rigel
0.34              Procyon                                α CMi                 Procyon
0.46              Achernar                               α Eri                  Achernar
0.50             Betelgeuse                            α Ori                  Betelgeuse

 

5. The variation of the appearance of the sky during a day and during a year for a certain place on Earth.

Before starting this new subchapter, you should know that the movement of the celestial vault lasts 23 hours and 56 minutes and 4 seconds. That's enough if you remember 23 hours and 56 minutes. As the Earth rotates from east to west and the celestial vault opens in different phases passing from east to west. Thus each constellation always changes its horizon and appears in different parts. There are also stars in the constellations, as we told you above. But there is always a star that always points in one direction, that is called the Polar Star. It is fixed at one degree from the North Pole, meaning it is at a distance of one degree from the North Pole, it is not fixed there, but always if you go after it you will find the geographical north. due to the fact that the constellations always appear in different parts of the begging vault, a classification of them was made. This is how they turned out: 

1) Circumpolar constellations (northern and southern) 

2) Spring constellations 

3) Summer constellations 

4) Autumn constellations 

5) Winter constellations 

Each of them can appear in all seasons, but what makes them classify themselves is the fact that they look better in one season than in another! It is quite difficult to approx. which of the constellations are seen only in the north or south, because there are constellations in the north that are also seen in the south. 


So if you ask at the Olympics why a constellation is called a constellation of a certain season, say that it is called a constellation of that season, because it looks better in that season, do not say that it is only seen in that season! And the circumpolar constellations can be seen in the clear sky and at night on any day of the year. We must tell you that in summer one day you see on the vault / celestial sphere a triangle approx. isosceles (all sides equal), so they are almost equal consisting of 3 stars: Vega, Deneb and Altair. And the most beautiful season of the constellations is winter with the beautiful constellation Orion. 

6. Orientation to certain objects or celestial bodies.

This section will teach you how to navigate certain things. Even though we are in the 21st century and we have the necessary technology to be able to orient ourselves. For example with phones or Google Maps, or smart watches as well as older habits with maps or objects that we have at hand. But what happens if we forget them? Or we lose them, maybe through a forest or if we go by boat and enter an area where the compass no longer knows the direction due to some phenomena or we go to exercises, in places where there are no people, we have no signal, and the map is at just a tourist guide, and we lose sight of the guide, how can we orient ourselves? Here are the things that are always in sight, such as stars or planets, the Sun or others. The first is the old watch , if we have it at hand. How can we orient ourselves after an hour? Easy! Through a process that will always show the south. The clock is held in a horizontal position with the lower tongue facing the Sun. Then we can see that the south is the bisector of the angle formed by the small tongue of the clock, the one towards the Sun and an imaginary line that passes fixedly through the center of the clock (12 o'clock). For example, if it is 8 o'clock in the morning or evening, then the south is indicated by the correct position of the number 10 on the clock. The second method is with the position approx. of the Sun. And that's easy. It's something mathematical that repeats itself. Below you will see. The numbers in the table represent the hours. Careful! In this regard, the hours may be different in some countries, but in most, these coordinates are.


   Spring                         Summer                       Autumn                         Winter                       Direction             


     7   am                             6    am                           7   am                           8   am                         Est


    12   pm                             12  pm                          12  pm                           12  pm                         South


     5    pm                             6  pm                            6  pm                           4  pm                          West



Orientation after the shadow. By this we can establish the east and the west. It's simple! We put a stick in the Earth and mark the top of the shadow with an object. Then we wait a while for the shadow to move and mark the next peak with another object, so we get that the line that joins them and starts from the first point to the second is the east direction, and the line that joins the second point to the first is the west. Then we have the North Star. We know, the North will show, but if we don't see it, how can we find out which of the billions of stars? First we have to find the Big Dipper (constellation). Then we extend 5 times the distance between the wheels of the chariot towards the direction of the wheels and we will reach a point, called: the end of the small chariot, there at that point is the North Star. Another is the orientation after the Moon. It is about the same as the Sun with only a few changes and depends on its phases. Below you have a table with the direction that a phase of it can indicate at a certain time. Careful! It may be different in some countries, but in most it is!


 Phase of the moon                                6 am                                 6 pm                                  12 am


The first quarter                                   Not seen                             South                                   West


Full moon                                              West                                     Est                                     South


The Last quarter                                   South                               Not seen                                 Est


New Moon                                         Not seen                            Not seen                               Not seen



7. Constellations in the sky. 

In many cases at various Olympics in other countries you may be asked to show on the sky (you will be given an image with the sky at a certain date and time) some constellations, for this we recommend you to take an astronomical atlas just for that to see exactly where the constellations are and how they can be determined after a certain time and how the cardinal points are determined on the celestial vault.

Or buy a sheet with a celestial vault or celestial sphere to see the constellations.


8. We know it was a little bigger chapter, but also beautiful, right? Below is a map that gives you a picture of the Earth. In Olympics can ask you things about it. 

You must know that the Greenwich meridian is the zero meridian through which the Zenith passes! 

9. Trigonometry

Attention, this chapter is difficult and is not given at all astronomy and astrophysics Olympics! It sometimes happens that some third parties ask for something like this in the category of grades 6-9, but it is a subject of carriages 10-12! Before learning this subject, please clearly check the subject limit of the country you are in! If you see trigonometry, then learn what is below, if not, then it is not mandatory, only if you want. Be careful! Trigonometry may also be given as a chapter of the celestial sphere / vault, so the best thing is to learn what is below, but the chances are low to give you, only in some countries it is given.

Source: (RechtwKugeldreieck.png) - public domain
Source: (RechtwKugeldreieck.png) - public domain

We won't hold on to it too long, you're definitely tired anyway. Trigonometry in astronomy as well as in astrophysics is actually spherical trigonometry. If so far you have learned in school that the sum of the measures of a triangle is 180 degrees and no more it is good, only that it applies only to flat triangles. Here in trigonometry, the sum of the measures of a triangle can exceed 180 degrees, and is called "spherical execs" because these triangles are on some spheres. As you can see in the picture we have three angles and three sides, and the formula of the sinuses in this drawing is: sine from angle a (Greek) on sine from side a is equal to sine from angle b (Greek) on sine from side b which is equal to sine from angle c (Greek) on sine from side c. This formula was discovered by: Abū al-Wafā 'al-Būzjānī. To calculate the sum of the angles of a spherical triangle, we can calculate it like this: we add all three angles, for example angles A, B and C. => A + B + C - 180° = E, E- spherical excesses. The area of ​​a spherical triangle is S = E x R ^ 2 (R at the power of 2). And the sum of the angles of a spherical triangle is:

Where "/" means division.

So: a,b,c angels in one triangle and A,B,C sides.

=> E= a + b + c - 180°

=> 0° < a + b + c < 360°

=> a < b + c ; a - b < c

=> 180° < A + B + C < 540°

=> A + B < 180° + C ; A - B > 180° - C

The above cases are valid in any situation! This case is a case that needs to be explained in more detail. But it's easy to learn, you just have to know that 1 radian measured in degrees = 57.296 °. So as an example: We have three angles of a spherical triangle whose sum is equal to 230 °. We subtract  180° and we obtain 50° - E. We take a problem that occurred at one of the astronomy and astrophysics Olympics. In which it was said that the radius of the earth is 6400 km and the horizontal diurnal parallax of a star is equal to 0.0025 ''. Below you have its solution, made by one of our members:

There was put 206264, 8 because 206264.8 is equal to 1 parsec. (1 pc = 206264.8). 

You should know that a radian is equal to approx. 57, 29 (more precisely 57, 296 degrees) degrees and a kiloradian is equal to approx. 5729 degrees. 

Congratulations! You finished the first chapter, you are champions, we know it was a long but beautiful chapter, right? It's amazing what you did, but to participate in an astronomy and astrophysics olympiad you have to stick with something from everything you learned, so come down we have prepared a test that will show you your level from this chapter! We also tell you how to consider the results: less than 30 = repeat everything again between 30 and 50, you learned something, but it would be good to see where you went wrong and recap that chapter between 50 and 70, you learned quite well, you could know most of the things from the Olympics to this chapter, but it would be good to see what you did wrong and to recap some portions of this chapter between 70 and 90, it's a very good thing, you may not know everything, but you will surely know a lot, but it would be good to see a little of what you did wrong and see if you can correct yourself with our explanations above between 90 and 99, you will do well, it is an extraordinary result, you will know a lot from this chapter, if you want you can look at our problems if you think it is necessary, but it is an extraordinary result 100 - you are a champion, you know everything from this chapter, you don't have to be afraid of this chapter at the Olympics, you will know, you can move on.

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