Questions.

1. The apparent movement of the luminaries as a consequence 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. Reasons for changing phases of the Moon, conditions for the occurrence and frequency of Solar and Lunar eclipses (P. 6 paragraphs 1,2).
4. Features of the daily movement of the Sun at different latitudes at different times of the year (P.4 pp. 2, P. 5).
5. The principle of operation and purpose of the telescope (P. 2).
6. Methods for determining distances to solar system bodies and their sizes (Ap. 12).
7. Possibilities of spectral analysis and extra-atmospheric observations for studying nature celestial bodies(P. 14, “Physics” P. 62).
8. The most important directions and tasks of research and development outer space.
9. Kepler's law, its discovery, significance, limits of applicability (P. 11).
10. Main characteristics of the terrestrial planets, giant planets (P. 18, 19).
11. Distinctive features of the Moon and planetary satellites (P. 17-19).
12. Comets and asteroids. Basic ideas about the origin of the Solar system (P. 20, 21).
13. The sun is like typical star. Main characteristics (P. 22).
14. The most important manifestations of solar activity. Their connection with geographical phenomena (P. 22 paragraph 4).
15. Methods for determining distances to stars. Units of distances and connections between them (P. 23).
16. Basic physical characteristics of stars and their relationships (P. 23, paragraph 3).
17. Physical meaning Stefan-Boltzmann law and its application to determine physical characteristics 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. The evolution of stars, its stages and final stages (P. 26).
21. Composition, structure and size of our Galaxy (P. 27 paragraph 1).
22. Star clusters, physical state of the interstellar medium (P. 27 pp. 2, P. 28).
23. Main types of galaxies and their distinctive features(P. 29).
24. Fundamentals of modern ideas about the structure and evolution of the Universe (P. 30).

Practical tasks.

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

Answers.

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

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

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

h = 90° - j + d,

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

Geographic longitude is the second coordinate, measured from the prime Greenwich meridian 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 longitude:

l m - l Gr = t m - t Gr

Local time- this is solar time at a given place on Earth. At each point, local time is different, so people live according to standard time, that is, according to the time of the middle meridian of a given zone. The date line is 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 visible movement of the Moon against the background of stars towards the rotation of the sky. Every day the Moon shifts east relative to the stars by about 13°, and after 27.3 days it returns to the same stars, described in celestial sphere full circle.

The apparent movement of the Moon is accompanied by a continuous change in its appearance - a change of phases. This happens because the Moon occupies different positions relative to the Sun and the Earth that illuminate it.

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

The Earth and Moon, illuminated by the Sun, cast shadow cones and penumbra cones. When the Moon falls completely or partially into the Earth's shadow, a total or partial lunar eclipse occurs. From the Earth it is visible simultaneously everywhere where the Moon is above the horizon. The total eclipse phase 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, refracted in the Earth's atmosphere, fall into the cone of the earth's shadow. In this case, the atmosphere strongly absorbs blue and neighboring rays, and transmits mainly red ones into the cone. This is why the Moon, during a major eclipse phase, turns reddish and does not disappear completely. Lunar eclipses there are up to three times a year and, of course, only on the full moon.

A solar eclipse as a total one is visible only where a spot of the lunar shadow falls on the Earth; the diameter of the spot does not exceed 250 km. As the Moon moves through its orbit, its shadow moves across the Earth from west to east, tracing a successively narrow band 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 smaller than the solar one, sometimes equal to it. In the first case, a total eclipse of the Sun lasts up to 7 minutes 40 seconds, in the second, the Moon does not completely cover the Sun, and in the third, only for one moment.

There can be from 2 to 5 solar eclipses in a year, in the latter case they are certainly partial.

Ticket number 4. During the year, the Sun moves along the ecliptic. The ecliptic passes through 12 zodiac 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 inclination of the earth's axis to the orbital plane.

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 September 22.

Ticket number 5. Telescopes come in two types: reflecting telescope and refracting telescope (pictures).

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

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

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

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

Ticket number 7. Spectral analysis is the most important means to explore the universe. Spectral analysis is a method used to determine chemical composition celestial bodies, their temperature, size, structure, distance to them and speed of their movement. Spectral analysis is carried out using spectrograph and spectroscope instruments. Using spectral analysis, the chemical composition of stars, comets, galaxies and solar system bodies was determined, since in the spectrum each line or set of lines is characteristic of an element. The intensity of the spectrum can be used to determine the temperature of stars and other bodies.

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

M = m + 5 + 5log p

log L = 0.4(5 - M)

find the absolute magnitude, luminosity, and therefore the size of the star.

Using Doppler's formula

Creation of modern space stations, reusable ships, as well as the launch spaceships to the planets (“Vega”, “Mars”, “Moon”, “Voyager”, “Hermes”) made it possible to install telescopes on them, through which these luminaries can be observed close up without atmospheric interference.

Ticket number 8. The beginning of the space age 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 multi-stage rockets to launch spacecraft. Russia was a pioneer in this concept. First artificial satellite The Earth 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 American flight to the Moon - 1964, launch of spaceships and space stations.

1. Scientific goals:

• human presence in space;
• space exploration;
• development of space flight technologies;

1. Military purposes (protection against nuclear attack);
2. Telecommunications (satellite communications carried out using communication satellites);
3. Weather forecasts, prediction of natural disasters (meteo 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 in an ellipse, with the Sun at one of the focuses.

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

Third law. The squares of the sidereal periods of revolution of the planets are related as the cubes of the semimajor 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 semimajor axis of the earth's orbit is taken as the 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. Talk 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 smaller than the Earth in mass, its average density is 3300 kg/m 3, i.e. less than that of the Earth. There is no atmosphere on the Moon, only a thin shell of dust. The huge differences in temperature of the lunar surface from day to night are explained not only by the absence of an atmosphere, but also by the duration of the lunar day and lunar night, which corresponds to our two weeks. The temperature at the subsolar point of the Moon reaches + 120°C, and at the opposite point of the night hemisphere - 170°C.

1. Relief, seas, craters;
2. Chemical features surfaces;
3. Presence of tectonic activity.

Satellites of the planets:

1. Mars (2 small satellites: Phobos and Deimos);
2. Jupiter (16 satellites, the most famous 4 Galilean 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:

• Comet Halley (T = 76 years; 1910 - 1986 - 2062);
• Comet Enck;
• Comet Hyakutaki;

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

Research of comets, asteroids, meteor showers showed 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 by academician O. Yu. Schmidt, the Earth and planets arose from a gas-dust cloud, which, due to the law universal gravity was captured by the Sun and rotated in the same direction as the Sun. Gradually, condensations formed in this cloud, which gave rise to planets. Evidence that planets were formed from such concentrations is the fall of meteorites on Earth and other planets. Thus, in 1975, the fall of comet Wachmann-Strassmann onto 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 its study 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 a hot ball of gas. It mainly consists of hydrogen with an admixture of 10% (by the number of atoms) of helium, 1-2% of the mass of the Sun is accounted for by other heavier elements.

On the Sun, matter is highly ionized, that is, the 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/m3. However, this is an average number, and the density in the outer layers is disproportionately less, and in the center it is 100 times greater.

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

Under such 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 clashes end 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 a zone located along the photosphere. At times, 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 across the visible disk of the Sun. On this basis, he concluded that the Sun rotates around 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. Around the spots, almost imperceptible light formations are sometimes visible, which are called torches. Main feature spots and torches is the presence of magnetic fields with induction reaching 0.4-0.5 Tesla.

Ticket number 14. Manifestation of solar activity on Earth:

1. Sunspots are an active source electromagnetic radiation, causing the so-called " magnetic storms" These “magnetic storms” affect television and radio communications and cause powerful auroras.
2. The sun emits the following types of radiation: ultraviolet, x-rays, infrared and cosmic rays (electrons, protons, neutrons and heavy particles hadrons). These radiations are almost entirely blocked by the Earth's atmosphere. This is why the Earth's atmosphere should be kept normal. Periodically appearing ozone holes They transmit radiation from the Sun, which reaches the earth's surface and has a detrimental effect on 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 changes in solar activity of the Sun affect the following factors:

• epidemiological situation on Earth;
• the number of various types of natural disasters (typhoons, earthquakes, floods, etc.);
• on the number of automobile and train accidents.

The maximum of all this occurs during the years of the active Sun. As the scientist Chizhevsky established, the active Sun affects a person’s well-being. Since then, periodic forecasts of human well-being have been compiled.

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

The annual parallax of a star is the angle at which the semimajor axis of the Earth's orbit could be seen from the star if it is perpendicular to the line of sight.

a- semi-major axis earth's orbit,

p - annual parallax.

The distance unit parsec is also used. Parsec is the distance from which the semimajor axis of the earth's orbit, perpendicular to the beam view is visible at an angle of 1².

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

By measuring the annual parallax, you can reliably determine the distance to stars located no further than 100 parsecs or 300 light years away. years.

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

Based on their size, stars are divided into dwarf stars, medium stars, normal stars, giant stars and supergiant stars. Dwarf stars - a satellite of the star Sirius; middle - Sun, Capella (Auriga); 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 - 10000 K), blue (Spica - 30000 K).

Stars are classified according to their luminosity as follows. If we take the luminosity of the Sun as 1, then white and blue stars have a luminosity of 100 and 10 thousand times more than the luminosity of the Sun, and red dwarfs have 10 times less luminosity of the Sun.

Based on their spectrum, stars are divided into spectral classes (see table).

Equilibrium conditions: as is known, stars are the only objects of nature 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 stars are in a stationary state, that is, they do not explode. Some stars explode (so-called novae and supernovae). Why are stars generally in equilibrium? The force of nuclear explosions in stationary stars is balanced by the force of gravity, which is why these stars maintain equilibrium.

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

e = sT 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, the wavelength at which the maximum radiation occurs is determined:

l max T = b b - Wien constant

You can proceed from the opposite, i.e., using luminosity and temperature to determine the sizes of stars.

Ticket number 18. Plan:

1. Cepheids
2. New stars
3. Supernovae

Ticket number 19. Plan:

1. Visually doubles, multiples
2. Spectral doubles
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 any patterns in this variety of stars, in their apparent chaos? Such patterns exist, despite different luminosities, temperatures and sizes of stars.

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

The more massive the star, the faster the main fuel - hydrogen - burns out, turning into helium ( ). Massive blue and white giants burn out within 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. The synthesis of 2C + He ® C 2 He occurs in them. As helium burns out, the star contracts and turns into a white dwarf. The white dwarf eventually turns into a very dense star, which consists only of neutrons. Reducing the size of a star leads to its very rapid rotation. This star seems to pulsate, 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 are compressed so much that they turn into so-called “black holes”, which, due to gravity, do not emit visible radiation.

Ticket number 21. Our star system - Galaxy is one of the elliptical galaxies. Milky Way, which we see is only a part of our Galaxy. With modern telescopes you can see stars up to magnitude 21. 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, you can notice a “split”, which is caused by interstellar dust, covering the stars of the Galaxy from us.

Population of the Galaxy.

There are many red giants and short-period Cepheids in the galactic core. The branches further from the center contain 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. solar system commits full turn around the center of the Galaxy for 200 million years. Based on the rotation of the Solar System, one can determine the approximate mass of the Galaxy - 2 * 10 11 m of the Earth. Stars are considered to be stationary, but in reality stars move. But since we are significantly removed from them, this movement can only be observed over thousands of years.

Ticket number 22. In our Galaxy, in addition to single stars, there are stars that are combined 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. With a simple eye in the Pleiades you can see 6 stars, but if you look through a telescope, you can see a scattering of stars. The size of open clusters is several parsecs. Open star clusters consist of hundreds of main sequence stars and supergiants.
2. Globular star clusters have sizes up to 100 parsecs. These clusters are characterized by short-period Cepheids and a peculiar magnitude (from -5 to +5 units).

Russian astronomer V. Ya. Struve discovered that interstellar absorption of light exists. It is interstellar absorption of light that dims the brightness of stars. Interstellar medium filled with cosmic dust, which forms so-called nebulae, for example, the dark nebulae Large Magellanic Clouds, Horsehead. In the constellation Orion there is a gas-dust nebula that glows with the reflected light of nearby stars. In the constellation Aquarius there is a Great Planetary Nebula, formed as a result of the ejection of gas from nearby stars. Vorontsov-Velyaminov proved that the emission of gases from giant stars is sufficient for the formation of new stars. Gas nebulae form a layer in the Galaxy 200 parsecs thick. They consist 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, the Galaxy has sources of bremsstrahlung (X-ray) radio emission (quasars).

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

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

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

Galaxies are classified into irregular, elliptical and spiral types. 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, there are so-called radio galaxies in stellar systems, i.e. powerful sources of radio emission. In the place of these radio galaxies, small luminous objects were found, the red shift of which is so high that they are obviously billions of light years away from us. They were called quasars because their radiation is sometimes more powerful than that of an entire galaxy. It is possible that quasars are the cores of very powerful star systems.

Ticket number 24. The latest star catalog contains more than 30 thousand galaxies brighter than magnitude 15, and hundreds of millions of galaxies can be photographed with a powerful telescope. All this, together with our Galaxy, forms the so-called metagalaxy. In terms of its size and number of objects, the metagalaxy is infinite; it has neither beginning nor end. By modern ideas In each galaxy, the extinction of stars and entire galaxies occurs, 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 general theory Einstein, such a Universe is expanding approximately 15 billion years ago, the nearest galaxies were closer to us than they are now. In some place in space, new stellar 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 represents the basis of the material world.

1. Sirius, Sun, Algol, Alpha Centauri, Albireo. Find an extra object in this list and explain your decision. Solution: The extra object is the Sun. All other stars are double or multiple. It can also be noted that the Sun is the only star on the list around which planets have been discovered. 2. Estimate the value of atmospheric pressure at the surface of Mars if it is known that the mass of its atmosphere is 300 times less than the mass of the Earth's atmosphere, and the radius of Mars is approximately 2 times less than the radius of the Earth. Solution: A simple but fairly accurate estimate can be obtained if we assume that the entire atmosphere of Mars is collected in a near-surface layer of constant density, equal to the density at the surface. Then the pressure can be calculated by well-known formula, where is the density of the atmosphere near the surface of Mars, is the acceleration free fall on the surface, is the height of such a homogeneous atmosphere. Such an atmosphere will be quite thin, so changes with height can be neglected. For the same reason, the mass of the atmosphere can be represented as where is the radius of the planet. Since where is the mass of the planet, is its radius, and is the gravitational constant, the expression for pressure can be written in the form The ratio is proportional to the density of the planet, so the pressure on the surface is proportional. Obviously, the same reasoning can be applied to Earth. Since the average densities of Earth and Mars - two terrestrial planets - are close, the dependence on the average density of the planet can be neglected. The radius of Mars is approximately 2 times smaller than the radius of the Earth, so the atmospheric pressure on the surface of Mars can be estimated as that of Earth, i.e. about kPa (actually it is about kPa). 3. It is known that angular velocity The Earth's rotation around its axis decreases over time. Why? Solution: Due to the existence of lunar and solar tides (in the ocean, atmosphere and lithosphere). Tidal humps move along the Earth's surface in the direction opposite to the direction of its rotation around its axis. Since the movement of tidal humps on the surface of the Earth cannot occur without friction, tidal humps slow down the rotation of the Earth. 4. Where is the day longer on March 21: in St. Petersburg or Magadan? Why? The latitude of Magadan is . Solution: The length of the day is determined by the average declination of the Sun during the day. In the vicinity of March 21st, the Sun's declination increases with time, so the day will be longer where March 21st occurs later. Magadan is located east of St. Petersburg, so the length of the day on March 21 in St. Petersburg will be longer. 5. At the core of the M87 galaxy is a black hole with the mass of the Sun. Find the gravitational radius of the black hole (the distance from the center at which the second escape velocity is equal to the speed of light), and also average density substances within the gravitational radius. Solution: Second escape velocity (also known as escape velocity or parabolic velocity) for any cosmic body can be calculated using the formula: where

From the sea of ​​information in which we are drowning, besides self-destruction, there is another way out. Experts with a sufficiently broad outlook can create updated notes or summaries that concisely summarize the main facts in a particular area. We present Sergei Popov's attempt to make such a set vital information in astrophysics.

S. Popov. Photo by I. Yarovaya

Contrary to popular belief, school teaching of astronomy was not at its best in the USSR either. Officially, the subject was on the curriculum, but in reality, astronomy was not taught in all schools. Often, even if lessons were held, teachers used them for additional lessons in their core subjects (mainly physics). And in very isolated cases, the teaching was of sufficient quality to enable schoolchildren to form an adequate picture of the world. In addition, astrophysics is one of the most rapidly developing sciences over the years. last decades, i.e. The knowledge of astrophysics that adults received in school 30-40 years ago is significantly outdated. Let us add that now there is almost no astronomy in schools. As a result, for the most part, people have a rather vague idea of ​​how the world works on a scale larger than the orbits of the planets of the solar system.

Spiral galaxy NGC 4414

Cluster of galaxies in the constellation Hairs of Veronica

Planet around the star Fomalhaut

In such a situation, it seems to me that it would be wise to do "Very short course astronomy." That is, to highlight the key facts that form the foundations of the modern astronomical picture of the world. Of course, different specialists may choose slightly different sets of basic concepts and phenomena. But it’s good if there are several good versions. It is important that everything can be presented in one lecture or fit into one short article. And then those who are interested will be able to expand and deepen their knowledge.

I set myself the task of making a set of the most important concepts and facts in astrophysics that would fit on one standard A4 page (approximately 3000 characters with spaces). In this case, of course, it is assumed that a person knows that the Earth revolves around the Sun and understands why eclipses and the change of seasons occur. That is, completely “childish” facts are not included in the list.

Star forming region NGC 3603

Planetary nebula NGC 6543

Supernova remnant Cassiopeia A

Practice has shown that everything on the list can be presented in about an hour-long lecture (or a couple of lessons at school, taking into account answers to questions). Of course, in an hour and a half it is impossible to form a stable picture of the structure of the world. However, the first step must be taken, and here such a “study in large strokes” should help, which captures all the main points that reveal the basic properties of the structure of the Universe.

All images received space telescope"Hubble" and taken from the sites http://heritage.stsci.edu and http://hubble.nasa.gov

1. The Sun is an ordinary star (one of about 200-400 billion) on the outskirts of our Galaxy - a system of stars and their remains, interstellar gas, dust and dark matter. The distance between stars in the Galaxy is usually several light years.

2. The solar system extends beyond the orbit of Pluto and ends where the gravitational influence of the Sun compares with that of nearby stars.

3. Stars continue to form today from interstellar gas and dust. During their lives and at the end of their lives, stars dump part of their matter, enriched with synthesized elements, into interstellar space. This is how the chemical composition of the universe is changing these days.

4. The sun is evolving. Its age is less than 5 billion years. In about 5 billion years, the hydrogen in its core will run out. The sun will turn into a red giant and then into a white dwarf. Massive stars explode at the end of their lives, leaving behind a neutron star or black hole.

5. Our Galaxy is one of many such systems. There are about 100 billion large galaxies in the visible universe. They are surrounded by small satellites. The size of the galaxy is about 100,000 light years. The nearest large galaxy is about 2.5 million light years away.

6. Planets exist not only around the Sun, but also around other stars, they are called exoplanets. Planetary systems are not alike. We now know more than 1000 exoplanets. Apparently, many stars have planets, but only a small part may be suitable for life.

7. The world as we know it is finite in age - just under 14 billion years. In the beginning, matter was in a very dense and hot state. Particles of ordinary matter (protons, neutrons, electrons) did not exist. The universe is expanding and evolving. During the expansion from a dense hot state, the universe cooled and became less dense, and ordinary particles appeared. Then stars and galaxies arose.

8. Due to the finite speed of light and the finite age of the observable universe, only a finite region of space is accessible to us for observation, but the physical world does not end at this boundary. At large distances, due to the finite speed of light, we see objects as they were in the distant past.

9. Majority chemical elements, which we encounter in life (and of which we are composed), arose in the stars during their lives as a result of thermonuclear reactions, or in the last stages of the life of massive stars - in supernova explosions. Before stars formed, ordinary matter primarily existed in the form of hydrogen (the most abundant element) and helium.

10. Ordinary matter contributes only about a few percent to the total density of the universe. About a quarter of the universe's density is due to dark matter. It consists of particles that weakly interact with each other and with ordinary matter. So far we are only observing the gravitational effect of dark matter. About 70 percent of the density of the universe is due to dark energy. Because of it, the expansion of the universe is going faster and faster. Nature dark energy unclear.

1.2 Some important concepts and formulas from general astronomy

Before we begin to describe eclipsing variable stars, which are the subject of this work, let us consider some basic concepts that we will need in the future.

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

Magnitude m and magnitude E are related by the formula:

In this formula, E i is the brightness of a star of the m i -th magnitude, E k is the brightness of a star of the m k -th magnitude. Using this formula, it is easy to see that stars of the first magnitude (1 m) brighter than the stars 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 log 2.512 =0.4, we obtain:

, (1.2)

(1.3)

The last formula shows that the difference in stellar magnitudes is directly proportional to the logarithm of the light ratio. The minus sign in this formula indicates that the magnitude increases (decreases) with a decrease (increase) in brightness. The difference in stellar magnitudes can be expressed not only as an integer, but also as a fraction. Using high-precision photoelectric photometers, it is possible to determine the difference in stellar magnitudes with an accuracy of 0.001 m. The accuracy of visual (eye) assessments by an experienced observer is about 0.05 m.

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

The brightness of a star, assessed by the eye, is called visual. It corresponds to a magnitude, denoted 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 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 systems of magnitudes, of which the most widely used are the systems of magnitudes U, B and V. The letter U denotes ultraviolet magnitudes, B stands for blue (close to photographic), V stands for 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 History of discovery and classification of eclipsing variable stars

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

The Algol light curve, which is shown in Fig. 1

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

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

From the graph of brightness changes it is clear (Fig. 1) that Algol immediately after reaching the main minimum ( smallest value shine) its rise begins. 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 value of the variable's brightness in the main minimum for a certain period of time. For example, for the eclipsing variable star U Cephei, which can be observed with powerful binoculars and amateur telescopes, at the main minimum the duration of the total phase is about 6 hours.

Having carefully examined the graph of Algol's brightness changes, 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 of the eclipse, light from both components of the binary system reaches the Earth. But both components are close to each other. Therefore, a weaker component (often larger in size), illuminated by a bright component, scatters the radiation incident on it. It is obvious that the greatest amount of scattered radiation will reach the earthly observer at the moment when the faint 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 decreases sharply due to the fact that an eclipse of one of the components occurs).

This effect is called the re-emission effect. On the graph, it is manifested by a gradual increase in the overall brightness of the system as it approaches the secondary minimum and a decrease in brightness, which is symmetrical to its increase relative to the secondary minimum.

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

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

In 1903 The eclipsing variable W of Ursa Major was discovered, with an orbital period of about 8 hours (0.3336834 days). During this time, two minima of equal or almost equal depth are observed (Fig. 3). Studying the star's light curve shows that the components are almost equal in size and their surfaces are almost touching.

In addition to stars such as Algol, b Lyrae and W Ursa Major, there are rarer objects that are also classified as eclipsing variable stars. These are ellipsoidal stars that rotate around an axis. Changing the disk area causes minor changes shine.

Hydrogen, while stars with a temperature of about 6 thousand K have lines of ionized calcium located on the border of the visible and ultraviolet parts of the spectrum. Note that the spectrum of our Sun has this type I. The sequence of spectra of stars, resulting from a continuous change in the temperature of their surface layers, is designated 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 spectrum), but the spectrum lines main star will fluctuate in the same way as in the first case. The periods of changes occurring in the spectra of spectroscopic double 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...