Celestial phenomena. The most beautiful and extraordinary phenomena in our sky The photographs show various celestial phenomena

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Sometimes unusual phenomena can be observed in the sky, for which it is not immediately possible to find a reasonable explanation. If it is not the Sun, not the Moon or the stars, and besides, something moving, changing its brightness and color, then many people who are not experienced in observations tend to classify the unknown phenomenon as "unidentified flying objects." Even astronomers sometimes find many reasons that for some time mislead them about the nature of this or that "unusual" phenomenon. However, careful observation and the ability to brainwash a little usually allows you to find a natural explanation for "unusual" phenomena.

Even orienting yourself well enough among the constellations, you can accidentally forget the exact position of a particular star in them. Variable stars, as well as the appearance of new stars, albeit rare, can cause some confusion in the picture of the location of stars. Planets can also create some confusion, but they are much easier to deal with, since they are observed near the ecliptic and even to the naked eye, as a rule, they look like more permanent objects in the sky than stars. Airplanes flying with the landing lights switched on can also look like bright objects, and if they move towards the observer, then for some time they even seem to be motionless. Before sunrise or after sunset, it is also possible to observe meteorological balloons, and long-term observations allow us to notice their movement. They are usually not visible at night.

Rice. 23. The entry of a satellite into the atmosphere is accompanied by a flash of light, very similar to a bright fireball.

Table 4

Identification of Objects Observed

When observing individual stars, it appears that they are moving slightly. This is often associated with the phenomenon of flickering, but more often it is explained by an optical illusion, from which no one is spared. Of course, many celestial bodies really move among the stars: the planets - slowly, the moon - a little faster. Small planets, or asteroids, as a rule, slowly change their position from night to night, but, being near the Earth, they can move much faster. Move faster across the sky Balloons, airplanes (most often equipped with colored and flashing lights) and satellites; their apparent movement significantly depends on the latitude and distance to them. Artificial satellites move across the sky much slower than meteors and fireballs, although their apparent speed depends on the altitude of the orbit (with the exception of geostationary satellites). In addition, satellites often disappear, falling into the shadow of the Earth (and reappearing, leaving it). As it enters the Earth's atmosphere, a flash of light occurs, similar to a fireball, but it travels much more slowly. And finally, the illusion of a faint meteor can be created by night birds if they, swiftly sweeping low above the Earth, fall into a strip of light.

“The appearance of luminous foggy formations in the sky can be explained by various reasons, depending on their size. Zodiacal light can only be observed along the ecliptic above the eastern or western part horizon. The aurora, especially at the very initial stage, is sometimes mistaken for a cloud illuminated by a distant light source. True noctilucent clouds have a very specific appearance and only appear around midnight. Rocket launches and artificial emissions of substances for the purpose of studying the atmosphere produce a colored glow, reminiscent of the pattern of aurora borealis. With binoculars and telescopes, star clusters, galaxies, gas and dust nebulae, and infrequent comets are also visible as small hazy spots.

The rapid color change of stars is usually due to scintillation, which is most noticeable in stars located low above the horizon. Refraction can contribute to the color fringing of planetary disks, especially if the latter are located low above the horizon.

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Zodiacal light

Zodiacal light very often disguises moonlight and artificial city light. On a quiet moonless night in nature, the likelihood that you will see the zodiacal light is quite high. This phenomenon is observed as a result of the reflection of sunlight from particles of cosmic dust that surrounds the Earth.

Rainbow wall

A rare atmospheric phenomenon also known as the "fire rainbow" occurs when the horizontal rays of the rising or setting sun are refracted through horizontally located cloud ice crystals. The result is a kind of wall painted in different colors rainbows. Photo taken in the sky of Washington in 2006.

The sun's rays are reflected from ice crystals located at an angle of 22 ° in relation to the Sun in high-altitude clouds. Different positions of ice crystals can cause halo modifications. On frosty days, the effect of "diamond dust" can be observed, in which case the sun's rays are repeatedly reflected from ice crystals.

Aircraft contrails

Aircraft exhaust and eddy currents on high altitudes turn ice particles into water. The long white streaks high in the sky are nothing more than suspended water droplets.

Twilight rays

The sun's rays from the setting sun, passing through the gaps in the clouds, form clearly visible separate beams sunlight... Very often, such sunbeams can be seen in various science fiction films. This photo was taken in one of Utah's national parks.

northern Lights

The Northern Lights are nothing more than a collision in the upper atmosphere of the sun's rays with charged gas particles magnetic field Earth.

Star trails

Visual demonstration of the rotation of the Earth. This phenomenon is invisible to the normal eye. To get such a photo, you need to set the camera to a long exposure. In the picture, only the single Polaris, located almost above the axis of the Earth, remains almost motionless.

White rainbow

Photo taken on the Golden Gate Bridge in San Francisco. The small size of air droplets of water makes it impossible for the sun's rays to decompose into color spectra, so the rainbow is only white.

Buddha light

This photo was taken in China. The phenomenon is similar to the "ghost of Brocken". The sun's rays are reflected from atmospheric water droplets over the sea, the shadow in the middle of the rainbow circle of reflected rays is the shadow of the plane.

Inverted rainbow

Such an unusual rainbow also appears as a result of the refraction of sunlight through ice crystals located only in certain parts of the clouds.

A very common atmospheric phenomenon. It can be observed not only in the desert, but also on the road in the sultry heat. This phenomenon is formed as a result of the refraction of sunlight through the "lens" formed by layers of colder (near the surface of the earth) and warmer (located above) air. This kind of lens reflects objects located above the horizon line, in this case the sky. Photo taken in Thuringia, Germany.

Iridescent clouds

The rays of the setting sun at right angles "stumble" on the water droplets of the clouds. As a result of diffraction (bending of water droplets by the sun's rays) and interference of the sun's rays (decomposition of the sun's rays into spectra), as in Photoshop, the shape of the cloud is filled with a gradient fill.

Rocket exhaust trail

Trail of a Minotaur rocket launched by the US Air Force in California. Air currents blowing at different heights at different speeds distort the trail of rocket exhaust. Atmospheric water droplets and melted ice crystals also cause sunlight to decompose into different colors of the rainbow.

Brocken's ghost, Germany

This phenomenon is observed on foggy mornings. The rainbow disc of the sun appears opposite the sun, as a result of the reflection of the sun's rays from the water droplets of fog. The curious triangular shadow tearing apart the rainbow disc of reflected sun rays is nothing more than a projection of the upper surface of the clouds.

Celestial phenomena ... Many people have witnessed unusual phenomena that took place both day and night. All this fascinates those who saw these phenomena and raises a lot of questions and disputes among those who could not do it.

The philosopher of the Middle Ages Thomas Aquinas is absolutely right in his statement: A miracle is a phenomenon that contradicts not the laws of nature, but our idea of these laws.

The 90s of the twentieth century were rich in celestial phenomena... And in the twentieth century, the century of technogenic progress ...

A lot of people have witnessed unusual phenomena that took place both day and night. All this fascinates those who saw these phenomena and raises a lot of questions and disputes among those who could not do it.

The philosopher of the Middle Ages Thomas Aquinas is absolutely right in his statement: "A miracle is a phenomenon that contradicts not the laws of nature, but our idea of these laws."

The 90s of the twentieth century were rich in heavenly phenomena. And in the twentieth century, the century of technogenic progress, in all of it ...

In a homogeneous medium, light propagates in a straight line only, and at the border of two media, the light beam is refracted. Such an inhomogeneous medium is, in particular, the air of the earth's atmosphere: its density increases near the earth's surface.

The beam of light is bent, and as a result, the luminaries look somewhat displaced, "elevated" relative to their true positions in the sky. This phenomenon is called refraction (from Latin refractus - "refracted").

Refraction is especially strong when ...

On December 9, between 7.00 am - 9.00 am local time, an extremely amazing celestial phenomenon occurred over Norway. It is so surprising that it did not make it into the world's news broadcasts, and is now discussed only by eyewitnesses (there are thousands of them) in their blogs.

(One of these eyewitnesses was our reader, Vladimir from Norway, who told us about this and also managed to take several pictures on his mobile phone and kindly sent the pictures to the editorial office). At the moment, the network does not yet have a complete ...

The Celestial Disc from Nebra is one of the most curious and, according to some scholars, controversial archaeological finds. recent years... It is a bronze disc from 1600 BC. NS. It measures 32cm in diameter (roughly the same size as a vinyl record) and weighs about 4 pounds.

The disc is painted blue-green and covered with gold leaf symbols. It contains a crescent moon, sun (or full moon), stars, an arched border (which is called a solar boat) and ...

I first met this amazing phenomenon in 1985 in Moscow. It was a rare success - I was holding in my hands the official report of the Coptic Patriarchate about this phenomenon (with photos !!!), where the Patriarchate confirmed that this phenomenon was not fiction.

Examples of phenomenal healings of people from incurable diseases during this phenomenon were given. To confirm the truth, the following were given: the patient's full name and surname, his place of residence, the exact diagnosis, as well as: the full name and surname of the treating person ...

Space and surroundings Solar system saturated with a lot of "heavenly debris". It consists of rock-like pieces of hard rock, chunks of ice and frozen gases. These can be asteroids or comets orbiting the Sun in complex orbits.

Their size ranges from a few kilometers to a millimeter. Such celestial objects bombard the Earth every day, and it is only thanks to the atmosphere that they most often burn out before reaching the surface of the planet.

Throughout history ...

IN JANUARY 1995, the German Astronomical Journal published short message, to which all scientific, religious and popular publications of the planet immediately responded. Each publisher drew the attention of its readers to completely different aspects of this message, but the essence boiled down to one thing: the Abode of God was discovered in the Universe.

After decoding a series of images transmitted from the Hubble telescope on film ...

The new discovery, unveiled this week by NASA, is very important for future lunar explorers: astronauts may find themselves "crackling from electricity like a sock pulled out of a hot electric dryer," according to the agency ...

Exercise 1

The photographs show various celestial phenomena. Indicate what kind of phenomenon is depicted in each image, bearing in mind that the images are not inverted, but observations were made from the middle latitudes of the Northern Hemisphere of the Earth.

Answers

Please note that the question asks about what phenomenon is depicted in the picture (and not the object!). Based on this, the assessment is made.

meteor (1 point; “meteorite” or “fireball” does not count);
meteor shower (another option is “meteor shower”) (1 point);
covering Mars by the Moon (another option is “covering the planet by the Moon”) (1 point);
sunset (1 point);
covering the star by the Moon (possible short version"Coverage") (1 point);
Moonset (the possible answer is “neomenia” - the first appearance of the young Moon in the sky after the new moon) (1 point);
annular solar eclipse(a short version "solar eclipse" is possible) (1 point);
lunar eclipse (1 point);
the opening of a star by the Moon (the "end of coverage" option is possible) (1 point);
total solar eclipse (the variant "solar eclipse" is possible) (1 point);
the passage of Venus along the disk of the Sun (the variant "the passage of Mercury along the disk of the Sun" or "the passage of the planet along the disk of the Sun" is possible) (1 point);
ash light of the moon (1 point).

Note: all valid answer choices are in parentheses.

The maximum for a task is 12 points.

Assignment 2

The figures show the figures of several constellations. Each figure has its number underneath. Indicate in the answer the name of each constellation (write down the pairs "figure number - name in Russian").

Answers

Swan (1 point);
Orion (1 point);
Hercules (1 point);
Big Dipper(1 point);
Cassiopeia (1 point);
Leo (1 point);
Lyra (1 point);
Cepheus (1 point);
Eagle (1 point).

Maximum per task - 9 points.

Assignment 3

Draw the correct shift sequence lunar phases(it is enough to draw the main phases) when observing from the middle latitudes of the Northern Hemisphere of the Earth. Sign their names. Start the drawing with a full moon, shade the parts of the moon that are not illuminated by the Sun.

Answer

One of possible options picture (2 points for the correct option):

The main phases are usually considered the full moon, last quarter, new moon, first quarter (3 points). The phases of the moon are listed here in the order in which they are shown in the figure.

In the absence of one of the phases in the figure, 1 point is deducted. For an erroneous indication of the name of the phase, 1 point is deducted. The score for a task cannot be negative.

When evaluating a drawing, one should pay attention to the fact that the terminator (the light / dark boundary on the surface of the Moon) passes through the poles of the Moon (that is, it is unacceptable to draw a phase like a "bitten off apple"). If this is not the case in the answer, the mark is reduced by 1 point.

Note: the solution contains the minimum version of the figure. It is not necessary to draw the full moon again at the end. The image of intermediate phases is acceptable:

Maximum per task - 5 points.

Assignment 4

The relative position of Mars, Earth and the Sun at some point in time is shown in the figure. At the same time, the moon is observed in conjunction with Mars. What is the phase of the moon at this moment? Explain the answer.

Answer

At the described position of the Moon, the last quarter will be observed (4 points). The answer "first quarter" is estimated at 1 point. The answer "a quarter" is worth 2 points. The answer "the left side of the moon will be illuminated" is estimated at 1 point.

Maximum per task - 4 points.

Assignment 5

What is the average speed of the day / night boundary along the surface of the Moon (R = 1738 km) in the region of its equator? Express your answer in km / h and round to the nearest whole. For reference: the synodic period of the Moon's revolution (the period of changing the lunar phases) is approximately 29.5 days, the sidereal period of revolution (the period of the axial rotation of the Moon) is approximately 27.3 days.

Answer

The length of the Moon's equator L = 2πR ≈ 2 × 1738 × 3.14 = 10 920.2 km (1 point). To solve the problem, it is necessary to use the value of the synodic period of revolution, since not only the rotation of the Moon around its axis is responsible for the movement of the day / night boundary on the surface of the Moon, but also the position of the Sun relative to the Moon, which changes due to the movement of the Earth in its orbit. The lunar phase change period is P ≈ 29.5 days. = 708 hours (2 points - if there is no explanation why this particular period was used; 4 points - if there is a correct explanation; 1 point for using the sidereal period). This means that the speed will be V = L / P = 10 920.2 / 708 km / h ≈ 15 km / h (1 point; this point is given for calculating the speed, including when using the value 27.3 - the answer will be 16.7 km / h).

Note: the solution can be done "in one line". At the same time, the score does not decrease. For an answer without a decision, the score is 1 point.

Maximum per task - 6 points.

Assignment 6

Are there regions on Earth (if so, where are they located) where at some point in time all the zodiacal constellations are on the horizon?

Answer

As you know, constellations are called zodiacal constellations along which the Sun passes, that is, which the ecliptic crosses. Hence, it is necessary to determine where and when the ecliptic coincides with the horizon. At this moment, not only the planes of the horizon and the ecliptic will coincide, but also the poles of the ecliptic with the zenith and nadir. That is, at this moment one of the poles of the ecliptic passes through the zenith. The coordinates of the north pole of the ecliptic (see figure):

δ n = 90 ° - ε = 66.5 °

and southern, because it is at the opposite point:

δ n = - (90 ° - ε) = –66.5 °

α n = 6 h

A point with a declination of ± 66.5 ° culminates at the zenith of the Arctic Circle (North or South): h = 90 - φ + δ.

Of course, deviations from the polar circle by several degrees are possible, since the constellations are fairly extended objects.

The score for the problem (full solution - 6 points) consists of the correct explanation of the condition (the culmination of the ecliptic pole at the zenith or, for example, the simultaneous upper and lower culmination of two opposite points of the ecliptic on the horizon), at which the described situation is possible (2 points), the correct definition latitude of observation (3 points), indicating that there will be two such areas - in the Northern and Southern hemispheres of the Earth (1 point).

Note: it is not necessary to determine the coordinates of the poles of the ecliptic, as is done in the solution (you can know them). Let us assume a different course of solution.

Maximum per task - 6 points.

Total for work - 42 points.

Answers and evaluation criteria

Exercise 1

The photographs show various celestial phenomena. Indicate what for

the phenomenon is depicted in each picture, bearing in mind that the pictures are not

inverted, and observations were made from the middle latitudes of the North

hemisphere of the Earth.

All-Russian Olympiad schoolchildren in astronomy 2016–2017 academic year G.

Municipal stage. 8-9 grades

Answers Please note that the question asks about what phenomenon is shown in the picture (and not the object!). Based on this, the assessment is made.

1) meteor (1 point; “meteorite” or “fireball” are not counted);

2) meteor shower (another option is “meteor shower”) (1 point);

3) covering Mars by the Moon (another option is “covering the planet by the Moon”) (1 point);

4) sunset (1 point);

5) the covering of the star by the Moon (the short version “covering” is possible) (1 point);

6) the setting of the moon (the possible answer is "neomenia" - the first appearance of the young moon in the sky after the new moon) (1 point);

7) annular solar eclipse (a short version "solar eclipse" is possible) (1 point);

8) lunar eclipse (1 point);

9) the opening of the star by the Moon (the option “end of coverage” is possible) (1 point);

10) total solar eclipse (the variant "solar eclipse" is possible) (1 point);

11) the passage of Venus across the disk of the Sun (the option “the passage of Mercury along the disk of the Sun” or “the passage of the planet along the disk of the Sun” is possible) (1 point);

12) ash light of the moon (1 point).

Note: all valid answer choices are written in brackets.

The maximum for a task is 12 points.

Task 2 The figures show the figures of several constellations. Each figure has its number underneath. Indicate in the answer the name of each constellation (write down the pairs "figure number - name in Russian").

2 All-Russian Olympiad in Astronomy for Schoolchildren 2016–2017 academic year G.

Municipal stage. Grades 8-9 Answers

1) Swan (1 point);

2) Orion (1 point);

3) Hercules (1 point);

4) Ursa Major (1 point);

5) Cassiopeia (1 point);

6) Leo (1 point);

7) Lyra (1 point);

8) Cepheus (1 point);

9) Eagle (1 point).

The maximum for a task is 9 points.

3 All-Russian Olympiad for schoolchildren in astronomy 2016–2017 academic year G.

Municipal stage. Grades 8-9 Task 3 Draw the correct sequence of the change of lunar phases (it is enough to draw the main phases) when observing from the middle latitudes of the Northern Hemisphere of the Earth. Sign their names. Start the drawing with the full moon, shade the parts of the moon that are not illuminated by the Sun.

One of the possible variants of the picture (2 points for the correct variant):

The main phases are usually considered the full moon, the last quarter, the new moon, the first quarter (3 points). The phases of the moon are listed here in the order in which they are shown in the figure.

In the absence of one of the phases in the figure, 1 point is deducted. For an erroneous indication of the name of the phase, 1 point is deducted. The score for a task cannot be negative.

Note: the solution contains the minimum version of the figure. It is not necessary to draw the full moon again at the end.

The image of intermediate phases is acceptable:

The maximum for a task is 5 points.

4 All-Russian Olympiad in Astronomy for Schoolchildren 2016–2017 academic year G.

Municipal stage. Grades 8-9 Task 4 Mars, in the eastern quadrature, and the Moon are observed in conjunction. What is the phase of the moon at this moment? Explain the answer, give a picture, which depict the described situation.

Answer The figure shows the positions of all bodies participating in the described situation (such a figure should be given in the work: 3 points). With this position of the Moon relative to the Earth and the Sun, the first quarter (the growing Moon) will be observed (2 points).

Note: the figure may be slightly different (for example, the view mutual disposition luminaries in the sky for an observer on the surface of the Earth), the main thing is that the relative position of the bodies is indicated correctly and it is clear why the Moon will be exactly in the phase that is given in the answer.

The maximum for a task is 5 points.

Task 5 What is the average speed of the day / night boundary along the surface of the Moon (R = 1738 km) in the region of its equator? Express your answer in km / h and round to the nearest whole.

For reference: the synodic period of the Moon's revolution (the period of changing the lunar phases) is approximately equal to 29.5 days, the sidereal period of revolution (the period of the axial rotation of the Moon) is approximately 27.3 days.

Answer The length of the equator of the Moon L = 2R 2 1738 3.14 = 10 920.2 km (1 point). To solve the problem, it is necessary to use the value of the synodic period 5 All-Russian Olympiad for schoolchildren in astronomy 2016–2017 academic year. G.

Municipal stage. 8-9 classes of circulation, because not only the rotation of the Moon around its axis is responsible for the movement of the day / night boundary on the surface of the Moon, but also the position of the Sun relative to the Moon, which changes due to the movement of the Earth in its orbit. The lunar phase change period is P 29.5 days. = 708 hours (2 points - if there is no explanation why this particular period was used; 4 points - if there is a correct explanation; 1 point for using the sidereal period). This means that the speed will be V = L / P = 10 920.2 / 708 km / h 15 km / h (1 point; this point is given for calculating the speed, including when using the value 27.3 - the answer will be 16 , 7 km / h).

Note: the solution can be done "in one line". At the same time, the score does not decrease. For an answer without a decision, the score is 1 point.

Task 6 Are there regions on Earth (if so, where are they located) where at some point in time all the zodiacal constellations are on the horizon?

Answer As you know, constellations are called zodiacal constellations along which the Sun passes, that is, which the ecliptic crosses. Hence, it is necessary to determine where and when the ecliptic coincides with the horizon. At this moment, not only the planes of the horizon and the ecliptic will coincide, but also the poles of the ecliptic with the zenith and nadir. That is, at this moment one of the poles of the ecliptic passes through the zenith. The coordinates of the north pole of the ecliptic (see.

drawing):

90 ° 66.5 ° and south, because it is at the opposite point:

90 ° 66.5 ° A point with a declination of ± 66.5 ° culminates at the zenith of the Arctic Circle (North or South) :.

Of course, deviations from the polar circle by several degrees are possible, since.

constellations are fairly extended objects.

The score for the problem (complete solution - 6 points) consists of the correct explanation of the condition (the culmination of the ecliptic pole at the zenith, or, for example, the simultaneous upper and lower culmination of two opposite points 6 All-Russian Olympiad in Astronomy for Schoolchildren 2016–2017 academic year)

Municipal stage. 8-9 grades of the ecliptic on the horizon), in which the described situation is possible (3 points), the correct determination of the observation latitude (2 points), an indication that there will be two such areas - in the Northern and Southern hemispheres of the Earth (1 point).

Note: it is not necessary to determine the coordinates of the poles of the ecliptic, as is done in the solution (you can know them). Let us assume a different course of solution.

The maximum for a task is 6 points.

- & nbsp– & nbsp–

Option 2 You can not immediately substitute numerical values in the formulas, but transform them by expressing the period of circulation through medium density Moon (the density value is not given in the condition, but the student can calculate it or know it - an approximate value of 3300 kg / m3):

- & nbsp– & nbsp–

(here M is the mass of the Sun, m is the mass of the satellite, Tz, mz and az are the period of the Earth's revolution around the Sun, the mass of the Earth and the radius of the Earth's orbit, respectively).

It is possible to write this law for another set of bodies, for example, for the Earth-Moon system (instead of the Sun-Earth system).

Neglecting small masses in comparison with large ones, we get:

- & nbsp– & nbsp–

And the period of the appearance of the station near the limb will be half the orbital:

Assessment Other solutions are also valid. All solution options should lead to the same answers (some deviations are allowed due to the fact that in options 2 and 3, as well as in other options, slightly different numerical values may be used).

Options 1 and 2. Determination of the satellite orbit length (2Rl 10 920 km) - 1 point; determination of the satellite orbital speed Vl - 2 points; computation 8 All-Russian Olympiad for schoolchildren in astronomy 2016–2017 academic year G.

Municipal stage. 8-9 grades of the circulation period - 1 point; finding the answer (dividing the orbital period by 2) - 2 points.

Option 3. Writing Kepler's third law in a refined form for the bodies participating in the problem - 2 points (if the law is written in general view and this is where the solution ends - 1 point).

Correct neglect of small masses (i.e., the mass of the satellite in comparison with the mass of the Moon, the mass of the Earth in comparison with the mass of the Sun, the mass of the Moon in comparison with the mass of the Earth) - 1 point (these masses can be immediately omitted in the formula, a point for all this equally exposed). Writing the expression for the satellite period - 1 point, finding the answer (dividing the orbital period by 2) - 2 points.

For exceeding the accuracy in the final answer (the number of decimal places is more than two), 1 point is deducted.

Note: you do not need to neglect the orbital altitude in comparison with the radius of the Moon (the numerical answer will hardly change). It is allowed to immediately use the ready-made formula for the circulation period (the last form of writing the formula in the solution in option 2) - the score for this does not decrease (with correct calculations - 4 points for this stage of the solution).

The maximum for a task is 6 points.

Task 8 Suppose scientists have created a stationary Large Polar Telescope to observe the diurnal rotation of stars directly near the pole of the world, directing its tube exactly at North Pole the world. Precisely in the center of their field of view, they found a Very Interesting Extragalactic Source. This telescope has a field of view of 10 arc minutes. In how many years will scientists no longer be able to observe this Source with this telescope?

Answer The Pole of the World revolves around the Pole of the Ecliptic with a period of approximately Tp 26,000 years (1 point). The angular distance between these poles (2 points) is nothing more than 23.5 ° (that is, 90 ° is the angle of inclination of the Earth's axis of rotation to the plane of the ecliptic). Since the pole of the world moves in a small circle of the celestial sphere, the angular velocity of its movement relative to the observer will be less angular velocity rotation of a point on the celestial equator by 1 / sin () times (2 points).

Since initially the telescope looks exactly at the pole of the world and at the Source, the maximum possible time Source observations will be:

15 years old (3 points).

° After this time, the Source will leave the field of view of the telescope (the pole of the world will remain in the center of the field, since the telescope is stationary on Earth, 9 All-Russian Olympiad for Schoolchildren in Astronomy 2016–2017 academic year)

Municipal stage. 8-9 grades being initially directed to the pole of the world; recall that the pole of the world is essentially the point of intersection of the continuation of the Earth's axis of rotation with the celestial sphere).

If in the final answer the student does not share the position of the pole of the world and the Source, then with the correct numerical answer, no more than 6 points are given.

Note: everywhere in the solution you can use cos (90-) or cos (66.5 °) instead of sin (). Other solutions to the problem are possible.

The maximum for a task is 8 points.