1.2 Some important concepts and formulas from general astronomy

Before proceeding to the description of eclipsing variable stars, to which this work is devoted, let us consider some basic concepts that we will need in what follows.

The stellar magnitude of a celestial body is the measure of its brightness adopted in astronomy. Brilliance is the intensity of light reaching the observer or the illumination created at the radiation receiver (eye, photographic plate, photomultiplier, etc.) The brilliance is inversely proportional to the square of the distance separating the source and the observer.

The magnitude m and the magnitude E are related by the formula:

In this formula, E i is the brightness of the star of the m i-th stellar magnitude, E k is the brightness of the star of the m k-th stellar magnitude. Using this formula, it is easy to see that the stars of the first magnitude (1 m) are brighter than the stars of the sixth magnitude (6 m), which are visible at the limit of visibility of the naked eye exactly 100 times. It was this circumstance that formed the basis for the construction of the magnitude scale.

Taking the logarithm of formula (1) and taking into account that lg 2.512 = 0.4, we get:

, (1.2)

(1.3)

The last formula shows that the magnitude difference is directly proportional to the logarithm of the magnitude ratio. The minus sign in this formula indicates that the magnitude increases (decreases) with decreasing (increasing) brightness. The difference in magnitude can be expressed not only as an integer, but also as a fractional number. With the help of high-precision photoelectric photometers, it is possible to determine the difference in magnitude with an accuracy of 0.001 m. The accuracy of visual (eye) estimates of an experienced observer is about 0.05 m.

It should be noted that formula (3) allows calculating not stellar magnitudes, but their differences. To build a scale of magnitudes, you need to select some zero point (origin) of this scale. Approximately it can be considered such a zero point Vega (a Lyrae) - a star of zero magnitude. There are stars with negative magnitudes. For example, Sirius (a Canis Major) is the brightest star in the earth's sky and has a magnitude of -1.46 m.

The brilliance of a star, assessed by the eye, is called visual. It has a stellar magnitude denoted by m u. or m visas. ... The brightness of stars, assessed by their image diameter and the degree of blackening on a photographic plate (photographic effect) is called photographic. It corresponds to the photographic stellar magnitude m pg or m phot. The difference C = m pg - m phot, depending on the color of the star, is called the color index.

There are several conventionally accepted magnitude systems, of which the most widespread magnitude systems are U, B, and V. The letter U denotes ultraviolet magnitudes, B — blue (close to photographic), V — yellow (close to visual). Accordingly, two color indices are determined: U - B and B - V, which are equal to zero for pure white stars.

Theoretical information about eclipsing variable stars

2.1 Discovery history and classification of eclipsing variable stars

The first eclipsing variable star Algol (b Perseus) was discovered in 1669. Italian mathematician and astronomer Montanari. He first explored it at the end of the 18th century. English astronomy lover John Goodrike. It turned out that the single star b Perseus, visible to the naked eye, is in fact a multiple system that does not separate even with telescopic observations. Two of the stars in the system revolve around a common center of mass in 2 days, 20 hours and 49 minutes. At certain points in time, one of the stars included in the system closes the other from the observer, which causes a temporary weakening of the total brightness of the system.

The brightness curve of Algol, which is shown in Fig. 1

This graph is based on accurate photoelectric observations. Two weakening of brightness are visible: a deep primary minimum - the main eclipse (the bright component is hidden behind a weaker one) and a slight decrease in brightness - a secondary minimum, when the brighter component eclipses the weaker one.

These phenomena are repeated after 2.8674 days (or 2 days 20 hours 49 minutes).

It can be seen from the graph of the brightness change (Fig. 1) that Algol begins to rise immediately after reaching the main minimum (the smallest brightness value). This means that a partial eclipse is occurring. In some cases, a total eclipse can also be observed, which is characterized by the preservation of the minimum brightness of the variable in the main minimum for a certain period of time. For example, in the eclipsing variable star U Cephei, which is accessible to observations with strong binoculars and amateur telescopes, in the main minimum, the duration of the full phase is about 6 hours.

Carefully examining the Algol brightness change graph, one can find that between the main and secondary minima, the star's brightness does not remain constant, as it might seem at first glance, but changes slightly. This phenomenon can be explained as follows. Outside the eclipse, light reaches the Earth from both components of the binary system. But both components are close to each other. Therefore, a weaker component (often larger in size) illuminated by a bright component scatters the incident radiation. Obviously, the largest amount of scattered radiation will reach the terrestrial observer at the moment when the weak component is located behind the bright one, i.e. near the moment of the secondary minimum (theoretically, this should occur immediately at the moment of the secondary minimum, but the total brightness of the system sharply decreases due to the fact that one of the components is eclipsed).

This effect is called the reradiation effect. On the graph, it manifests itself as a gradual rise in the total brightness of the system as it approaches the secondary minimum and decreases in brightness, which is symmetric to its increase relative to the secondary minimum.

In 1874. Goodrike discovered the second eclipsing variable star, b Lyrae. It changes brilliance relatively slowly with a period of 12 days 21 hours 56 minutes (12.914 days). In contrast to Algol, the light curve has a smoother shape. (Fig. 2) This is due to the proximity of the components to each other.

The tidal forces arising in the system force both stars to stretch along the line connecting their centers. The components are no longer spherical, but ellipsoidal. During orbital motion, the disks of the components, which have an elliptical shape, smoothly change their area, which leads to a continuous change in the brightness of the system even outside the eclipse.

In 1903. the eclipsing variable W of the Big Dipper was discovered, in which the orbital period is about 8 hours (0.3336834 days). During this time, two minima of equal or almost equal depth are observed (Fig. 3). The study of the light curve of the star shows that the components are almost equal in size and almost touching surfaces.

In addition to stars like Algol, b Lyrae and W Ursa Major, there are rarer objects that are also referred to as eclipsing variable stars. These are ellipsoidal stars that rotate around an axis. Changing the area of ​​the disc causes slight changes in gloss.

Hydrogen, while stars with a temperature of about 6 thousand K. have lines of ionized calcium located at the border of the visible and ultraviolet parts of the spectrum. Note that the spectrum of our Sun has such a form I. The sequence of spectra of stars, obtained with a continuous change in the temperature of their surface layers, is denoted by the following letters: O, B, A, F, G, K, M, from the hottest to ...

No lines will be observed (due to the weakness of the satellite's spectrum), but the lines of the main star's spectrum will fluctuate in the same way as in the first case. The periods of changes occurring in the spectra of spectroscopic binary stars, which are obviously also the periods of their revolution, are very different. The shortest known period is 2.4H (g Ursa Minor), and the longest is tens of years. For...

Questions.

1. The visible movement of the luminaries as a result of their own movement in space, the rotation of the Earth and its revolution around the Sun.
2. Principles of determining geographic coordinates from astronomical observations (P. 4 p. 16).
3. The reasons for the change in the phases of the moon, the conditions of the onset and the frequency of solar and lunar eclipses (P. 6 pp 1.2).
4. Features of the diurnal movement of the Sun at different latitudes at different times of the year (A.4, pp 2, P. 5).
5. The principle of operation and purpose of the telescope (P. 2).
6. Methods for determining the distances to the bodies of the solar system and their sizes (P. 12).
7. Possibilities of spectral analysis and extra-atmospheric observations for studying the nature of celestial bodies (P. 14, "Physics" P. 62).
8. The most important directions and tasks of research and exploration of outer space.
9. Kepler's law, its discovery, meaning, limits of applicability (P. 11).
10. The main characteristics of the terrestrial planets, giant planets (P. 18, 19).
11. Distinctive features of the Moon and satellites of the planets (P. 17-19).
12. Comets and asteroids. Basic ideas about the origin of the solar system (P. 20, 21).
13. The sun is like a typical star. Main characteristics (P. 22).
14. The most important manifestations of solar activity. Their connection with geographical phenomena (P. 22, item 4).
15. Methods for determining distances to stars. Distance units and the relationship between them (P. 23).
16. The main physical characteristics of stars and their relationship (P. 23 pp 3).
17. The physical meaning of the Stefan-Boltzmann law and its application to determine the physical characteristics of stars (P. 24 pp 2).
18. Variable and non-stationary stars. Their significance for studying the nature of stars (P. 25).
19. Binary stars and their role in determining the physical characteristics of stars.
20. Evolution of stars, its stages and final stages (P. 26).
21. Composition, structure and size of our Galaxy (P. 27 pp 1).
22. Star clusters, the physical state of the interstellar medium (P. 27, item 2, P. 28).
23. The main types of galaxies and their distinctive features (P. 29).
24. Foundations of modern ideas about the structure and evolution of the Universe (P. 30).

Practical tasks.

1. Star map assignment.
2. Determination of geographic latitude.
3. Determination of the declination of a luminary by latitude and altitude.
4. Calculation of the size of the star by parallax.
5. Conditions of visibility of the Moon (Venus, Mars) according to the school astronomical calendar.
6. Calculation of the orbital period of the planets based on Kepler's 3rd law.

Answers.

Ticket number 1. The Earth makes complex movements: it rotates around its axis (T = 24 hours), moves around the Sun (T = 1 year), rotates with the Galaxy (T = 200 thousand years). This shows that all observations made from the Earth differ in apparent trajectories. The planets are divided into internal and external (internal: Mercury, Venus; external: Mars, Jupiter, Saturn, Uranus, Neptune and Pluto). All of these planets revolve in the same way as the Earth around the Sun, but due to the movement of the Earth, one can observe the loop-like movement of the planets (calendar page 36). Due to the complex motion of the Earth and the planets, various configurations of the planets arise.

Comets and meteorite bodies move along elliptical, parabolic and hyperbolic trajectories.

Ticket number 2. There are 2 geographic coordinates: geographic latitude and geographic longitude. Astronomy as a practical science allows you to find these coordinates (figure "the height of the star at the upper culmination"). The height of the pole of the world above the horizon is equal to the latitude of the place of observation. You can determine the latitude of the observation site by the height of the luminary at the upper culmination ( Climax- the moment the luminary passes through the meridian) according to the formula:

h = 90 ° - j + d,

where h is the height of the luminary, d is the declination, j is the latitude.

Geographic longitude is the second coordinate, measured from the zero meridian of Greenwich to the east. The earth is divided into 24 time zones, the time difference is 1 hour. The difference in local times is equal to the difference in longitudes:

l m - l Gr = t m - t Gr

Local time- this is the solar time in a given place on the Earth. At each point, the local time is different, so people live according to standard time, that is, according to the time of the middle meridian of a given belt. The date line runs in the east (Bering Strait).

Ticket number 3. The moon moves around the earth in the same direction in which the earth rotates around its axis. The reflection of this movement, as we know, is the apparent movement of the Moon against the background of stars towards the rotation of the sky. Every day the Moon shifts to the east relative to the stars by about 13 °, and after 27.3 days it returns to the same stars, having described a full circle on the celestial sphere.

The apparent movement of the moon is accompanied by a continuous change in its appearance - a change in phases. This is due to the fact that the moon occupies different positions relative to the sun and the earth that illuminates it.

When the Moon is visible to us as a narrow crescent, the rest of its disk also glows slightly. This phenomenon is called ash light and is explained by the fact that the Earth illuminates the night side of the Moon with reflected sunlight.

The Earth and the Moon, illuminated by the Sun, cast shadow cones and penumbra cones. When the Moon falls into the shadow of the Earth in whole or in part, a total or partial eclipse of the Moon occurs. From the Earth, it is visible at the same time wherever the Moon is above the horizon. The phase of total eclipse of the Moon continues until the Moon begins to emerge from the earth's shadow, and can last up to 1 hour 40 minutes. The sun's rays, refracting in the Earth's atmosphere, fall into the cone of the earth's shadow. At the same time, the atmosphere strongly absorbs blue and neighboring rays, and passes mainly red rays into the cone. That is why the Moon turns reddish with a large eclipse phase, and does not disappear altogether. Lunar eclipses occur up to three times a year and, of course, only on a full moon.

A solar eclipse as a total is visible only where a spot of the lunar shadow falls on the Earth, the spot diameter does not exceed 250 km. As the Moon moves in its orbit, its shadow moves across the Earth from west to east, tracing a consistently narrow strip of total eclipse. Where the penumbra of the Moon falls on the Earth, a partial eclipse of the Sun is observed.

Due to a slight change in the distances of the Earth from the Moon and the Sun, the apparent angular diameter is sometimes slightly larger, sometimes slightly less than the solar one, sometimes equal to it. In the first case, the total eclipse of the Sun lasts up to 7 min 40 s, in the second - the Moon does not completely cover the Sun at all, and in the third - only one instant.

There can be from 2 to 5 solar eclipses per year, in the latter case it is certainly private.

Ticket number 4. Throughout the year, the Sun moves along the ecliptic. The ecliptic passes through the 12 zodiacal constellations. During the day, the Sun, like an ordinary star, moves parallel to the celestial equator
(-23 ° 27 ¢ £ d £ + 23 ° 27 ¢). This change in declination is caused by the tilt of the earth's axis to the plane of the orbit.

At the latitude of the tropics of Cancer (South) and Capricorn (North), the Sun is at its zenith on the days of the summer and winter solstices.

At the North Pole, the Sun and stars do not set between March 21 and September 22. The polar night begins on 22 September.

Ticket number 5. There are two types of telescopes: a reflector telescope and a refractor telescope (pictures).

In addition to optical telescopes, there are radio telescopes, which are devices that register space radiation. The radio telescope is a parabolic antenna with a diameter of about 100 m. Natural formations, such as craters or mountain slopes, are used as a bed for the antenna. Radio emission makes it possible to explore planets and stellar systems.

Ticket number 6. Horizontal parallax is called the angle at which the Earth's radius is seen from the planet, perpendicular to the line of sight.

p² - parallax, r² - angular radius, R - radius of the Earth, r - radius of the star.

Now, to determine the distance to the luminaries, they use radar methods: they send a radio signal to the planet, the signal is reflected and recorded by the receiving antenna. Knowing the travel time of the signal, the distance is determined.

Ticket number 7. Spectral analysis is an essential tool for exploring the universe. Spectral analysis is a method by which the chemical composition of celestial bodies, their temperature, size, structure, distance to them and their speed of movement are determined. Spectral analysis is carried out using spectrograph and spectroscope instruments. With the help of spectral analysis, the chemical composition of stars, comets, galaxies and bodies of the solar system was determined, since in the spectrum each line or their combination is characteristic of some element. By the intensity of the spectrum, one can determine the temperature of stars and other bodies.

According to the spectrum, stars are assigned to one or another spectral class. From the spectral diagram, you can determine the apparent stellar magnitude of the star, and then using the formulas:

M = m + 5 + 5lg p

log L = 0.4 (5 - M)

find the absolute stellar magnitude, luminosity, and hence the size of the star.

Using the Doppler formula

The creation of modern space stations, reusable ships, as well as the launch of spaceships to planets (Vega, Mars, Luna, Voyager, Hermes) made it possible to install telescopes on them through which these stars can be observed close without atmospheric interference.

Ticket number 8. The beginning of the space era was laid by the works of the Russian scientist K.E. Tsiolkovsky. He proposed using jet engines for space exploration. He first proposed the idea of ​​using multistage rockets to launch spaceships. Russia was a pioneer in this idea. The first artificial Earth satellite was launched on October 4, 1957, the first flyby of the Moon with taking photographs - 1959, the first manned flight into space - April 12, 1961 The first flight to the Moon by Americans - 1964, the launch of spaceships and space stations ...

1. Scientific purposes:

• man's stay in space;
• space exploration;
• development of space flight technologies;

1. Military objectives (protection against nuclear attack);
2. Telecommunications (satellite communications carried out using communication satellites);
3. Weather forecasts, prediction of natural disasters (meteorological satellites);
4. Production goals:

• search for minerals;
• environmental monitoring.

Ticket number 9. The merit of discovering the laws of planetary motion belongs to the outstanding scientist Johannes Kepler.

First law. Each planet revolves around an ellipse, in one of the focuses of which is the Sun.

Second law. (the law of areas). The radius vector of the planet describes equal areas over equal time intervals. It follows from this law that the speed of the planet when moving in its orbit is the greater, the closer it is to the Sun.

Third law. The squares of the stellar orbital periods of the planets are referred to as cubes of the semi-major axes of their orbits.

This law made it possible to establish the relative distances of the planets from the Sun (in units of the semi-major axis of the earth's orbit), since the sidereal periods of the planets had already been calculated. The semi-major axis of the earth's orbit is taken as an astronomical unit (AU) of distances.

Ticket number 10. Plan:

1. List all planets;
2. Division (terrestrial planets: Mercury, Mars, Venus, Earth, Pluto; and giant planets: Jupiter, Saturn, Uranus, Neptune);
3. Tell about the features of these planets based on the table. 5 (p. 144);
4. Indicate the main features of these planets.

Ticket number 11 ... Plan:

1. Physical conditions on the Moon (size, mass, density, temperature);

The Moon is 81 times less than the Earth in mass, its average density is 3300 kg / m 3, that is, less than that of the Earth. There is no atmosphere on the moon, only a thin shell of dust. The huge changes in the temperature of the lunar surface from day to night are explained not only by the absence of the atmosphere, but also by the duration of the lunar day and lunar night, which corresponds to our two weeks. The temperature at the sunflower point of the Moon reaches + 120 ° С, and at the opposite point of the night hemisphere - 170 ° С.

1. Relief, seas, craters;
2. Chemical features of the surface;
3. The presence of tectonic activity.

Satellites of the planets:

1. Mars (2 small moons: Phobos and Deimos);
2. Jupiter (16 satellites, the most famous are 4 Gallilean satellites: Europa, Callisto, Io, Ganymede; an ocean of water was discovered on Europa);
3. Saturn (17 satellites, Titan is especially famous: it has an atmosphere);
4. Uranus (16 satellites);
5. Neptune (8 satellites);
6. Pluto (1 satellite).

Ticket number 12. Plan:

1. Comets (physical nature, structure, orbits, types), the most famous comets:

• Halley's comet (T = 76 years; 1910 - 1986 - 2062);
• comet Enka;
• comet Hyakutaki;

1. Asteroids (minor planets). The most famous are Ceres, Vesta, Pallas, Juno, Icarus, Hermes, Apollo (more than 1500 in total).

The study of comets, asteroids, meteor showers has shown that they all have the same physical nature and the same chemical composition. Determining the age of the solar system suggests that the sun and the planets are approximately the same age (about 5.5 billion years). According to the theory of the origin of the solar system, academician O. Yu. Schmidt, the Earth and the planets arose from a gas-dust cloud, which, due to the law of universal gravitation, was captured by the Sun and rotated in the same direction as the Sun. Gradually, condensations formed in this cloud, which gave rise to the planets. The evidence that the planets were formed from such condensations is the fallout of meteorites on the Earth and on other planets. So in 1975 the fall of the Wachmann-Strassmann comet on Jupiter was noted.

Ticket number 13. The Sun is the closest star to us, in which, unlike all other stars, we can observe the disk and use a telescope to study small details on it. The sun is a typical star, and therefore studying it helps to understand the nature of stars in general.

The mass of the Sun is 333 thousand times greater than the mass of the Earth, the power of the total radiation of the Sun is 4 * 10 23 kW, the effective temperature is 6000 K.

Like all stars, the Sun is an incandescent ball of gas. Basically it consists of hydrogen with an admixture of 10% (by the number of atoms) helium, 1-2% of the mass of the Sun falls on other heavier elements.

On the Sun, matter is highly ionized, that is, atoms have lost their outer electrons and together with them become free particles of ionized gas - plasma.

The average density of solar matter is 1400 kg / m 3. However, this is an average number, and the density in the outer layers is incommensurably less, and 100 times more in the center.

Under the action of the forces of gravitational attraction directed towards the center of the Sun, a huge pressure is created in its depths, which reaches 2 * 10 8 Pa in the center, at a temperature of about 15 million K.

Under these conditions, the nuclei of hydrogen atoms have very high speeds and can collide with each other, despite the action of the electrostatic repulsive force. Some collisions end in nuclear reactions, in which helium is formed from hydrogen and a large amount of heat is released.

The surface of the sun (photosphere) has a granular structure, that is, it consists of "grains" with an average size of about 1000 km. Granulation is a consequence of the movement of gases in the zone located along the photosphere. From time to time, in certain regions of the photosphere, the dark gaps between the spots increase, and large dark spots are formed. Observing sunspots through a telescope, Galileo noticed that they were moving along the visible disk of the sun. On this basis, he concluded that the Sun rotates on its axis, with a period of 25 days. at the equator and 30 days. near the poles.

Spots are unstable formations, most often appear in groups. Almost imperceptible light formations, which are called torches, are sometimes visible around the spots. The main feature of spots and flares is the presence of magnetic fields with induction reaching 0.4-0.5 T.

Ticket number 14. The manifestation of solar activity on Earth:

1. Sunspots are an active source of electromagnetic radiation that causes so-called "magnetic storms". These "magnetic storms" affect television and radio communications, causing powerful auroras.
2. The sun emits the following types of radiation: ultraviolet, x-ray, infrared and cosmic rays (electrons, protons, neutrons and heavy particles hadrons). These emissions are almost entirely retained by the Earth's atmosphere. This is why the Earth's atmosphere should be kept in good condition. Periodically appearing ozone holes allow the radiation from the Sun to reach the earth's surface and adversely affect organic life on Earth.
3. Solar activity occurs every 11 years. The last maximum solar activity was in 1991. The expected maximum is 2002. Maximum solar activity means the greatest number of sunspots, radiation and prominences. It has long been established that a change in solar activity of the Sun affects the following factors:

• the epidemiological situation on Earth;
• the number of various kinds of natural disasters (typhoons, earthquakes, floods, etc.);
• on the number of road and rail accidents.

The maximum of all this falls on the years of the active Sun. As the scientist Chizhevsky established, the active Sun affects the well-being of a person. Since then, periodic forecasts of human well-being have been made.

Ticket number 15. The radius of the earth turns out to be too small to serve as a basis for measuring the parallax displacement of stars and the distance to them. Therefore, use the annual parallax instead of the horizontal one.

The annual parallax of a star is the angle at which one could see the semi-major axis of the earth's orbit from the star if it is perpendicular to the line of sight.

a - semi-major axis of the earth's orbit,

p - annual parallax.

The unit of distance is also parsec. Parsec is the distance from which the semi-major axis of the earth's orbit, perpendicular to the line of sight, is seen at an angle of 1².

1 parsec = 3.26 light years = 206265 AU. e. = 3 * 10 11 km.

By measuring the annual parallax, you can reliably establish the distance to stars that are no more than 100 parsecs or 300 sv. years.

Ticket number 16. Stars are classified according to the following parameters: size, color, luminosity, spectral class.

By size, stars are divided into dwarf stars, middle stars, normal stars, giant stars, and supergiant stars. Dwarf stars are a companion of the star Sirius; middle - the Sun, Chapel (Charioteer); normal (t = 10 thousand K) - have dimensions between the Sun and Capella; giant stars - Antares, Arcturus; supergiants - Betelgeuse, Aldebaran.

By color, stars are divided into red (Antares, Betelgeuse - 3000 K), yellow (Sun, Capella - 6000 K), white (Sirius, Deneb, Vega - 10,000 K), blue (Spica - 30,000 K).

By luminosity, stars are classified as follows. If we take the luminosity of the Sun as 1, then the white and blue stars have luminosities 100 and 10 thousand times greater than the luminosity of the Sun, and red dwarfs - 10 times less than the luminosity of the Sun.

According to the spectrum, stars are divided into spectral classes (see table).

Equilibrium conditions: as you know, stars are the only natural objects within which uncontrolled thermonuclear fusion reactions occur, which are accompanied by the release of a large amount of energy and determine the temperature of the stars. Most of the stars are stationary, that is, they do not explode. Some stars explode (so-called novae and supernovae). Why are the stars in general in equilibrium? The force of nuclear explosions near stationary stars is balanced by the force of gravity, which is why these stars remain in equilibrium.

Ticket number 17. The Stefan-Boltzmann law determines the relationship between radiation and the temperature of stars.

e = sТ 4 s - coefficient, s = 5.67 * 10 -8 W / m 2 to 4

e - radiation energy per unit surface of the star

L is the luminosity of the star, R is the radius of the star.

Using the Stefan-Boltzmann formula and Wien's law, determine the wavelength at which the maximum radiation falls:

l max T = b b - Wien's constant

One can proceed from the opposite, that is, using the luminosity and temperature, determine the size of the stars.

Ticket number 18. Plan:

1. Cepheids
2. New stars
3. Supernovae

Ticket number 19. Plan:

1. Visually double, multiples
2. Spectral binaries
3. Eclipsing variable stars

Ticket number 20. There are different types of stars: single, double and multiple, stationary and variable, giant and dwarf stars, novae and supernovae. Are there regularities in this variety of stars, in their seeming chaos? Such regularities exist, despite different luminosities, temperatures and sizes of stars.

1. It has been established that with increasing mass the luminosity of stars increases, and this dependence is determined by the formula L = m 3.9, in addition, for many stars the regularity L »R 5.2 is valid.
2. Dependence of L on t ° and color (diagram “color - luminosity).

The more massive the star, the faster the main fuel, hydrogen, burns out, turning into helium ( ). Massive blue and white giants burn out in 10 7 years. Yellow stars like Capella and the Sun burn out in 10 10 years (t Sun = 5 * 10 9 years). White and blue stars burn out and turn into red giants. They synthesize 2C + He ® C 2 He. As the helium burns out, the star contracts and turns into a white dwarf. Over time, the white dwarf turns into a very dense star, which consists of some neutrons. Decreasing the size of a star leads to its very fast rotation. This star pulsates, emitting radio waves. They are called pulsars - the final stage of giant stars. Some stars with a mass much greater than the mass of the Sun shrink so much that so-called "black holes" turn, which, due to gravity, do not emit visible radiation.

Ticket number 21. Our star system - the Galaxy is one of the elliptical galaxies. The Milky Way that we see is only part of our Galaxy. In modern telescopes, stars up to magnitude 21 can be seen. The number of these stars is 2 * 10 9, but this is only a small part of the population of our Galaxy. The diameter of the Galaxy is approximately 100 thousand light years. Observing the Galaxy, one can notice a "split", which is caused by interstellar dust, which blocks the stars of the Galaxy from us.

Population of the Galaxy.

There are many red giants and short-period Cepheids in the galactic core. In the branches further from the center, there are many supergiants and classical Cepheids. The spiral arms contain hot supergiants and classical Cepheids. Our Galaxy revolves around the center of the Galaxy, which is located in the constellation Hercules. The solar system makes a complete revolution around the center of the Galaxy in 200 million years. By the rotation of the solar system, one can determine the approximate mass of the Galaxy - 2 * 10 11 m of the Earth. The stars are considered to be stationary, but in reality the stars are moving. But since we are significantly removed from them, this movement can only be observed for thousands of years.

Ticket number 22. In our Galaxy, apart from single stars, there are stars that unite into clusters. There are 2 types of star clusters:

1. Open star clusters, such as the Pleiades star cluster in the constellations Taurus and Hyades. A simple eye in the Pleiades can see 6 stars, but if you look through a telescope, you can see a scattering of stars. The size of open clusters is a few parsecs. Open star clusters are made up of hundreds of main sequence stars and supergiants.
2. Globular star clusters are up to 100 parsecs in size. These clusters are characterized by short-period Cepheids and a peculiar stellar magnitude (from -5 to +5 units).

The Russian astronomer V. Ya. Struve discovered that there is interstellar absorption of light. It is interstellar absorption of light that weakens the brightness of stars. The interstellar medium is filled with cosmic dust, which forms the so-called nebulae, for example, the dark nebulae Large Magellanic Clouds, Horsehead. In the constellation of Orion, there is a gas and dust nebula that glows with the reflected light of nearby stars. In the constellation of Aquarius, there is the Great Planetary Nebula, formed as a result of the emission of gas from nearby stars. Vorontsov-Velyaminov proved that the emission of gases from giant stars is sufficient for the formation of new stars. Gaseous nebulae form a 200 parsec layer in the Galaxy. They are composed of H, He, OH, CO, CO 2, NH 3. Neutral hydrogen emits a wavelength of 0.21 m. The distribution of this radio emission determines the distribution of hydrogen in the Galaxy. In addition, there are sources of bremsstrahlung (X-ray) radio emission (quasars) in the Galaxy.

Ticket number 23. William Herschel in the 17th century mapped a lot of nebulae on the star map. Subsequently, it turned out that these are giant galaxies that are outside our Galaxy. With the help of Cepheids, the American astronomer Hubble proved that the nearest galaxy, M-31, is located at a distance of 2 million light years. In the constellation Veronica, about a thousand of such galaxies have been discovered, located millions of light years away from us. Hubble proved that there is a redshift in the spectra of galaxies. This shift is the greater, the further from us the galaxy. In other words, the further the galaxy is, the faster its distance from us is.

V offset = D * H H - Hubble constant, D - shift in the spectrum.

The model of the expanding universe based on Einstein's theory was confirmed by the Russian scientist Friedman.

Galaxies are irregular, elliptical and spiral in type. Elliptical galaxies are in the constellation Taurus, a spiral galaxy is ours, the Andromeda nebula, an irregular galaxy is in the Magellanic clouds. In addition to visible galaxies in stellar systems, there are so-called radio galaxies, that is, powerful sources of radio emission. In the place of these radio galaxies, small luminous objects were found, the redshift of which is so great that they are obviously distant from us by billions of light years. They were called quasars because their radiation is sometimes more powerful than the radiation of an entire galaxy. It is possible that quasars are the nuclei of very powerful stellar systems.

Ticket number 24. The latest stellar catalog contains more than 30 thousand galaxies brighter than magnitude 15, and with the help of a strong telescope, hundreds of millions of galaxies can be photographed. All this together with our Galaxy forms the so-called metagalaxy. In terms of its size and the number of objects, the metagalaxy is infinite, it has no beginning or end. According to modern concepts, in every galaxy there is an extinction of stars and entire galaxies, as well as the emergence of new stars and galaxies. The science that studies our Universe as a whole is called cosmology. According to the theory of Hubble and Friedman, our universe, taking into account the general theory of Einstein, such a universe is expanding about 15 billion years ago, the nearest galaxies were closer to us than they are now. In some place in space, new star systems arise and, taking into account the formula E = mc 2, since we can say that since masses and energies are equivalent, their mutual transformation into each other is the basis of the material world.

1. Local time.

The time measured on a given geographic meridian is called local time this meridian. For all places on the same meridian, the hour angle of the vernal equinox (or the Sun, or the middle sun) is the same at any moment. Therefore, on the entire geographic meridian, local time (sidereal or solar) at the same moment is the same.

If the difference in geographic longitudes of two places is D l, then in a more eastern place the hour angle of any star will be at D l greater than the hour angle of the same star in a more westerly place. Therefore, the difference between any local times on two meridians at the same physical moment is always equal to the difference in longitudes of these meridians, expressed in hourly measure (in units of time):

those. the local mean time of any point on Earth is always equal to universal time at that moment plus the longitude of that point, expressed in an hour, and considered positive east of Greenwich.

In astronomical calendars, the moments of most phenomena are indicated by universal time T 0. Moments of these phenomena in local time T t. are easily determined by formula (1.28).

3. Zone time... It is inconvenient to use both local mean solar time and universal time in everyday life. The first because there are, in principle, the same number of local time systems as there are geographic meridians, i.e. countless. Therefore, in order to establish the sequence of events or phenomena noted in local time, it is absolutely necessary to know, in addition to the moments, also the difference in longitudes of those meridians on which these events or phenomena took place.

The sequence of events noted in UTC is easy to establish, but the large difference between UTC and the local time of meridians far from Greenwich makes it inconvenient to use UTC in everyday life.

In 1884 it was proposed belt average time counting system, the essence of which is as follows. Time is counted only at 24 major geographical meridians located from each other in longitude exactly 15 ° (or after 1 h), approximately in the middle of each time zone. Time Zones Areas of the earth's surface are called, into which it is conventionally divided by lines running from its north pole to the south and spaced approximately 7 °, 5 from the main meridians. These lines, or the boundaries of time zones, exactly follow the geographic meridians only in the open seas and oceans and in uninhabited land areas. For the rest of their length, they follow the state, administrative, economic or geographical boundaries, deviating from the corresponding meridian in one direction or another. Time zones are numbered from 0 to 23. Greenwich is taken as the main meridian of the zero zone. The main meridian of the first time zone is located from Greenwich exactly 15 ° to the east, the second - at 30 °, the third - at 45 °, etc. to 23 time zone, the main meridian of which has an east longitude of 345 ° from Greenwich (or west longitude 15 °).

Standard timeT p is called the local mean solar time, measured at the main meridian of a given time zone. It is used to keep track of time throughout the territory that lies in a given time zone.

Zone time of the given zone NS is associated with universal time by the obvious relationship

It is also quite obvious that the difference in the zone times of two points is an integer number of hours equal to the difference in the numbers of their time zones.

4. Summer time... In order to more efficiently distribute electricity going to lighting enterprises and residential premises, and to make the fullest use of daylight in the summer months of the year, in many countries (including our republic), the hour hands of the standard time clock are moved forward by 1 hour or half hour. The so-called summer time... In autumn, the clock is again set to standard time.

Daylight saving time link T l any item with its standard time T p and with universal time T 0 is given by the following relations:

(1.30)

1. Theoretical resolution of the telescope:

Where λ - average length of a light wave (5.5 · 10 -7 m), D Is the diameter of the telescope objective, or, where D Is the diameter of the telescope objective in millimeters.

2. Telescope magnification:

Where F- focal length of the lens, f- the focal length of the eyepiece.

3. The height of the luminaries at the culmination:

the height of the luminaries at the upper culmination, culminating south of the zenith ( d < j):

, where j- latitude of the place of observation, d- declination of the luminary;

the height of the luminaries at the upper culmination, culminating north of the zenith ( d > j):

, where j- latitude of the place of observation, d- declination of the luminary;

the height of the luminaries at the bottom culmination:

, where j- latitude of the place of observation, d- the declination of the luminary.

4. Astronomical refraction:

An approximate formula for calculating the angle of refraction, expressed in arc seconds (at a temperature of + 10 ° C and atmospheric pressure of 760 mm Hg):

, where z- zenith distance of the luminary (for z<70°).

sidereal time:

Where a- right ascension of any luminary, t- its hour angle;

mean solar time (local mean time):

T m = T  + h, where T- true solar time, h- equation of time;

universal time:

Where l is the longitude of the point with local mean time T m, expressed in hourly measure, T 0 - universal time at this moment;

standard time:

Where T 0 - universal time; n- time zone number (for Greenwich n= 0, for Moscow n= 2, for Krasnoyarsk n=6);

Daylight saving time:

or

6. Formulas connecting the sidereal (stellar) period of the planet's orbital T with the synodic period of her circulation S:

for the upper planets:

for the lower planets:

, where TÅ - stellar period of the Earth's revolution around the Sun.

7. Kepler's third law:

, where T 1 and T 2- periods of planetary circulation, a 1 and a 2 - semi-major axes of their orbit.

8. The law of universal gravitation:

Where m 1 and m 2- the masses of attracting material points, r- the distance between them, G- gravitational constant.

9. The third generalized Kepler's law:

, where m 1 and m 2- the masses of two mutually attracting bodies, r- the distance between their centers, T- the period of revolution of these bodies around the common center of mass, G- gravitational constant;

for the system Sun and two planets:

, where T 1 and T 2- sidereal (stellar) periods of planetary revolution, M- the mass of the Sun, m 1 and m 2- the masses of the planets, a 1 and a 2 - major semiaxes of the orbits of the planets;

for the systems Sun and planet, planet and satellite:

, where M- the mass of the sun; m 1 - the mass of the planet; m 2 - the mass of the satellite of the planet; T 1 and a 1- the period of the planet's revolution around the Sun and the semi-major axis of its orbit; T 2 and a 2- the period of revolution of the satellite around the planet and the semi-major axis of its orbit;

at M >> m 1, a m 1 >> m 2 ,

10. Linear velocity of the body in a parabolic orbit (parabolic velocity):

, where G M- the mass of the central body, r Is the radius vector of the chosen point of the parabolic orbit.

11. Linear velocity of the body in an elliptical orbit at a selected point:

, where G- gravitational constant, M- the mass of the central body, r- radius vector of the selected point of the elliptical orbit, a- semi-major axis of an elliptical orbit.

12. Linear speed of the body in a circular orbit (circular speed):

, where G- gravitational constant, M- the mass of the central body, R- orbital radius, v p is the parabolic velocity.

13. Eccentricity of an elliptical orbit, characterizing the degree of deviation of the ellipse from the circle:

, where c- the distance from the focus to the center of the orbit, a- semi-major axis of the orbit, b Is the semi-minor axis of the orbit.

14. Relationship between the distances of the periapsis and the apocenter with the semi-major axis and the eccentricity of the elliptical orbit:

Where r P - the distance from the focus, in which the central celestial body is located, to the periapsis, r A - the distance from the focus, in which the central celestial body is located, to the apocenter, a- semi-major axis of the orbit, e- orbital eccentricity.

15. Distance to the star (within the solar system):

, where R ρ 0 - horizontal parallax of the luminary, expressed in arc seconds,

or where D 1 and D 2 - distances to the stars, ρ 1 and ρ 2 - their horizontal parallaxes.

16. Radius of the luminary:

Where ρ - the angle at which the radius of the luminary's disk is visible from the Earth (angular radius), RÅ is the equatorial radius of the Earth, ρ 0 - horizontal parallax of the star; m - apparent magnitude, R Is the distance to the star in parsecs.

20. Stefan-Boltzmann law:

ε = σT 4 where ε Is the energy emitted per unit of time from a unit of surface, T Is the temperature (in kelvin), and σ Is the Stefan – Boltzmann constant.

21. The Law of Wine:

Where λ max is the wavelength at which the maximum blackbody radiation falls (in centimeters), T Is the absolute temperature in Kelvin.

22. Hubble's Law:

, where v- the radial velocity of the galaxy receding, c- speed of light, Δ λ - Doppler shift of lines in the spectrum, λ - the wavelength of the radiation source, z- redshift, r- distance to the galaxy in megaparsecs, H Is the Hubble constant equal to 75 km / (s × Mpc).

TICKETS FOR ASTRONOMY CLASS 11

TICKET number 1

The visible movements of the luminaries, as a result of their own movement in space, the rotation of the Earth and its revolution around the Sun.

The Earth makes complex movements: it rotates around its axis (T = 24 hours), moves around the Sun (T = 1 year), rotates with the Galaxy (T = 200 thousand years). This shows that all observations made from the Earth differ in apparent trajectories. The planets move across the sky either from east to west (forward movement), then from west to east (backward movement). Moments of direction change are called stands. If you plot this path on a map, you get a loop. The larger the distance between the planet and the Earth, the smaller the size of the loop. The planets are divided into lower and upper (lower - inside the earth's orbit: Mercury, Venus; upper: Mars, Jupiter, Saturn, Uranus, Neptune and Pluto). All of these planets revolve in the same way as the Earth around the Sun, but due to the movement of the Earth, one can observe the loop-like movement of the planets. The relative positions of the planets relative to the Sun and the Earth are called planetary configurations.

Planet configurations, decomp. geometric the location of the planets in relation to the Sun and the Earth. Certain positions of the planets, visible from the Earth and measured relative to the Sun, are special. titles. Fig. V - inner planet, I- outer planet, E - Earth, S - The sun. When int. the planet lies on a straight line with the Sun, it is in connection. K. p. EV 1 S and ESV 2 are called bottom and top connection respectively. Ext. planet I is in upper conjunction when it lies on a straight line with the Sun ( ESI 4) and in confrontation, when it lies in the direction opposite to the Sun (I 3 ES). The angle between the directions to the planet and to the Sun with apex on the Earth, eg. I 5 ES is called elongation. For int. planets max, elongation occurs when the angle EV 8 S is 90 °; for ext. planets can elongate in the range from 0 ° ESI 4) to 180 ° (I 3 ES). When the elongation is 90 °, the planet is said to be in squaring(I 6 ES, I 7 ES).

The period during which the planet revolves around the Sun in its orbit is called the sidereal (stellar) orbital period - T, the time period between two identical configurations - the synodic period - S.

The planets move around the Sun in one direction and make a complete revolution around the Sun for a period of time = sidereal period

for inner planets

for outer planets

S - sidereal period (relative to the stars), T - synodic period (between phases), T Å = 1 year.

Comets and meteorite bodies move along elliptical, parabolic and hyperbolic trajectories.

Calculating the distance to the galaxy based on Hubble's law.

H = 50 km / s * Mpc - Hubble constant

TICKET number 2

Principles for determining geographic coordinates from astronomical observations.

There are 2 geographic coordinates: geographic latitude and geographic longitude. Astronomy as a practical science allows you to find these coordinates. The height of the pole of the world above the horizon is equal to the latitude of the observation site. The approximate geographic latitude can be determined by measuring the height of the North Star, because it is approximately 1 0 from the North Pole of the world. You can determine the latitude of the observation site by the height of the luminary at the upper culmination ( Climax- the moment the luminary passes through the meridian) according to the formula:

j = d ± (90 - h), depending on whether it culminates south or north from the zenith. h - luminary height, d - declination, j - latitude.

Geographic longitude is the second coordinate, measured from the zero meridian of Greenwich to the east. The earth is divided into 24 time zones, the time difference is 1 hour. The difference in local times is equal to the difference in longitudes:

T λ 1 - T λ 2 = λ 1 - λ 2 Thus, having learned the time difference at two points, the longitude of one of which is known, it is possible to determine the longitude of the other point.

Local time- this is the solar time in a given place on the Earth. At each point, the local time is different, so people live according to standard time, that is, according to the time of the middle meridian of a given belt. The date line runs in the east (Bering Strait).

Calculation of the temperature of a star based on data on its luminosity and size.

L - luminosity (Lc = 1)

R - radius (Rc = 1)

T - Temperature (Tc = 6000)

TICKET number 3

The reasons for the change in the phases of the moon. Conditions for the onset and frequency of solar and lunar eclipses.

Phase, in astronomy, the phase change occurs due to periodic. changes in the conditions of illumination of celestial bodies in relation to the observer. The change in the F. of the Moon is due to a change in the relative position of the Earth, the Moon and the Sun, as well as the fact that the Moon shines with light reflected from it. When the Moon is between the Sun and the Earth on a straight line connecting them, the unlit part of the lunar surface is facing the Earth, so we do not see it. This F. - new moon. After 1 - 2 days the Moon departs from this straight line, and a narrow lunar crescent is visible from the Earth. During the new moon, that part of the moon that is not illuminated by direct sunlight is still visible in the dark sky. This phenomenon was named ash light. A week later, F. comes - first quarter: the illuminated part of the moon is half the disk. Then comes full moon- The Moon is again on the line connecting the Sun and the Earth, but on the other side of the Earth. The full disk of the moon is visible. Then the visible part begins to decrease and last quarter, those. again one can observe half of the disk illuminated. The full changeover period of the F. Moon is called a synodic month.

Eclipse, an astronomical phenomenon, when one celestial body completely or partially covers another, or the shadow of one body falls on another. Solar 3. occur when the Earth falls into the shadow cast by the Moon, and lunar ones - when the Moon falls into the shadow of the Earth. The shadow of the moon during solar 3. consists of the central shadow and the surrounding penumbra. Under favorable conditions, the full lunar 3. can last 1 hour. 45 minutes If the Moon does not completely enter the shadow, then an observer on the night side of the Earth will see the lunar quotient 3. The angular diameters of the Sun and the Moon are almost the same, so the total solar 3. lasts only a few. minutes. When the Moon is at its apogee, its angular size is slightly smaller than that of the Sun. Solar 3.can occur if the line connecting the centers of the sun and moon crosses the earth's surface. The diameters of the lunar shadow when falling on the Earth can reach several. hundreds of kilometers. The observer sees that the dark lunar disk has not completely covered the Sun, leaving its edge open in the form of a bright ring. This is the so-called. annular solar 3. If the angular dimensions of the Moon are greater than the Sun, then the observer in the vicinity of the point of intersection of the line connecting their centers with the earth's surface will see the full solar 3. Since The Earth revolves around its axis, the Moon around the Earth, and the Earth around the Sun, the lunar shadow quickly slides along the earth's surface from the point where it fell on it, to others, where it leaves it, and traces on the Earth * a strip of full or annular 3. Particular 3. can be observed when the moon obscures only part of the sun. The time, duration and pattern of the solar or lunar 3. depend on the geometry of the Earth-Moon-Sun system. Due to the inclination of the lunar orbit relative to * the ecliptic, solar and lunar 3. do not occur on every new moon or full moon. Comparison of prediction 3. with observations makes it possible to refine the theory of the motion of the moon. Since the geometry of the system is almost exactly repeated every 18 years 10 days, 3. occur with this period, called saros. Registration 3. Since ancient times, it is possible to check the effect of tides on the lunar orbit.

Determination of the coordinates of the stars on the star map.

TICKET number 4

Features of the diurnal movement of the Sun at different geographic latitudes at different times of the year.

Consider the annual movement of the Sun across the celestial sphere. The Earth makes a complete revolution around the Sun in a year, in one day the Sun moves along the ecliptic from west to east by about 1 °, and in 3 months - by 90 °. However, at this stage, it is important that since the movement of the Sun along the ecliptic is accompanied by a change in its declination ranging from δ = -e (winter solstice) to δ = + e (summer solstice), where e is the angle of inclination of the earth's axis. Therefore, during the year, the location of the diurnal parallel of the Sun also changes. Consider the mid-latitudes of the northern hemisphere.

During the passage of the vernal equinox by the Sun (α = 0 h), at the end of March, the declination of the Sun is 0 °, therefore on this day the Sun is practically at the celestial equator, rises in the east, rises in the upper culmination to a height of h = 90 ° - φ and sets in the west. Since the celestial equator divides the celestial sphere in half, the Sun is half of the day above the horizon, half - below it, i.e. day is equal to night, which is reflected in the name "equinox". At the moment of equinox, the tangent to the ecliptic at the location of the Sun is inclined to the equator by a maximum angle equal to e, therefore, the rate of increase in the declination of the Sun at this time is also maximum.

After the vernal equinox, the declination of the Sun increases rapidly, so every day more and more of the diurnal parallel of the Sun is above the horizon. The sun rises earlier, rises higher in the upper climax, and sets later. The rising and setting points are shifting north each day, and the day is lengthening.

However, the angle of inclination of the tangent to the ecliptic at the location of the Sun decreases every day, and with it the rate of increase in declination decreases. Finally, at the end of June, the Sun reaches the northernmost point of the ecliptic (α = 6 hours, δ = + e). By this moment, it rises in the upper culmination to a height of h = 90 ° - φ + e, rises approximately in the northeast, sets in the northwest, and the length of the day reaches its maximum value. At the same time, the daily increase in the height of the Sun at the upper culmination ceases, and the midday Sun, as it were, "stops" in its movement to the north. Hence the name "summer solstice".

After that, the declination of the Sun begins to decrease - very slowly at first, and then faster and faster. It rises every day later, sets earlier, the points of rising and setting move back to the south.

By the end of September, the Sun reaches the second point of intersection of the ecliptic with the equator (α = 12 hours), and the equinox comes again, now in the autumn. Again, the rate of change in the Sun's declination is peaking and is rapidly shifting south. The night is getting longer than the day, and the height of the Sun at the top climax decreases with each passing day.

By the end of December, the Sun reaches the southernmost point of the ecliptic (α = 18 hours) and its movement to the south stops, it "stops" again. This is the winter solstice. The sun rises almost in the southeast, sets in the southwest, and at noon rises in the south to a height of h = 90 ° - φ - e.

And then everything starts all over again - the declination of the Sun increases, the height in the upper climax increases, the day lengthens, the points of sunrise and sunset are shifted to the north.

Due to the scattering of light by the earth's atmosphere, the sky continues to remain light for some time after sunset. This period is called twilight. By the depth of the sun's immersion under the horizon, civil twilight is distinguished (-8 ° -12 °) and astronomical (h> -18 °), after which the brightness of the night sky remains approximately constant.

In summer, at d = + e, the height of the Sun at the lower culmination is h = φ + e - 90 °. Therefore, north of latitude ~ 48 ° .5 at the summer solstice, the Sun at the lower climax plunges below the horizon by less than 18 °, and summer nights become bright due to astronomical twilight. Similarly, at φ> 54 ° .5 in the summer solstice, the height of the Sun is h> -12 ° - navigational twilight lasts all night (Moscow falls into this zone, where it does not get dark for three months a year - from early May to early August). Still further north, at φ> 58 ° .5, civil twilight does not stop in summer (St. Petersburg with its famous "white nights" is located here).

Finally, at latitude φ = 90 ° - e, the diurnal parallel of the Sun during the solstices will touch the horizon. This latitude is the Arctic Circle. Even further north, the Sun for some time in summer does not set beyond the horizon - the polar day sets in, and in winter it does not rise - the polar night.

Now let's look at more southerly latitudes. As already mentioned, south of latitude φ = 90 ° - e - 18 ° the nights are always dark. With further movement to the south, the Sun rises higher and higher at any time of the year, and the difference between the parts of its diurnal parallel, located above and below the horizon, decreases. Accordingly, the length of the day and night, even during the solstices, differ less and less. Finally, at latitude j = e, the diurnal parallel of the Sun for the summer solstice will pass through the zenith. This latitude is called the northern tropic; at the time of the summer solstice, at one of the points at this latitude, the Sun is exactly at its zenith. Finally, at the equator, the diurnal parallels of the Sun are always divided by the horizon into two equal parts, that is, day there is always equal to night, and the Sun is at its zenith during the equinoxes.

South of the equator, everything will be similar to that described above, only for most of the year (and always south of the southern tropic), the upper climax of the Sun will occur north of the zenith.

Aiming at a Target and Focusing the Telescope .

TICKET number 5

1. The principle of operation and purpose of the telescope.

Telescope, an astronomical device for observing celestial bodies. A well-designed telescope is capable of collecting electromagnetic radiation in various ranges of the spectrum. In astronomy, an optical telescope is designed to magnify an image and collect light from faint sources, especially those invisible to the naked eye. it is capable of collecting more light and providing high angular resolution compared to it, so more detail can be seen in the enlarged image. In a refractor telescope, a large lens is used as an objective, collecting and focusing light, and the image is viewed using an eyepiece consisting of one or more lenses. The main problem in the design of refractor telescopes is chromatic aberration (the colored border around the image created by a simple lens due to the fact that light of different wavelengths is focused at different distances.). It can be eliminated by using a combination of convex and concave lenses, but lenses larger than a certain size limit (about 1 meter in diameter) cannot be made. Therefore, at present, preference is given to reflector telescopes in which a mirror is used as an objective. The first reflector telescope was invented by Newton according to his scheme, called Newton's system. Now there are several methods of image observation: Newton, Cassegrain systems (the focus position is convenient for registering and analyzing light with the help of other devices, such as a photometer or spectrometer), Kude (the scheme is very convenient when bulky equipment is required for light analysis), Maksutov ( the so-called meniscus), Schmidt (used when it is necessary to make large-scale sky surveys).

Along with optical telescopes, there are telescopes that collect electromagnetic radiation in other ranges. For example, various types of radio telescopes are widespread (with a parabolic mirror: fixed and full-revolving; RATAN-600 type; in-phase; radio interferometers). Telescopes are also available for recording X-rays and gamma rays. Since the latter is absorbed by the earth's atmosphere, X-ray telescopes are usually mounted on satellites or airborne probes. Gamma astronomy uses telescopes on satellites.

Calculation of the planet's orbital period based on Kepler's third law.

T z = 1 year

a z = 1 astronomical unit

1 parsec = 3.26 light years = 206265 AU. e. = 3 * 10 11 km.

TICKET number 6

Methods for determining the distances to the bodies of the solar system and their sizes.

First, the distance to some accessible point is determined. This distance is called the baseline. The angle at which the basis is visible from an inaccessible place is called parallax... Horizontal parallax is the angle at which the Earth's radius is seen from the planet, perpendicular to the line of sight.

p² - parallax, r² - angular radius, R - radius of the Earth, r - radius of the star.

Radar method. It consists in the fact that a powerful short-term impulse is sent to a celestial body, and then a reflected signal is received. The speed of propagation of radio waves is equal to the speed of light in a vacuum: known. Therefore, if you accurately measure the time it took for the signal to reach the celestial body and return back, then it is easy to calculate the desired distance.

Radar observations make it possible to determine with great accuracy the distances to the celestial bodies of the solar system. This method has been used to clarify the distances to the Moon, Venus, Mercury, Mars, Jupiter.

Laser location of the moon. Soon after the invention of powerful sources of light radiation - optical quantum generators (lasers) - experiments on laser location of the moon began to be carried out. The laser ranging method is similar to radar, but the measurement accuracy is much higher. Optical location makes it possible to determine the distance between selected points of the lunar and earth's surface with an accuracy of centimeters.

To determine the size of the Earth, the distance between two points located on the same meridian is determined, then the length of the arc l , corresponding to 1 ° - n .

To determine the size of the bodies of the solar system, you can measure the angle at which they are visible to the terrestrial observer - the angular radius of the star r and the distance to the star D.

Taking into account p 0 - the horizontal parallax of the star and that the angles p 0 and r are small,

Determination of the luminosity of a star based on data on its size and temperature.

L - luminosity (Lc = 1)

R - radius (Rc = 1)

T - Temperature (Tc = 6000)

TICKET number 7

1. Possibilities of spectral analysis and extra-atmospheric observations for studying the nature of celestial bodies.

The decomposition of electromagnetic radiation into wavelengths for the purpose of studying them is called spectroscopy. Spectrum analysis is the main method for studying astronomical objects used in astrophysics. The study of spectra provides information on temperature, speed, pressure, chemical composition and other important properties of astronomical objects. By the absorption spectrum (more precisely, by the presence of certain lines in the spectrum), one can judge the chemical composition of the star's atmosphere. By the intensity of the spectrum, you can determine the temperature of stars and other bodies:

l max T = b, b - Wien's constant. You can learn a lot about a star using the Doppler effect. In 1842, he established that the wavelength λ, received by the observer, is related to the wavelength of the radiation source by the ratio: , where V is the projection of the source velocity onto the line of sight. The law he discovered was called Doppler's law:. The shift of lines in the spectrum of the star relative to the comparison spectrum towards the red side indicates that the star is moving away from us, the shift towards the violet side of the spectrum - that the star is approaching us. If the lines in the spectrum change periodically, then the star has a companion and they revolve around a common center of mass. The Doppler effect also makes it possible to estimate the speed of rotation of stars. Even when the emitting gas has no relative motion, spectral lines emitted by individual atoms will shift from the laboratory value due to erratic thermal motion. For the total mass of the gas, this will be expressed in broadening of the spectral lines. In this case, the square of the Doppler spectral line width is proportional to the temperature. Thus, the width of the spectral line can be used to judge the temperature of the emitting gas. In 1896, the Dutch physicist Zeeman discovered the effect of the splitting of spectral lines in a strong magnetic field. With the help of this effect, it has now become possible to "measure" cosmic magnetic fields. A similar effect (called the Stark effect) is observed in an electric field. It manifests itself when a strong electric field appears in a star for a short time.

The Earth's atmosphere retains some of the radiation coming from space. Visible light passing through it is also distorted: the movement of air blurs the image of celestial bodies, and the stars twinkle, although in reality their brightness is unchanged. Therefore, from the middle of the 20th century, astronomers began to conduct observations from space. Outside atmospheric telescopes collect and analyze X-ray, ultraviolet, infrared and gamma radiation. The first three can be studied only outside the atmosphere, while the latter partially reaches the Earth's surface, but mixes with the IR of the planet itself. Therefore, it is preferable to take infrared telescopes into space. X-rays reveal areas in the Universe where energy is released especially violently (for example, black holes), as well as objects invisible in other rays, for example pulsars. Infrared telescopes allow you to explore heat sources hidden by optics over a wide temperature range. Gamma astronomy makes it possible to detect sources of electron-positron annihilation, i.e. sources of high energies.

2. Determining the declination of the Sun on a given day from a star chart and calculating its height at noon.

h - luminary height

TICKET number 8

The most important directions and tasks of research and exploration of outer space.

The main problems of modern astronomy:

There is no solution to many particular problems of cosmogony:

· How the Moon was formed, how the rings were formed around the giant planets, why Venus rotates very slowly and in the opposite direction;

In stellar astronomy:

· There is no detailed model of the Sun that can accurately explain all of its observable properties (in particular, the neutrino flux from the core).

· There is no detailed physical theory of some manifestations of stellar activity. For example, the reasons for supernova explosions are not completely clear; it is not entirely clear why narrow jets of gas are ejected from the vicinity of some stars. Particularly mysterious, however, are the short bursts of gamma rays that regularly occur in various directions in the sky. It is not even clear whether they are associated with stars or other objects, and at what distance these objects are from us.

In galactic and extragalactic astronomy:

· The problem of hidden mass has not been solved, which consists in the fact that the gravitational field of galaxies and clusters of galaxies is several times stronger than the observed matter can provide. Most of the material in the universe is probably still hidden from astronomers;

· There is no unified theory of the formation of galaxies;

· The main problems of cosmology have not been resolved: there is no complete physical theory of the birth of the Universe and its fate in the future is not clear.

Here are some of the questions astronomers hope to answer in the 21st century:

· Do the nearest stars have terrestrial planets and do they have biospheres (do they have life on them)?

· What processes contribute to the beginning of the formation of stars?

· How are biologically important chemical elements such as carbon and oxygen formed and distributed in the Galaxy?

· Are black holes the source of energy for active galaxies and quasars?

· Where and when did galaxies form?

· Will the Universe expand forever, or will its expansion be replaced by a collapse?

TICKET number 9

Kepler's laws, their discovery, meaning and limits of applicability.

The three laws of motion of the planets relative to the Sun were deduced empirically by the German astronomer Johannes Kepler at the beginning of the 17th century. This became possible thanks to many years of observations by the Danish astronomer Tycho Brahe.

First Kepler's law. Each planet moves along an ellipse, in one of the focuses of which is the Sun ( e = c / a, where with- distance from the center of the ellipse to its focus, a- semi-major axis, e - eccentricity ellipse. The larger e, the more the ellipse differs from the circle. If with= 0 (foci coincide with the center), then e = 0 and the ellipse turns into a circle with radius a).

Second Kepler's law (law of equal areas). The radius vector of the planet for equal time intervals describes equal areas. Another formulation of this law: the sectorial speed of the planet is constant.

Third Kepler's law. The squares of the orbital periods of the planets around the Sun are proportional to the cubes of the semi-major axes of their elliptical orbits.

The modern formulation of the first law is supplemented as follows: in unperturbed motion, the orbit of a moving body is a second-order curve - an ellipse, parabola, or hyperbola.

Unlike the first two, Kepler's third law applies only to elliptical orbits.

The speed of the planet at perihelion: where V c = circular speed at R = a.

Aphelion speed :.

Kepler discovered his laws empirically. Newton derived Kepler's laws from the law of universal gravitation. To determine the masses of celestial bodies, it is important that Newton generalizes Kepler's third law to any system of revolving bodies. In generalized form, this law is usually formulated as follows: the squares of the periods T 1 and T 2 of the revolution of two bodies around the Sun, multiplied by the sum of the masses of each body (M 1 and M 2, respectively) and the Sun (M s), are related as cubes of the semi-major axes a 1 and a 2 of their orbits: ... In this case, the interaction between the bodies M 1 and M 2 is not taken into account. If we neglect the masses of these bodies in comparison with the mass of the Sun, we get the formulation of the third law given by Kepler himself: ... Kepler's third law can be used to determine the mass of binaries.

Drawing an object (planet, comet, etc.) on a star map at specified coordinates.

TICKET number 10

Terrestrial planets: Mercury, Mars, Venus, Earth, Pluto. They have small sizes and masses, the average density of these planets is several times higher than the density of water. They slowly rotate around their axes. They have few companions. Terrestrial planets have hard surfaces. The similarity of the terrestrial planets does not exclude a significant difference. For example, Venus, unlike other planets, rotates in the direction opposite to its movement around the Sun, and is 243 times slower than the Earth. Pluto is the smallest of the planets (Pluto diameter = 2260 km, satellite - Charon is 2 times smaller, approximately the same as the Earth - Moon system, it is a "double planet"), but in terms of physical characteristics it is close to this group.

Pluto / Charon.

Weight: 1.3 * 10 23 kg / 1.8 * 10 11 kg

Orbit R: 29.65-49.28 AU

D planet: 2324/1212 km

Atmospheric composition: Thin layer of methane

Features: A binary planet, possibly a planetezemal, the orbit does not lie in the plane of other orbits. Pluto and Charon always face each other on the same side

The giant planets: Jupiter, Saturn, Uranus, Neptune.

They are large in size and mass (the mass of Jupiter> the mass of the Earth by 318 times, by volume - by 1320 times). The giant planets revolve very quickly around their axes. The result is a lot of compression. The planets are located far from the Sun. They differ in a large number of satellites (Jupiter has 16, Saturn has 17, Uranus has 16, and Neptune has 8). A feature of the giant planets is the rings, consisting of particles and blocks. These planets do not have hard surfaces, their density is low, and consist mainly of hydrogen and helium. The gaseous hydrogen of the atmosphere passes into a liquid and then into a solid phase. At the same time, the rapid rotation and the fact that hydrogen becomes a conductor of electricity causes significant magnetic fields of these planets, which catch charged particles flying from the Sun and form radiation belts.

Setting the model of the celestial sphere for a given latitude and its orientation to the sides of the horizon.

TICKET number 11

Distinctive features of the moon and satellites of the planets.

moon- the only natural satellite of the Earth. The surface of the moon is highly heterogeneous. The main large-scale formations - seas, mountains, craters and bright rays, possibly - are emissions of matter. The seas, dark, smooth plains, are depressions filled with solidified lava. The diameters of the largest of them exceed 1000 km. Dr. three types of formations are most likely a consequence of the bombardment of the lunar surface in the early stages of the existence of the solar system. The bombardment lasted several. hundreds of millions of years, and debris settled on the surface of the moon and planets. Fragments of asteroids ranging in diameter from hundreds of kilometers to the smallest dust particles formed Ch. details of the moon and surface rock. The period of the bombardment was followed by the filling of the seas with basaltic lava generated by the radioactive heating of the lunar interior. Cosmic devices Apparatus of the Apollo series recorded the seismic activity of the Moon, the so-called. l unquake. Samples of the lunar soil, delivered to Earth by astronauts, showed that the age of L. 4.3 billion years, probably the same as that of the Earth, consists of the same chemical. elements as the Earth, with approximately the same ratio. There is no atmosphere on L., and probably never was, and there is no reason to assert that life ever existed there. According to the latest theories, L. was formed as a result of collisions of planetesimals the size of Mars and the young Earth. The temp-pa of the lunar surface reaches 100 ° C on a lunar day and drops to -200 ° C on a lunar night. On L. there is no erosion, for a claim. slow destruction of rocks due to alternating thermal expansion and contraction; and occasional sudden local catastrophes due to meteorite impacts.

The mass of L. is accurately measured by studying the orbits of its arts, satellites, and refers to the mass of the Earth as 1 / 81.3; its diameter of 3476 km is 1 / 3.6 of the Earth's diameter. L. has the shape of an ellipsoid, although three mutually perpendicular diameters differ by no more than a kilometer. The period of rotation of the moon is equal to the period of revolution around the earth, so that, apart from the effects of libration, it is always turned towards it with one side. Wed density 3330 kg / m 3, the value is very close to the density of the main rocks, lying under the earth's crust, and the force of gravity on the surface of the moon is 1/6 of the earth. The moon is the celestial body closest to the Earth. If the Earth and the Moon were point masses or rigid spheres, the density of which changes only with distance from the center, and there would be no other celestial bodies, then the Moon's orbit around the Earth would be an unchanging ellipse. However, the Sun and, to a much lesser extent, the planets have gravitational effects. impact on the L., causing perturbation of its orbital elements; therefore, the semi-major axis, eccentricity, and inclination are continuously subjected to cyclical perturbations, oscillating relative to the mean values.

Natural satellites, a natural body orbiting the planet. More than 70 satellites of various sizes are known in the solar system and new ones are being discovered all the time. The seven largest moons are the Moon, the four Galilean moons of Jupiter, Titan and Triton. All of them have diameters exceeding 2500 km, and are small "worlds" with complex geology. history; some have an atmosphere. All other satellites are comparable in size to asteroids, i.e. from 10 to 1500 km. They can be composed of rock or ice, the shape ranges from nearly spherical to irregular, the surface is either ancient with numerous craters, or has undergone changes associated with activity in the interior. The sizes of the orbits are in the range from less than two to several hundred radii of the planet, the orbital period is from several hours to more than a year. It is believed that some satellites were captured by the planet's gravitational pull. They have irregular orbits and sometimes rotate in the opposite direction to the orbital motion of the planet around the Sun (the so-called reverse motion). Orbits of S.E. can be strongly inclined to the plane of the planet's orbit or very elongated. Extended systems C.E. with regular orbits around the four giant planets, probably arose from the gas and dust cloud that surrounded the parent planet, similar to the formation of planets in the protosolar nebula. S.E. sizes less than several. hundreds of kilometers are irregular in shape and are likely formed by destructive collisions of larger bodies. In ext. regions of the solar system, they often orbit near the rings. Orbital elements ext. SE, especially eccentricities, are subject to strong disturbances caused by the Sun. Several pairs and even S.E. have periods of circulation connected by a simple ratio. For example, Jupiter's moon Europa has a period nearly half that of Ganymede. This phenomenon is called resonance.

Determination of visibility conditions for the planet Mercury according to the "School Astronomical Calendar".

TICKET number 12

Comets and asteroids. Foundations of modern ideas about the origin of the solar system.

Comet, the celestial body of the solar system, consisting of ice and dust particles, moving in highly elongated orbits, which means that, at a distance from the Sun, they look like faintly luminous oval specks. As it approaches the Sun, a coma is formed around this nucleus (An almost spherical gas-dust envelope surrounding the comet's head as it approaches the Sun. This "atmosphere", continuously blown away by the solar wind, is replenished by gas and dust escaping from the nucleus. The diameter of the comet reaches 100 thousand . km. The escape velocity of gas and dust is several kilometers per second relative to the nucleus, and they are scattered in interplanetary space partially through the comet's tail.) space of the comet's atmosphere.In most comets, X. appears when they approach the Sun at a distance of less than 2 AU X. is always directed from the Sun. Gas X. is formed by ionized molecules ejected from the nucleus, under the influence of solar radiation has a bluish color, distinct boundaries, typical width is 1 million km, length is tens of millions of kilometers. The structure of X. can change markedly during several. hours. The speed of individual molecules ranges from 10 to 100 km / sec. Dusty X. is more vague and curved, and its curvature depends on the mass of dust particles. Dust is continuously released from the core and carried away by the gas flow.). The center, part of the planet, is called the core and is an icy body - the remnants of huge clusters of icy planetesimals that formed during the formation of the solar system. Now they are focused on the periphery - in the Oort-Epic cloud. The average mass of a core is 1-100 billion kg, diameter is 200-1200 m, density is 200 kg / m a third of the dusty island. Ice is mainly water, but there are impurities of other compounds. Each time it returns to the Sun, the ice melts, gas molecules leave the core and carries away dust and ice particles, while a spherical shell is formed around the core - a coma, a long plasma tail directed away from the Sun and a dust tail The amount lost depends on the amount of dust covering the core and the distance from the Sun at perihelion. Halley's comet at close range, confirmed many theories of the structure of K.

To. Are usually named after their discoverers, indicating the year when they were last observed. Subdivided into short-period. and long-term game. Short-period To. Revolve around the sun with a period of several. years, on Wed. OK. 8 years; the shortest period - a little over 3 years - has K. Encke. These K. were captured by the gravitats. field of Jupiter and began to rotate in relatively small orbits. A typical one has a distance at perihelion of 1.5 AU. and completely collapses after 5 thousand revolutions, giving rise to a meteor shower. Astronomers observed the disintegration of K. West in 1976 and K. * Biel. On the contrary, the periods of circulation are long-period. K. can reach 10 thousand, or even 1 million years, and their aphelions can be located at "one third of the distance to the nearest stars. At the present, the time is known about 140 short-period and 800 long-period. K., and every year opens about 30 new K. Our knowledge of these objects is incomplete, because they are detected only when they approach the Sun at a distance of about 2.5 AU It is assumed that about a trillion K.

Asteroid(asteroid), a small planet, which has a close-to-circular orbit lying near the plane of the ecliptic between the orbits of Mars and Jupiter. The newly discovered A. is assigned a serial number after determining their orbit, accurate enough so that A. “is not lost”. In 1796, the French. astronomer Joseph Jérôme Lalande proposed to begin the search for the “missing” planet between Mars and Jupiter, predicted by Bode's rule. On New Year's Eve 1801 Italian. astronomer Giuseppe Piazzi discovered Ceres during observations to compile a star catalog. Him. scientist Karl Gauss calculated its orbit. By the crust, about 3500 asteroids are known. The radii of Ceres, Pallas and Vesta are 512, 304 and 290 km, respectively, the rest are smaller. According to estimates in Ch. the belt is approx. 100 million A., their total mass, apparently, is about 1/2200 of the mass originally present in this area. The emergence of modern. A., possibly, is associated with the destruction of the planet (traditionally called Phaeton, the modern name is Olbers' planet) as a result of collisions with another body. The surfaces of the monitored A. are composed of metals and rocks. Depending on their composition, asteroids are divided into types (C, S, M, U). U-type train not identified.

A. are also grouped according to the elements of the orbits, forming the so-called. of the Hirayama family. Most A. has a circulation period of approx. 8 hours All A. with a radius of less than 120 km have an irregular shape, and their orbits are subject to gravity. the influence of Jupiter. As a result, there are gaps in the distribution of A. along the semi-major axes of the orbits, called Kirkwood hatches. A., trapped in these hatches, would have periods that are multiples of the orbital period of Jupiter. The orbits of the asteroids in these hatches are extremely unstable. Int. and ext. the edges of the belt A. lie in areas where this ratio is 1: 4 and 1: 2. A.

When a protostar contracts, it forms a disk of matter that surrounds the star. Part of the material of this disk falls back onto the star, obeying the force of gravity. The gas and dust that remain in the disc gradually cool down. When the temperature drops low enough, the material of the disk begins to collect in small clumps - the centers of condensation. This is how planetesimals arise. During the formation of the solar system, some of the planetesimals collapsed as a result of collisions, while others combined to form planets. In the outer part of the solar system, large planetary cores formed, which were able to hold on themselves a certain amount of gas in the form of a primary cloud. Heavier particles were held by the gravity of the Sun and, under the influence of tidal forces, could not form into planets for a long time. This was the beginning of the formation of "gas giants" - Jupiter, Saturn, Uranus and Neptune. They likely developed their own mini-disks of gas and dust, which eventually formed moons and rings. Finally, in the inner solar system, solid matter forms Mercury, Venus, Earth and Mars.

Determination of the conditions of visibility of the planet Venus according to the "School Astronomical Calendar".

TICKET number 13

The sun is like a typical star. Its main characteristics.

The sun, the central body of the solar system, is an incandescent plasma ball. The star around which the Earth revolves. An ordinary main sequence star of spectral type G2, a self-luminous mass of gas, consisting of 71% hydrogen and 26% helium. The absolute stellar magnitude is +4.83, the effective surface temperature is 5770 K. At the center of the Sun it is 15 * 10 6 K, which provides pressure that can withstand the force of gravity, which on the surface of the Sun (photosphere) is 27 times greater than on Earth. Such a high temperature occurs due to thermonuclear reactions of the conversion of hydrogen into helium (proton-proton reaction) (energy output from the surface of the photosphere is 3.8 * 10 26 W). The sun is a spherically symmetrical body in equilibrium. Depending on the change in physical conditions, the Sun can be divided into several concentric layers that gradually merge into each other. Almost all of the Sun's energy is generated in the central region - core, where the thermonuclear fusion reaction takes place. The nucleus occupies less than 1/1000 of its volume, the density is 160 g / cm 3 (the density of the photosphere is 10 million times less than the density of water). Due to the huge mass of the Sun and the opacity of its substance, radiation goes from the core to the photosphere very slowly - about 10 million years. During this time, the frequency of the X-ray radiation decreases and it becomes visible light. However, neutrinos produced in nuclear reactions freely leave the Sun and, in principle, provide direct information about the nucleus. The discrepancy between the observed and predicted neutrino flux has given rise to serious controversy about the internal structure of the Sun. Over the last 15% of the radius, there is a convective zone. Convective motions also play a role in the transfer of magnetic fields generated by currents in its rotating inner layers, which manifests itself as solar activity, the strongest fields are observed in sunspots. Outside the photosphere, there is the solar atmosphere, in which the temperature reaches a minimum value of 4200 K, and then increases again due to the dissipation of shock waves generated by subphotospheric convection in the chromosphere, where it sharply increases to a value of 2 * 10 6 K, characteristic of the corona. The high temperature of the latter leads to a continuous outflow of plasma matter into interplanetary space in the form of the solar wind. In some areas, the magnetic field strength can rapidly and strongly increase. This process is accompanied by a whole complex of solar activity phenomena. These include solar flares (in the chromosphere), prominences (in the solar corona), and coronal holes (special regions of the corona).

The mass of the Sun is 1.99 * 10 30 kg, the average radius, determined by an approximately spherical photosphere, is 700,000 km. This is equivalent to 330,000 Earth masses and 110 Earth radii, respectively; the Sun can fit 1.3 million bodies like the Earth. The rotation of the Sun causes the movement of its surface formations, such as sunspots, in the photosphere and the layers above it. The average rotation period is 25.4 days, with 25 days at the equator and 41 days at the poles. Rotation causes the solar disk to shrink by 0.005%.

Determination of visibility conditions for the planet Mars according to the "School Astronomical Calendar".

TICKET number 14

The most important manifestations of solar activity, their relationship with geophysical phenomena.

Solar activity is a consequence of the convection of the middle layers of the star. The reason for this phenomenon is that the amount of energy coming from the core is much greater than that removed by thermal conductivity. Convection causes strong magnetic fields generated by currents in the convective layers. The main manifestations of solar activity affecting the earth are sunspots, solar wind, prominences.

Sun spots, formations in the photosphere of the Sun, have been observed since ancient times, and at present, they are considered areas of the photosphere with a temperature 2000 K lower than in the surrounding, due to the presence of a strong magnetic field (about 2000 G). S. p. consist of a relatively dark center, a part (shadow) and a lighter fibrous penumbra. The gas flow from shadow to penumbra is called the Evershed effect (V = 2 km / s). Number of C. p. and their appearance changes over the 11 year the cycle of solar activity, or the cycle of sunspots, which is described by Sperer's law and is graphically illustrated by the Maunder butterfly diagram (movement of spots in latitude). Zurich relative sunspot number indicates the total surface area covered by the C. p. Long-term variations are superimposed on the main 11-year cycle. For example, S.p. change the magn. polarity over a 22-year solar cycle. But naib, a striking example of long-term variation is the minimum. Maunder (1645-1715), when S. p. were absent. Although it is generally accepted that variations in the number of S.p. determined by the diffusion of the magnetic field from the rotating solar interior, the process is not yet fully understood. The strong magnetic field of sunspots affects the Earth's field, causing radio interference and the aurora. there are several. irrefutable short-period effects, the statement about the existence of long-period. the relationship between climate and the number of S.p., especially the 11-year cycle, is highly controversial, which is due to difficulties in meeting the conditions that are necessary when conducting an accurate statistical analysis of data.

sunny wind The outflow of high-temperature plasma (electrons, protons, neutrons and hadrons) of the solar corona, the emission of intense radio spectrum waves, X-rays into the surrounding space. Forms the so-called. a heliosphere extending over 100 AU. from the sun. The solar wind is so intense that it can damage the outer layers of comets, causing a "tail". S.V. it ionizes the upper layers of the atmosphere, thereby forming the ozone layer, causing auroras and an increase in radioactive background and radio interference in places where the ozone layer is depleted.

The last maximum solar activity was in 2001. Maximum solar activity means the greatest number of sunspots, radiation and prominences. It has long been established that a change in solar activity of the Sun affects the following factors:

* epidemiological situation on Earth;

* the number of different kinds of natural disasters (typhoons, earthquakes, floods, etc.);

* on the number of road and rail accidents.

The maximum of all this falls on the years of the active Sun. As the scientist Chizhevsky established, the active Sun affects the well-being of a person. Since then, periodic forecasts of human well-being have been made.

2. Determination of the visibility conditions of the planet Jupiter according to the "School astronomical calendar".

TICKET number 15

Methods for determining distances to stars, distance units and the relationship between them.

The parallax method is used to measure the distance to the bodies of the solar system. The radius of the earth turns out to be too small to serve as a basis for measuring the parallax displacement of stars and the distance to them. Therefore, use the annual parallax instead of the horizontal one.

The annual parallax of a star is the angle (p) at which one could see the semi-major axis of the earth's orbit from the star if it is perpendicular to the line of sight.

a - semi-major axis of the earth's orbit,

p - annual parallax.

The unit of distance is also parsec. Parsec is the distance from which the semi-major axis of the earth's orbit, perpendicular to the line of sight, is seen at an angle of 1².

1 parsec = 3.26 light years = 206265 AU. e. = 3 * 10 11 km.

By measuring the annual parallax, you can reliably establish the distance to stars that are no more than 100 parsecs or 300 sv. years.

If the absolute and apparent stellar magnitudes are known, then the distance to the star can be determined by the formula log (r) = 0.2 * (m-M) +1

Determination of the conditions for the visibility of the Moon according to the "School Astronomical Calendar".

TICKET number 16

The main physical characteristics of stars, the relationship of these characteristics. Equilibrium conditions for the stars.

The main physical characteristics of stars: luminosity, absolute and visible magnitudes, mass, temperature, size, spectrum.

Luminosity- energy emitted by a star or other celestial body per unit of time. Usually given in units of the luminosity of the Sun, it is expressed by the formula log (L / Lc) = 0.4 (Mc - M), where L and M are the luminosity and absolute magnitude of the source, Lc and Mc are the corresponding values ​​for the Sun (Mc = +4 , 83). Also determined by the formula L = 4πR 2 σT 4. Stars are known whose luminosity is many times greater than the luminosity of the Sun. Aldebaran's luminosity is 160, and Rigel's is 80,000 times that of the Sun. But the overwhelming majority of stars have luminosities comparable to the solar one or less.

Magnitude - a measure of the brightness of a star. З.в. does not give a true idea of ​​the radiation power of the star. A faint star close to Earth may appear brighter than a distant bright star because the radiation flux received from it decreases in inverse proportion to the square of the distance. Visible Z. - the shine of a star, which the observer sees when looking at the sky. Absolute Z.v. - a measure of true brightness, represents the brightness level of a star, which it would have, being at a distance of 10 pc. Hipparchus invented the system of visible ZV. in the 2nd century. BC. The stars were assigned numbers according to their apparent brightness; the brightest stars were 1st magnitude, and the faintest ones were 6th. All R. 19th century this system has been modified. Modern scale of z.v. was established by determining З.в. representative sample of stars near sowing. poles of the world (north polar row). According to them, the Z.V. were determined. all other stars. This is a logarithmic scale, where 1st magnitude stars are 100 times brighter than 6th magnitude stars. As the measurement accuracy increased, it was necessary to introduce tenths. The brightest stars are brighter than 1st magnitude, and some even have negative stellar magnitudes.

Stellar mass - a parameter directly determined only for the components of binary stars with known orbits and distances (M 1 + M 2 = R 3 / T 2). That. the masses of only a few tens of stars have been established, but for a much larger number, the mass can be determined from the mass-luminosity dependence. Masses greater than 40 solar masses and less than 0.1 solar masses are very rare. Most stars are less than solar masses. The temperature in the center of such stars cannot reach the level at which nuclear fusion reactions begin, and the source of their energy is only the Kelvin-Helmholtz compression. Such objects are called brown dwarfs.

Mass-luminosity ratio, found in 1924 by Eddington, the relationship between the luminosity L and the stellar mass M. a usually lies in the 3-5 range. The ratio follows from the fact that the observed holy islands of normal stars are determined mainly by their mass. This ratio for dwarf stars is in good agreement with observations. It is believed that it is also valid for supergiants and giants, although their mass is difficult to measure directly. The ratio is not applicable to white dwarfs, since overestimates their luminosity.

Stellar temperature- the temperature of a certain region of the star. Refers to the most important physical characteristics of any object. However, due to the fact that the temperature of different regions of the star is different, and also due to the fact that temperature is a thermodynamic quantity that depends on the flux of electromagnetic radiation and the presence of various atoms, ions and nuclei in a certain region of the stellar atmosphere, all these differences are united into the effective temperature, which is closely related to the radiation of the star in the photosphere. Effective temperature, a parameter characterizing the total amount of energy emitted by a star from a unit of its surface area. This is an unambiguous method for describing stellar temperature. This. is defined in terms of the temperature of a black body, which, according to the Stefan-Boltzmann law, would emit the same power per unit surface area as a star. Although the spectrum of a star in details differs significantly from the spectrum of an absolutely black body, nevertheless, the effective temperature characterizes the energy of the gas in the outer layers of the stellar photosphere and allows, using Wien's displacement law (λ max = 0.29 / T), to determine at what wavelength accounts for the maximum stellar radiation, and therefore the color of the star.

By size stars are divided into dwarfs, subdwarfs, normal stars, giants, subgiants, and supergiants.

Spectrum stars depends on its temperature, pressure, gas density of its photosphere, magnetic field strength and chemical. composition.

Spectral classes, classification of stars according to their spectra (primarily according to attribution, the intensities of spectral lines), first introduced by ital. astronomer Secchi. Introduced letter designations, to-rye were modified as the knowledge of internal equipment expanded. the structure of the stars. The color of a star depends on the temperature of its surface, therefore, in modern times. Draper's spectral classification (Harvard) S. to. are arranged in decreasing order of temperature:

Hertzsprung - Russell diagram, the graph, which allows you to determine the two main characteristics of stars, expresses the relationship between absolute magnitude and temperature. Named after Danish astronomer Hertzsprung and American astronomer Russell, who published the first diagram in 1914. The hottest stars are in the left diagram, and the highest luminosity stars are at the top. From the top-left corner to the bottom-right corner passes main sequence, reflecting the evolution of stars, and ending in dwarf stars. Most of the stars belong to this sequence. The sun also belongs to this sequence. Above this sequence, subgiants, supergiants and giants are located in the indicated order, below - subdwarfs and white dwarfs. These groups of stars are called luminosity classes.

Equilibrium conditions: as you know, stars are the only natural objects within which uncontrolled thermonuclear fusion reactions occur, which are accompanied by the release of a large amount of energy and determine the temperature of the stars. Most of the stars are stationary, that is, they do not explode. Some stars explode (so-called novae and supernovae). Why are the stars in general in equilibrium? The force of nuclear explosions near stationary stars is balanced by the force of gravity, which is why these stars remain in equilibrium.

Calculation of the linear dimensions of the luminary from the known angular dimensions and distance.

TICKET number 17

1. The physical meaning of the Stefan-Boltzmann law and its application to determine the physical characteristics of stars.

Stephen-Boltzmann law, the ratio between the total radiation power of an absolutely black body and its temperature. The total power of a unit radiation area in W per 1 m 2 is given by the formula P = σ T 4, where σ = 5.67 * 10 -8 W / m 2 K 4 is the Stefan-Boltzmann constant, T is the absolute temperature of the black body. Although, astronomer, objects rarely emit as a black body, their emission spectrum is often a good model for the spectrum of a real object. The dependence on temperature to the 4th degree is very strong.

e - radiation energy per unit surface of the star

L is the luminosity of the star, R is the radius of the star.

Using the Stefan-Boltzmann formula and Wien's law, determine the wavelength at which the maximum radiation falls:

l max T = b, b - Wien's constant

We can proceed from the opposite, that is, using the luminosity and temperature to determine the size of the stars

2. Determination of the geographic latitude of the place of observation by the given height of the luminary at the culmination and its declination.

H = 90 0 - +

h - luminary height

TICKET number 18

Variable and non-stationary stars. Their importance for studying the nature of stars.

The brightness of variable stars changes over time. Now it is known approx. 3 * 10 4. P.Z. They are subdivided into physical, the brightness of which changes due to processes occurring in them or around them, and optical P.Z., where this change is due to rotation or orbital motion.

The most important types of physical. P.Z .:

Pulsing - Cepheids, Mira Ceti-like stars, semi-regular and irregular red giants;

Eruptive(explosive) - stars with envelopes, young irregular variables, incl. T Tauri stars (very young irregular stars associated with diffuse nebulae), Hubble-Sainage supergiants "Blowing off" of stellar shells. Potential supernovae.), Flashing red dwarfs;

Cataclysmic - new, supernova, symbiotic;

X-ray binaries

The specified P.z. include 98% of the known physical p.z. Optical binaries include eclipsing binaries and rotating ones such as pulsars and magnetic variables. The sun is a rotating one, because its magnitude changes little when sunspots appear on the disk.

Among the pulsating stars, the Cepheids are very interesting, named after one of the first discovered variables of this type - 6 Cephei. Cepheids are stars of high luminosity and moderate temperature (yellow supergiants). In the course of evolution, they acquired a special structure: at a certain depth, a layer arose that accumulates energy coming from the depths, and then gives it back again. The star periodically contracts, warming up, and expands, cooling. Therefore, the radiation energy is either absorbed by the stellar gas, ionizing it, then it is released again when, when the gas cools, the ions capture electrons, emitting light quanta. As a result, the brightness of the Cepheid changes, as a rule, several times with a period of several days. Cepheids play a special role in astronomy. In 1908, the American astronomer Henrietta Leavitt, who studied the Cepheids in one of the nearest galaxies, the Small Magellanic Cloud, drew attention to the fact that these stars turned out to be brighter, the longer the period of their brightness change. The Small Magellanic Cloud is small compared to its distance, which means that the difference in apparent brightness reflects a difference in luminosity. Thanks to the period - luminosity relationship found by Leavitt, it is easy to calculate the distance to each Cepheid by measuring its average brightness and the period of variability. And since supergiants are clearly visible, Cepheids can be used to determine distances even to relatively distant galaxies in which they are observed. There is a second reason for the special role of Cepheids. In the 60s. Soviet astronomer Yuri Nikolaevich Efremov found that the longer the period of the Cepheid, the younger this star. According to the period - age dependence, it is easy to determine the age of each Cepheid. By selecting stars with maximum periods and studying the stellar groupings they belong to, astronomers are exploring the youngest structures in the Galaxy. More than other pulsating stars, Cepheids deserve the name of periodic variables. Each subsequent cycle of brightness changes usually repeats the previous one quite accurately. However, there are exceptions, the most famous of which is the North Star. It has long been discovered that it belongs to the Cepheids, although it changes brightness within rather insignificant limits. But in recent decades, these fluctuations began to fade, and by the mid-90s. The Pole Star has practically ceased to pulsate.

Stars with shells, stars, continuously or at irregular intervals, ejecting a ring of gas from the equator or a spherical shell. 3.with about. - giants or dwarf stars of spectral class B, rapidly rotating and close to the destruction limit. The shedding of the shell is usually accompanied by a drop or increase in gloss.

Symbiotic stars, stars whose spectra contain emission lines and combine the characteristic features of a red giant and a hot object - a white dwarf or accretion disk around such a star.

RR Lyrae stars represent another important group of pulsating stars. These are old stars about the same mass as the Sun. Many of them are found in globular star clusters. As a rule, they change their brightness by one magnitude in about a day. Their properties, like those of Cepheids, are used to calculate astronomical distances.

R of the Northern Crown and stars like her behave in completely unpredictable ways. Usually this star can be seen with the naked eye. Every few years, its brightness drops to about the eighth magnitude, and then gradually increases, returning to the previous level. Apparently, the reason is that this supergiant star is throwing off clouds of carbon, which condenses into grains, forming something like soot. If one of these thick black clouds passes between us and the star, it blocks the star's light until the cloud dissipates into space. Stars of this type produce thick dust, which is important in areas where stars are formed.

Flashing stars... Magnetic phenomena on the Sun cause sunspots and solar flares, but they cannot significantly affect the brightness of the Sun. For some stars - red dwarfs - this is not the case: on them, such flares reach enormous scales, and as a result, the light emission can increase by an entire stellar magnitude, or even more. The closest star to the Sun, Proxima Centaur, is one such flare star. These light emissions cannot be predicted in advance and only last for a few minutes.

Calculation of the declination of a star based on data on its height at the culmination at a certain latitude.

H = 90 0 - +

h - luminary height

TICKET number 19

Binary stars and their role in determining the physical characteristics of stars.

A binary star, a pair of stars bound into one system by gravitational forces and revolving around a common center of gravity. The stars that make up a binary star are called its components. Binary stars are quite common and come in several types.

Each component of the visual binary is clearly visible through a telescope. The distance between them and the mutual orientation slowly change over time.

The elements of the eclipsing binary alternately block each other, so the brightness of the system temporarily weakens, the period between two changes in brightness is equal to half the orbital period. The angular distance between the components is very small and we cannot observe them individually.

Spectroscopic binaries are detected by changes in their spectra. With mutual circulation, the stars periodically move in the direction of the Earth, then away from the Earth. The Doppler effect in the spectrum can be used to determine changes in motion.

Polarization binaries are characterized by periodic changes in the polarization of light. In such systems, stars, in their orbital motion, illuminate gas and dust in the space between them, the angle of incidence of light on this substance periodically changes, while the scattered light is polarized. Accurate measurements of these effects allow one to calculate orbits, stellar mass ratios, sizes, velocities and distance between components... For example, if a star is simultaneously eclipsing and spectroscopic binary, then one can determine the mass of each star and the inclination of the orbit... By the nature of the brightness change at the moments of eclipses, it is possible to determine the relative sizes of stars and study the structure of their atmospheres... Binary stars that emit X-ray radiation are called X-ray binaries. In a number of cases, a third component is observed, orbiting the center of mass of the binary system. Sometimes one of the components of the binary system (or both), in turn, can turn out to be binary stars. The close components of a binary star in a triple system can have a period of several days, while the third element can revolve around the common center of mass of a close pair with a period of hundreds or even thousands of years.

Measuring the velocities of stars in a binary system and applying the law of gravitation are an important method for determining the masses of stars. Studying binary stars is the only direct way to calculate stellar masses.

In a system of closely spaced binary stars, mutual gravitational forces tend to stretch each of them, give it the shape of a pear. If gravity is strong enough, a critical moment comes when matter begins to flow away from one star and fall onto another. Around these two stars there is a certain area in the shape of a three-dimensional figure eight, the surface of which is the critical boundary. These two pear-shaped figures, each around its own star, are called Roche lobes. If one of the stars grows so much that it fills its Roche lobe, then matter from it rushes to another star at the point where the cavities touch. Often stellar material does not land directly on the star, but first swirls, forming a so-called accretion disk. If both stars have expanded enough to fill their Roche lobes, then a contact double star is formed. The material of both stars is mixed and merged into a ball around two stellar cores. Since all stars ultimately swell to become giants, and many stars are binaries, interacting binaries are not uncommon.

Calculation of the height of the luminary at the culmination of the known declination for a given latitude.

H = 90 0 - +

h - luminary height

TICKET number 20

Evolution of stars, its stages and final stages.

Stars form in interstellar clouds of gas and dust and nebulae. The main force "forming" stars is gravity. Under certain conditions, a very rarefied atmosphere (interstellar gas) begins to contract under the influence of gravity. A cloud of gas condenses in the center, where the heat released during compression is retained - a protostar appears, emitting in the infrared range. The protostar heats up under the influence of the material falling on it, and nuclear fusion reactions begin with the release of energy. In this state, it is already a variable star of the T Tauri type. The remains of the cloud dissipate. Further, gravitational forces pull the hydrogen atoms to the center, where they merge, forming helium and releasing energy. The increasing pressure in the center prevents further compression. This is a stable phase of evolution. This star is the star of the Main Sequence. The luminosity of a star increases as its core thickens and warms up. The time during which a star belongs to the Main Sequence depends on its mass. The Sun has approximately 10 billion years of age, but stars that are much more massive than the Sun have been stationary for only a few million years. After the star has used up the hydrogen contained in its central part, major changes take place inside the star. The hydrogen begins to burn out not in the center, but in the shell, which increases in size and swells. As a result, the size of the star itself increases dramatically, and its surface temperature drops. It is this process that gives rise to red giants and supergiants. The final stages of a star's evolution are also determined by the mass of the star. If this mass does not exceed the solar mass by more than 1.4 times, the star will stabilize, becoming a white dwarf. Catastrophic compression does not occur due to the basic property of electrons. There is such a degree of compression at which they begin to repel, although there is no longer any source of thermal energy. This only happens when electrons and atomic nuclei are compressed incredibly tightly, forming extremely dense matter. A white dwarf with the mass of the Sun is approximately equal in volume to the Earth. The white dwarf gradually cools down, eventually turning into a dark ball of radioactive ash. According to astronomers, no less than a tenth of all stars in the Galaxy are white dwarfs.

If the mass of a contracting star is more than 1.4 times the mass of the Sun, then such a star, having reached the stage of a white dwarf, will not stop there. The gravitational forces in this case are so great that the electrons are pressed into the atomic nuclei. As a result, the protons turn into neutrons that can adhere to each other without any gaps. The density of neutron stars is even greater than that of white dwarfs; but if the mass of the material does not exceed 3 solar masses, neutrons, like electrons, are able to prevent further compression themselves. A typical neutron star is only 10 to 15 km across, and one cubic centimeter of its substance weighs about a billion tons. In addition to their enormous density, neutron stars have two other special properties that allow them to be detected, despite their small size: they are fast rotation and a strong magnetic field.

If the mass of a star exceeds 3 times the mass of the Sun, then the final stage of its life cycle is probably a black hole. If the mass of the star, and, consequently, the gravitational force is so great, then the star is subjected to catastrophic gravitational compression, which cannot be resisted by any stabilizing forces. The density of matter in the course of this process tends to infinity, and the radius of the object - to zero. According to Einstein's theory of relativity, a space-time singularity arises at the center of a black hole. The gravitational field on the surface of the contracting star grows, making it increasingly difficult for radiation and particles to leave it. In the end, such a star ends up under the event horizon, which can be visualized as a one-sided membrane that allows matter and radiation to pass only inward and does not release anything outward. The collapsing star turns into a black hole, and it can only be detected by a sharp change in the properties of space and time around it. The radius of the event horizon is called the Schwarzschild radius.

Stars with a mass of less than 1.4 solar masses at the end of their life cycle slowly shed their upper shell, which is called a planetary nebula. More massive stars, which turn into a neutron star or black hole, first explode as supernovae, their brightness increases by 20 magnitudes or more in a short time, more energy is released than the sun emits in 10 billion years, and the remnants of the exploding star scatter at a speed of 20 000 km per second.

Observing and sketching the positions of sunspots with a telescope (on the screen).

TICKET number 21

Composition, structure and size of our Galaxy.

Galaxy, the star system to which the Sun belongs. The galaxy contains at least 100 billion stars. Three main constituents: the central bulge, the disk, and the galactic halo.

The central bulge consists of old population II stars (red giants), located very densely, and in its center (core) there is a powerful radiation source. It was assumed that there is a black hole in the core, initiating the observed powerful energy processes accompanied by radiation in the radio spectrum. (The ring of gas revolves around the black hole; hot gas escaping from its inner edge falls onto the black hole, releasing energy, which we observe.) But recently, a burst of visible radiation was detected in the core and the hypothesis of a black hole has disappeared. The central thickening is 20,000 light years across and 3,000 light years thick.

The disk of the Galaxy, containing young population I stars (young blue supergiants), interstellar matter, open star clusters and 4 spiral arms, is 100,000 light years across and only 3,000 light years thick. The galaxy rotates, its inner parts pass through their orbits much faster than the outer ones. The sun makes a complete revolution around the core in 200 million years. The spiral arms are in continuous process of star formation.

The galactic halo is concentric with the disk and central bulge and consists of stars that are predominantly members of globular clusters and belong to type II populations. However, most of the matter in the halo is invisible and cannot be trapped in ordinary stars, it is not gas or dust. Thus, the halo contains dark invisible substance. Calculations of the speed of rotation of the Large and Small Magellanic Clouds, which are satellites of the Milky Way, show that the mass contained in the halo is 10 times the mass that we observe in the disk and thickening.

The Sun is located 2/3 from the center of the disk in the Orion Arm. Its localization in the plane of the disk (galactic equator) makes it possible to see from the Earth the stars of the disk in the form of a narrow strip The Milky Way, covering the entire celestial sphere and tilted at an angle of 63 ° to the celestial equator. The center of the Galaxy lies in Sagittarius, but it is not observable in visible light due to dark nebulae of gas and dust absorbing the light of the stars.

Calculation of the radius of a star from data on its luminosity and temperature.

L - luminosity (Lc = 1)

R - radius (Rc = 1)

T - Temperature (Tc = 6000)

TICKET number 22

Star clusters. The physical state of the interstellar medium.

Star clusters are groups of stars located relatively close to each other and linked by common motion in space. Apparently, almost all stars are born in groups, and not individually. Therefore, star clusters are a very common thing. Astronomers love to study star clusters because all the stars in the cluster formed at about the same time and at approximately the same distance from us. Any noticeable differences in brightness between such stars are true differences. It is especially useful to study star clusters from the point of view of the dependence of their properties on mass - after all, the age of these stars and their distance from the Earth are approximately the same, so that they differ from each other only in their mass. There are two types of star clusters: open and globular. In an open cluster, each star is visible separately; they are distributed more or less evenly over a certain area of ​​the sky. Globular clusters, on the other hand, are like a sphere so densely filled with stars that individual stars in its center are indistinguishable.

Open clusters contain between 10 and 1000 stars, among them much more young than old ones, and the oldest are hardly more than 100 million years old. The fact is that in older clusters, stars gradually move away from each other until they mix with the main set of stars. Although gravity holds the open clusters together to some extent, they are still rather fragile, and the gravity of another object can tear them apart.

The clouds in which stars are formed are concentrated in the disk of our Galaxy, and it is there that open star clusters are found.

In contrast to the open, globular clusters are spheres densely filled with stars (from 100 thousand to 1 million). A typical globular cluster is 20 to 400 light years across.

In the densely packed centers of these clusters, the stars are so close to each other that mutual gravity binds them together, forming compact binaries. Sometimes the stars even merge completely; with close proximity, the outer layers of the star can collapse, exposing the central core to a direct view. In globular clusters, binaries are 100 times more common than anywhere else.

Around our Galaxy, we know about 200 globular star clusters, which are distributed throughout the halo, which contains the Galaxy. All of these clusters are very old, and they arose more or less at the same time as the Galaxy itself. The clusters appear to have formed when portions of the cloud from which the Galaxy was created split into smaller fragments. Globular clusters do not diverge, because the stars in them sit very closely, and their powerful mutual gravitational forces bind the cluster into a dense whole.

The matter (gas and dust) in the space between the stars is called the interstellar medium. Most of it is concentrated in the spiral arms of the Milky Way and makes up 10% of its mass. In some areas, the substance is relatively cold (100 K) and is detectable by infrared radiation. Such clouds contain neutral hydrogen, molecular hydrogen, and other radicals that can be detected with radio telescopes. In regions near high luminosity stars, the gas temperature can reach 1000–10,000 K, and hydrogen is ionized.

The interstellar medium is very rarefied (about 1 atom per cm 3). However, in dense clouds, the concentration of matter can be 1000 times higher than the average. But even in a dense cloud, there are only a few hundred atoms per cubic centimeter. The reason why we still manage to observe interstellar matter is that we see it in a large thickness of space. The particles are 0.1 microns in size, contain carbon and silicon, and enter the interstellar medium from the atmosphere of cool stars as a result of supernova explosions. The resulting mixture forms new stars. The interstellar medium has a weak magnetic field and is permeated by streams of cosmic rays.

Our solar system is located in that region of the Galaxy where the density of interstellar matter is unusually low. This area is called the Local Bubble; it extends in all directions for about 300 light years.

Calculation of the angular dimensions of the Sun for an observer on another planet.

TICKET number 23

The main types of galaxies and their distinctive features.

Galaxies, a system of stars, dust and gas with a total mass of 1 million to 10 trillion. masses of the sun. The true nature of galaxies was not finally explained until the 1920s. after heated discussions. Until that time, when observed with a telescope, they looked like diffuse spots of light, resembling nebulae, but only with the help of the 2.5-meter reflector telescope of the Mount Wilson Observatory, first used in the 1920s, it was possible to obtain images of the department. stars in the Andromeda nebula and prove that it is a galaxy. The same telescope was used by Hubble to measure the periods of the Cepheids in the Andromeda nebula. These variable stars have been studied well enough to accurately determine their distances. The Andromeda Nebula is approx. 700 kpc, i.e. it lies far beyond our Galaxy.

There are several types of galaxies, the main ones are spiral and elliptical. Attempts have been made to classify them using alphabetic and numerical schemes, such as the Hubble classification, but some galaxies do not fit into these schemes, in this case they are named after the astronomers who first identified them (for example, the Seyfert and Markarian galaxies), or give alphabetic designation of classification schemes (for example, N-type and cD-type galaxies). Galaxies without a distinct shape are classified as irregular. The origin and evolution of galaxies are not yet fully understood. The best studied are spiral galaxies. These include objects with a bright core, from which spiral arms of gas, dust and stars emanate. Most spiral galaxies have 2 arms emanating from opposite sides of the core. As a rule, the stars in them are young. These are normal spirals. There are also crossed spirals, which have a central bridge of stars connecting the inner ends of the two arms. Our G. also belongs to the spiral. The masses of almost all spiral stars are in the range from 1 to 300 billion solar masses. About three quarters of all galaxies in the universe are elliptical... They are elliptical in shape with no discernible spiral structure. Their shape can vary from almost spherical to cigar-shaped. They are very diverse in size - from dwarf masses of several million solar to gigantic masses of 10 trillion solar. The largest known - CD galaxies... They have a large nucleus, or possibly several nuclei moving rapidly relative to each other. These are often quite strong radio sources. The Markarian galaxies were identified by the Soviet astronomer Veniamin Markarian in 1967. They are strong sources of radiation in the ultraviolet range. Galaxies N-type have a star-like faintly luminous core. They are also strong radio sources and are expected to evolve into quasars. In the photo, Seyfert galaxies look like normal spirals, but with a very bright core and spectra with broad and bright emission lines, indicating the presence of a large amount of rapidly rotating hot gas in their cores. This type of Galaxies was discovered by the American astronomer Karl Seyfert in 1943. Galaxies that are observed optically and at the same time are strong radio sources are called radio galaxies. These include Seyfert Galaxies, D- and N-type galaxies, and some quasars. The mechanism of energy generation in radio galaxies is not yet understood.

Determination of the visibility conditions of the planet Saturn according to the data of the School Astronomical Calendar.

TICKET number 24

Foundations of modern concepts of the structure and evolution of the Universe.

In the 20th century. understanding of the universe as a whole was achieved. The first important step was taken in the 1920s, when scientists came to the conclusion that our Galaxy - the Milky Way - is one of millions of galaxies, and the Sun is one of the millions of stars in the Milky Way. Subsequent studies of galaxies have shown that they are moving away from the Milky Way, and the further they are, the greater this speed (measured by the redshift in its spectrum). Thus, we live in the expanding universe. The scattering of galaxies is reflected in Hubble's law, according to which the redshift of a galaxy is proportional to the distance to it. In addition, on the largest scale, i.e. at the level of superclusters of galaxies, the Universe has a cellular structure. Modern cosmology (the doctrine of the evolution of the Universe) is based on two postulates: the Universe is homogeneous and isotropic.

There are several models of the universe.

In the Einstein - de Sitter model, the expansion of the Universe continues indefinitely; in the static model, the Universe does not expand and does not evolve; in a pulsating Universe, the cycles of expansion and contraction are repeated. However, the static model is the least likely, not only Hubble's law speaks in its favor, but also the background relict radiation discovered in 1965 (i.e., the radiation of the primary expanding incandescent four-dimensional sphere).

Some cosmological models are based on the theory of the "hot universe", which is presented below.

In accordance with Friedman's solutions to Einstein's equations, 10-13 billion years ago, at the initial moment of time, the radius of the Universe was equal to zero. All the energy of the Universe, all of its mass was concentrated in zero volume. The energy density is infinite, and the density of matter is also infinite. This state is called singular.

In 1946, Georgy Gamov and his colleagues developed a physical theory of the initial stage of the expansion of the Universe, explaining the presence of chemical elements in it by fusion at very high temperatures and pressures. Therefore, the beginning of the expansion, according to Gamow's theory, was called the "Big Bang". Gamow's co-authors were R. Alfer and G. Bethe, therefore this theory is sometimes called "α, β, γ-theory".

The universe is expanding from a state of infinite density. In a singular state, the usual laws of physics do not apply. Apparently, all fundamental interactions at such high energies are indistinguishable from each other. And from what radius of the Universe does it make sense to talk about the applicability of the laws of physics? The answer is from the Planck length:

Starting from the moment of time t p = R p / c = 5 * 10 -44 s (c is the speed of light, h is Planck's constant). Most likely, it was through t P that the gravitational interaction separated from the rest. According to theoretical calculations, during the first 10 -36 s, when the temperature of the Universe was more than 10 28 K, the energy per unit volume remained constant, and the Universe expanded at a speed significantly exceeding the speed of light. This fact does not contradict the theory of relativity, since not matter, but space itself, was expanding at such a speed. This stage of evolution is called inflationary... From modern theories of quantum physics, it follows that at this time the strong nuclear force separated from the electromagnetic and weak. The energy released as a result was the cause of the catastrophic expansion of the Universe, which in a tiny time interval of 10 - 33 s increased from the size of an atom to the size of the Solar system. At the same time, the usual elementary particles and a slightly smaller amount of antiparticles appeared. Matter and radiation were still in thermodynamic equilibrium. This era is called radiation stage of evolution. At a temperature of 5 ∙ 10 12 K, the stage ended recombinations: almost all protons and neutrons annihilated, turning into photons; only those remained for which there were not enough antiparticles. The initial excess of particles over antiparticles is one billionth of their number. It is from this "excess" substance that the substance of the observed Universe mainly consists. A few seconds after the Big Bang, the stage began primary nucleosynthesis when nuclei of deuterium and helium were formed, which lasted for about three minutes; then the quiet expansion and cooling of the universe began.

About a million years after the explosion, the balance between matter and radiation was disturbed, atoms began to form from free protons and electrons, and radiation began to pass through the substance as through a transparent medium. It was this radiation that was called relict, its temperature was about 3000 K. At present, a background with a temperature of 2.7 K is recorded. The relic background radiation was discovered in 1965. It turned out to be highly isotropic and by its existence confirms the model of a hot expanding Universe. After primary nucleosynthesis matter began to evolve independently, due to variations in the density of matter, formed in accordance with the Heisenberg uncertainty principle during the inflationary stage, protogalaxies appeared. Where the density was slightly higher than the average, centers of attraction were formed, areas with a lower density became increasingly rarefied, as matter left them in denser areas. This is how the practically homogeneous medium was divided into separate protogalaxies and their clusters, and hundreds of millions of years later the first stars appeared.

Cosmological models lead to the conclusion that the fate of the Universe depends only on the average density of the substance filling it. If it is below a certain critical density, the expansion of the Universe will continue forever. This option is called "open universe". A similar development scenario awaits a flat Universe, when the density is equal to the critical one. After a googol of years, all the matter in the stars will burn out, and the galaxies will plunge into darkness. Only the planets, white and brown dwarfs, will remain, and collisions between them will be extremely rare.

However, even in this case, the metagalaxy is not eternal. If the theory of the grand unification of interactions is correct, the protons and neutrons that make up the former stars will decay in 10 40 years. About 10 100 years later, giant black holes will evaporate. In our world, only electrons, neutrinos and photons will remain, remote from each other at great distances. In a sense, this will be the end of time.

If the density of the Universe turns out to be too high, then our world will be closed, and the expansion will sooner or later be replaced by a catastrophic contraction. The universe will end its life in gravitational collapse, in a sense it's even worse.

Calculation of the distance to the star from the known parallax.