All elements of the celestial sphere. The movement of the luminaries across the sky

One of the most important astronomical problems, without which it is impossible to solve all other problems of astronomy, is to determine the position of the celestial body on the celestial sphere.

Celestial sphere is an imaginary sphere of arbitrary radius, described from the observer's eye as from the center. We project the position of all celestial bodies onto this sphere. Distances on the celestial sphere can only be measured in angular units, degrees, minutes, seconds, or radians. For example, the angular diameters of the Moon and the Sun are approximately 0. o 5.

One of the main directions relative to which the position of the observed celestial body is determined is plumb line... A plumb line anywhere in the world is directed towards the center of gravity of the Earth. The angle between the plumb line and the plane of the earth's equator is called astronomical latitude.

The plane perpendicular to the plumb line is called horizontal plane.

At every point on the Earth, the observer sees half of the sphere, smoothly rotating from east to west, together with stars as if attached to it. This apparent rotation of the celestial sphere is explained by the uniform rotation of the Earth around its axis from west to east.

The plumb line crosses the celestial sphere at a point zenith, Z and at the point nadira, Z".

Figure: 2. Heavenly sphere

The great circle of the celestial sphere along which the horizontal plane passing through the eye of the observer (point C in Fig. 2) intersects with the celestial sphere is called true horizon... Recall that the great circle of the celestial sphere is the circle passing through the center of the celestial sphere. The circles formed by the intersection of the celestial sphere with planes that do not pass through its center are called small circles.

A line parallel to the earth's axis and passing through the center of the celestial sphere is called axis of the world... She crosses the celestial sphere in north pole of the world, P, and in south pole of the world P ".

Fig. 1 it can be seen that the axis of the world is tilted to the plane of the true horizon at an angle. The apparent rotation of the celestial sphere occurs around the axis of the world from east to west, in the direction opposite to the true rotation of the Earth, which rotates from west to east.

The great circle of the celestial sphere, the plane of which is perpendicular to the axis of the world, is called celestial equator... The celestial equator divides the celestial sphere into two parts: north and south. The celestial equator is parallel to the equator of the Earth.

The plane passing through the plumb line and the axis of the world crosses the celestial sphere along the line celestial meridian... Heavenly meridian intersects with the true horizon at points north, N, and south, S... And the planes of these circles intersect along midday line... The celestial meridian is a projection onto the celestial sphere of the earth meridian where the observer is located. Therefore, there is only one meridian on the celestial sphere, because the observer cannot be on two meridians at the same time!

The celestial equator intersects with the true horizon at points east, E, and west, W... The EW line is perpendicular to the noon line. Point Q is the top of the equator and Q "is the bottom of the equator.

Large circles, the planes of which pass through the plumb line, are called verticals... The vertical passing through points W and E is called first vertical.

Large circles, the planes of which pass through the axis of the world, are called declination or hourly circles.

Small circles of the celestial sphere, the planes of which are parallel to the celestial equator, are called heavenly or diurnal parallels. They are called daily because the daily movement of heavenly bodies occurs along them. The equator is also a diurnal parallel.

The small circle of the celestial sphere, the plane of which is parallel to the plane of the horizon, is called almucantara.

Questions

1 ... Is there a place on Earth where the rotation of the celestial sphere occurs around a plumb line?

Tasks

1. Draw the celestial sphere in projection onto the horizon plane.

Decision: As you know, the projection of any point A onto any plane is the point of intersection of the plane and the perpendicular dropped from point A to the plane. The projection of a line segment perpendicular to the plane is a point. The projection of a circle parallel to the plane is the same circle on the plane, the projection of a circle perpendicular to the plane is a segment, and the projection of a circle inclined to the plane is an ellipse, the more oblate, the closer the angle of inclination is to 90 o ... Thus, in order to draw the projection of the celestial sphere onto any plane, it is necessary to lower on this plane perpendiculars from all points of the celestial sphere. The sequence of actions is as follows. First of all, it is necessary to draw a circle lying in the projection plane, in this case it will be the horizon. Then draw all points and lines that lie in the plane of the horizon. In this case, it will be the center of the celestial sphere C, and the points of south S, north N, east E and west W, as well as the noon line NS. Next, we lower the perpendiculars to the horizon plane from the rest of the celestial sphere points and obtain that the projection of the zenith Z, nadir Z "and plumb line ZZ" on the horizon plane is the point coinciding with the center of the celestial sphere C (see Fig. 3). The projection of the first vertical is the segment EW, the projection of the celestial meridian coincides with the noon line NS. The points lying on the celestial meridian: the poles P and P ", as well as the upper and lower points of the equator Q and Q" are therefore projected onto the noon line too. The equator is a large circle of the celestial sphere, tilted to the horizon plane, so its projection is an ellipse passing through the points east E, west W, and the projection points Q and Q ".

2. Draw the celestial sphere in projection onto the plane of the celestial meridian.

Decision: Shown in Fig. 4

3. Draw the celestial sphere in projection onto the plane of the celestial equator.

4. Draw the celestial sphere in projection onto the plane of the first vertical.

§ 48. Heavenly sphere. Major points, lines and circles on the celestial sphere

The celestial sphere is called a sphere of any radius centered at an arbitrary point in space. For its center, depending on the formulation of the problem, take the observer's eye, the center of the instrument, the center of the Earth, etc.

Consider the main points and circles of the celestial sphere, for the center of which is taken the eye of the observer (Fig. 72). Draw a plumb line through the center of the celestial sphere. The points of intersection of the plumb line with the sphere are called zenith Z and nadir n.

Figure: 72.

The plane passing through the center of the celestial sphere perpendicular to the plumb line is called plane of the true horizon. This plane, intersecting with the celestial sphere, forms a large circle, called the true horizon. The latter divides the celestial sphere into two parts: above-horizon and sub-horizon.

The straight line passing through the center of the celestial sphere parallel to the earth's axis is called the y axis of the world. The points of intersection of the axis of the world with the celestial sphere are called poles of the world. One of the poles, corresponding to the poles of the Earth, is called the north pole of the world and denoted by Pn, the other - the south pole of the world Ps.

The plane QQ "passing through the center of the celestial sphere perpendicular to the axis of the world is called plane of the celestial equator. This plane, intersecting with the celestial sphere, forms the circumference of a great circle - celestial equator, which divides the celestial sphere into northern and southern parts.

The great circle of the celestial sphere passing through the poles of the world, zenith and nadir, is called observer meridian PN nPsZ. The axis of the world divides the observer meridian into noon PN ZPs and midnight PN nPs.

The observer's meridian intersects with the true horizon at two points: the north point N and the south point S. The straight line connecting the points north and south is called the midday line.

If you look from the center of the sphere at point N, then the east point O st will be on the right, and the west point W on the left. Small circles of the celestial sphere aa "parallel to the plane of the true horizon are called almucantaras; small bb "parallel to the plane of the celestial equator, - heavenly parallels.

The circles of the Zon celestial sphere passing through the zenith and nadir points are called verticals. The vertical passing through the points of the east and west is called the first vertical.

The circles of the celestial sphere PNoPs passing through the poles of the world are called circles of declination.

The observer's meridian is both the vertical and the declination circle. He divides the celestial sphere into two parts - east and west.

The pole of the world located above the horizon (below the horizon) is called the elevated (lowered) pole of the world. The name of the elevated pole of the world is always the same name as the name of the latitude of the place.

The axis of the world with the plane of the true horizon makes an angle equal to the geographical latitude of the place.

The position of the luminaries on the celestial sphere is determined using spherical coordinate systems. In nautical astronomy, the horizontal and equatorial coordinate systems are used.

Heavenly sphere is called an imaginary sphere of an arbitrary radius with a center at an arbitrary point, on the surface of which the positions of the luminaries are plotted as they are visible in the sky at a certain moment in time from a given point.

The celestial sphere rotates. It is easy to verify this by simply observing the change in the position of celestial bodies relative to the observer or horizon. If you aim the camera at the Ursa Minor star and open the lens for several hours, then the images of the stars on the photographic plate will describe arcs, the central angles of which are the same (Fig. 17). Material from the site

Due to the rotation of the celestial sphere, each star moves in a small circle, the plane of which is parallel to the plane of the equator - diurnal parallel... As can be seen from Figure 18, the diurnal parallel can cross the mathematical horizon, but it does not need to cross it. The crossing of the horizon by a luminary is called sunrise, if it passes into the upper part of the celestial sphere, and setting when the light passes into the lower part of the celestial sphere. In the event that the diurnal parallel along which the luminary moves does not cross the horizon, the luminary is called non-ascending or unavailable depending on where it is: always at the top or always at the bottom of the celestial sphere.

Astronomy answer book for grade 11 for lesson number 2 (workbook) - Heavenly sphere

1. Complete the sentence.

A constellation is a section of the starry sky with a characteristic observed group of stars.

2. Using the map of the starry sky, enter in the corresponding columns of the table constellation schemes with bright stars. In each constellation, select the brightest star and indicate its name.

3. Complete the sentence.

Star charts do not indicate the position of the planets, since the charts are intended to describe the stars and constellations.

4. Place the following stars in decreasing order of magnitude:

1) Betelgeuse; 2) Spica; 3) Aldebaran; 4) Sirius; 5) Arcturus; 6) Capella; 7) Procyon; 8) Vega; 9) Altair; 10) Pollux.

5. Complete the sentence.

Stars of the 1st magnitude are 100 times brighter than stars of the 6th magnitude.

The ecliptic is the apparent annual path of the Sun among the stars.

6. What is called the celestial sphere?

An imaginary sphere of arbitrary radius.

7. Indicate the names of points and lines of the celestial sphere, indicated by numbers 1-14 in Figure 2.1.

North pole of the world
zenith; zenith point
vertical line
celestial equator
west; west point
center of the celestial sphere
midday line
south; point south
skyline
east; point east
south pole of the world
nadir; toka nadir
north point
line of the celestial meridian

8. Using Figure 2.1, answer the questions.

How is the axis of the world located relative to the earth's axis?

Parallel.

How is the axis of the world located relative to the plane of the celestial meridian?

Lies on a plane.

At what points does the celestial equator intersect with the horizon line?

At the points of the east and west.

At what points does the celestial meridian intersect with the horizon line?

At the points of the north and south.

9. What observations convince us of the daily rotation of the celestial sphere?

If you watch the stars for a long time, the stars appear to be a single sphere.

10. Using a moving star chart, write in the table two or three constellations visible at latitude 55 ° in the Northern Hemisphere.

The solution to task 10 corresponds to the reality of the events of 2015, however, not all teachers check the solution of each student's task on the star map for compliance with reality

You asked ...

What is the custom to designate the brightest stars in the constellation?

Answer. On star maps and in literature, the brightest star in the constellation is denoted by the Greek letter a (alpha), followed by the less bright b (beta), followed by gamma, etc. In addition, the designation in numbers is used, for example: the star 61 Cygnus. Some types of stars have special designations: this is how variable stars are denoted in Latin letters.

When I look at the sky, it seems to me that a spherical dome strewn with stars stretches over my head. How can this be explained?

Answer. The seemingly spherical dome is explained by the peculiarity of our eyes not to catch the difference in distances if these distances exceed 500 meters.

Why does the polar star hardly change its position?

Answer. Because it is located near the pole of the world.

How is the axis of the world located relative to the earth's axis? Answer. The axis of the world is parallel to the axis of rotation of the Earth.

What is nadir? Answer. The point is opposite the zenith.

The stars noticeably change their position from month to month from season to season. Tell me why the view of the starry sky repeats itself in a year? Answer. Remember, the period of revolution of the Earth around the Sun is a year.

What celestial circle do all the stars cross twice a day? Answer. Heavenly meridian.

Is it possible to determine by the appearance of the starry sky that you are at the North Pole of the Earth?

Answer. Yes. The North Star will always be visible almost at the zenith; during the daily rotation of the earth, the stars do not rise or set. Only the stars of the northern hemisphere are visible above the horizon.

Is it true that the Sun rotates unevenly around its axis?

Answer. Since the Sun is an incandescent plasma ball, the equatorial regions have a period of 25 days, and the pole regions - 30.

Which total eclipse (solar or lunar) is longer?

Answer. It takes a long time for the moon to pass through the earth's shadow, while the lunar shadow, which is smaller, quickly passes through a given point on the earth.

About the moon ...

During the lunar day, the temperature on the Moon changes by 300 degrees C. (+130 degrees on the sunny side, - 170 on the opposite). How can such significant temperature differences be explained?

Answer. The lunar surface has low thermal conductivity and high porosity.

Is it true that the first footprint of astronaut Neil Armstrong on the Moon, even in a million years, will look exactly the same as on July 20, 1969?

Answer. It is quite possible, since the epoch of active volcanism on the Moon has long ended, the bombardment of the surface by meteorites has practically stopped. Lack of atmosphere - speaks of the impossibility of the appearance of wind, rain.

Explain why the moon rises on average every day 50 minutes later than the day before?

Answer. The moon moves faster against the background of the starry sky than other planets that are more distant from the Earth. The speed is 13 degrees per day from west to east, in the direction opposite to the daily rotation of the celestial sphere, therefore it comes to the celestial meridian with a delay of 50 minutes. Why do planets move in a loop?

Do you know?

Wonders of the Magellanic clouds

Francesco Antonio Pigafetta, a 28-year-old native of the city of Vincenza, an expert in mathematics and maritime affairs, in 1519 decided to takethe first round the world trip. Together with Magellan, he went to the southern hemisphere of the Earth, through a narrow strait in the south of America. the Kan continent entered the Pacific Ocean and, having crossed it, participated inbattle with the natives of the Philippine Islands. In this battle, it is known Magellan died, and the badly wounded Pigafetta in the fall of 1522 returned to Seville and described in detail everything that he saw during his long travels. He especially remembered the strangeglowing clouds resembling scraps of the Milky Way. They are awkward bosom accompanied the expedition of Magellan and did not at all resemble usual cloudiness. In honor of the great traveler, Pigafetta named them the Magellanic Clouds. So for the first time a European saw blthe galaxies closest to us, completely, however, not realizing what it is. The Magellanic Clouds are relatively close to us. Large from stands from the center of our Galaxy at a distance of 182,000 St. yo, maloe - a little closer (165,000 light years). The diameter of the Big Cloud is about33,000 St. years, Small Cloud - about three times less. In fact,these are huge star systems, of which the large one unites 6 billion stars, the smaller one is about half a billion. In the Magellanic The clouds are visible binary and variable stars, star clusters and nebulae of different types. It is noteworthy that in the Big Cloud a lot of blue supergiant stars, each of which has luminosity tens of thousands of times brighter than the Sun. Both clouds belong to the type of irregular galaxies, but in In the Big Cloud, observers noticed long ago that both clouds oncewere spiral galaxies, like our star system.Now they are immersed in a discharged gas veil that stretches into side of the Galaxy, and thus both clouds and our stellar sleepralrepresent a triple galaxy. A star has long been known in the Large Magellanic Cloud S out with star Golden Fish. It's a white hot giant extraordinary starbrightness. It emits light a million times more intense than the Sun. If only S Place the Golden Fish in the place of Alpha Centauri, she would shine at night five times brighter than the full moon. Firefly and the most powerful searchlight - this is approximately the ratio in brightness between the Sun and S Golden Fish. If this amazing star could be placed in the place of the Sun, it would take up space almost to its orbit Mars and Earth would be inside a star! But Ma's wonders are not limited to this star giantgellan Clouds. In the same constellation Golden Fish where you can see Large Magellanic Cloud, glitters "A strange nebula that appearsin some scattered and torn apart ",- as Flammarion once wrote. Probably because of this appearance, the gas the nebula is named Tarantula. She reaches in across 660 St. years, and from the substance of Tarantula it would be possible to make 5 million Suns. There is nothing similar in our Galaxy, and the largest in its gas-dust nebula is many times smaller than Tarantula. If The tarantula was in the place of the famous Orion nebula, then it would occupy the entire constellation and the light from it would be like this bright at night earthly objects would cast a shadow. Source. Astronomy. Grade 11: lesson plans based on the textbook by E.P. Levitan / author-comp. V.T.Oskina. - Volgograd: Teacher, 2007.