1. The theoretical resolution of the telescope:

Where λ - the average length of the 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 is the focal length of the lens, f is the focal length of the eyepiece.

3. The height of the luminaries at the climax:

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

, where j- latitude of the observation site, d- declination of the star;

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

, where j- latitude of the observation site, d- declination of the star;

the height of the luminaries at the lower climax:

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

4. Astronomical refraction:

Approximate formula for calculating the angle of refraction, expressed in seconds of arc (at a temperature of +10°C and an atmospheric pressure of 760 mmHg):

, where z is the zenith distance of the star (for z<70°).

sidereal time:

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

mean solar time (local mean time):

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

world time:

Where l is the longitude of the point with local mean time T m , expressed in hours, 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);

maternity time:

or

6. Formulas relating the sidereal (stellar) period of the planet's revolution T with the synodic period of its circulation S:

for upper planets:

for the lower planets:

, where TÅ is the sidereal period of the Earth's revolution around the Sun.

7. Kepler's third law:

, where T 1 and T 2- periods of rotation of the planets, a 1 and a 2 are major semi-axes of their orbit.

8. Law of gravity:

Where m 1 and m2 are the masses of attracted material points, r- the distance between them, G is the gravitational constant.

9. Kepler's third generalized law:

, where m 1 and m2 are the masses of two mutually attracted bodies, r is the distance between their centers, T is the period of revolution of these bodies around a common center of mass, G is the gravitational constant;

for the system Sun and two planets:

, where T 1 and T 2- sidereal (stellar) periods of planetary revolution, M is the mass of the sun, m 1 and m2 are the masses of the planets, a 1 and a 2 - major semi-axes of the orbits of the planets;

for systems Sun and planet, planet and satellite:

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

at M >> m 1 , and m 1 >> m 2 ,

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

, where G M is 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 chosen point:

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

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

, where G is the gravitational constant, M is the mass of the central body, R is the radius of the orbit, v p is the parabolic speed.

13. The eccentricity of the elliptical orbit, characterizing the degree of deviation of the ellipse from the circle:

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

14. Relation of distances of periapsis and apoapsis with semi-major axis and eccentricity of elliptical orbit:

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

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

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

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

16. Luminary radius:

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 radiated per unit time from a unit surface, T is the temperature (in kelvins), and σ is the Stefan-Boltzmann constant.

21. Wine's Law:

Where λ max - wavelength, which accounts for the maximum radiation of a black body (in centimeters), T is the absolute temperature in kelvins.

22. Hubble's law:

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

1. Sirius, Sun, Algol, Alpha Centauri, Albireo. Find an extra object in this list and explain your decision. Decision: The other object is the Sun. All other stars are binary or multiple. It can also be noted that the Sun is the only star on the list around which planets have been found. 2. Estimate the atmospheric pressure near 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. Decision: 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 using the well-known formula , where is the density of the atmosphere near the surface of Mars, is the free fall acceleration on the surface, and is the height of such a homogeneous atmosphere. Such an atmosphere will turn out to be quite thin, so the change 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, is the gravitational constant, the expression for pressure can be written as Ratio proportional to the density of the planet , so the pressure on the surface is proportional to . Obviously, the same reasoning can be applied to the Earth. Since the average densities of the 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 about 2 times less than the radius of the Earth, so the atmospheric pressure on the surface of Mars can be estimated as Earth's, i.e. about kPa (actually it is about kPa). 3. It is known that the angular velocity of the Earth's rotation around its axis decreases with time. Why? Decision: Due to the existence of lunar and solar tides (in the ocean, atmosphere and lithosphere). Tidal humps move along the surface of the Earth in the opposite direction 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 of March 21 longer: in St. Petersburg or Magadan? Why? The latitude of Magadan is . Decision: The length of the day is determined by the average declination of the Sun during the day. Around March 21, the declination of the Sun increases with time, so the day will be longer where March 21 comes later. Magadan is located to the east of St. Petersburg, so the duration 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 mass of the Sun. Find the black hole's gravitational radius (the distance from the center where the second cosmic velocity equals the speed of light) and the average density of matter within the gravitational radius. Decision: The second cosmic velocity (it is also the escape velocity or parabolic velocity) for any cosmic body can be calculated by the formula: where

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, we consider some basic concepts that we will need in what follows.

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

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

In this formula, E i is the brightness of a star of m i -th magnitude, E k is the brightness of a star of m k -th 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 constructing a scale of stellar magnitudes.

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 stellar 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 fractional number. With the help of 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) estimates of an experienced observer is about 0.05 m.

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

The brilliance of a star, estimated by the eye, is called visual. It corresponds to a stellar magnitude, denoted by m u . or m visas. . The brilliance of stars, estimated 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 \u003d m pg - m ph, depending on the color of the star, is called the color index.

There are several conventionally accepted systems of magnitudes, of which the systems of magnitudes U, B and V are most widely used. The letter U denotes ultraviolet magnitudes, B is blue (close to photographic), V is 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 Perseus) was discovered in 1669. Italian mathematician and astronomer Montanari. It was first explored at the end of the 18th century. English amateur astronomer John Goodryke. It turned out that the single star b Perseus, visible to the naked eye, is actually a multiple system that is not separated even with telescopic observations. Two of the stars included in the system revolve around a common center of mass in 2 days 20 hours and 49 minutes. At certain moments of 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 Algol light curve shown in Fig. one

This graph is based on accurate photoelectric observations. Two brightness decreases are visible: a deep primary minimum - the main eclipse (the bright component is hidden behind the weaker one) and a slight decrease in brightness - the secondary minimum, when the brighter component outshines 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 brightness changes (Fig. 1) that immediately after reaching the main minimum (the lowest brightness value), Algol begins to rise. This means that a partial eclipse is taking place. In some cases, a total eclipse may also be observed, which is characterized by the persistence of the minimum value of the brightness of the variable in the main minimum for a certain period of time. For example, the eclipsing variable star U Cephei, which is accessible to observations with strong binoculars and amateur telescopes, has a total phase duration of about 6 hours at the main minimum.

By carefully examining the graph of changes in the brightness of Algol, you can find that between the main and secondary minima, the brightness of the star 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 Earth 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 decreases sharply due to the fact that one of the components is eclipsed).

This effect is called the re-emission effect. On the graph, it manifests itself as a gradual rise 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 Goodryk discovered the second eclipsing variable star - b Lyra. It changes brightness 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 that arise 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 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 Ursa Major was discovered, in which the period of revolution is about 8 hours (0.3336834 days). During this time, two minima of equal or almost equal depth are observed (Fig. 3). A study of the star's light curve shows that the components are almost equal in size and almost touching surfaces.

In addition to stars like Algol, b Lyra 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. A change in disk area causes small changes in brightness.

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 this type of I has the spectrum of our Sun. The sequence of spectra of stars obtained by continuously changing 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 spectrum), but the lines of the spectrum of the main star 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 rotation, are quite different. The shortest of the known periods is 2.4 hours (g of Ursa Minor), and the longest - tens of years. For...

Questions.

1. The apparent 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 for determining geographic coordinates from astronomical observations (P. 4 p. 16).
3. Reasons for changing the phases of the moon, the conditions for the onset and the frequency of solar and lunar eclipses (P. 6, paragraphs 1.2).
4. Features of the daily motion of the Sun at different latitudes at different times of the year (P.4, paragraph 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. The 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 development of outer space.
9. Kepler's law, its discovery, meaning, limits of applicability (P. 11).
10. The main characteristics of the planets of the Earth group, the 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 pp 4).
15. Methods for determining the distances to stars. Units of distances and the connection between them (P. 23).
16. The main physical characteristics of stars and their relationship (P. 23, paragraph 3).
17. The physical meaning of the Stefan-Boltzmann law and its application to determine the physical characteristics of stars (P. 24, paragraph 2).
18. Variable and non-stationary stars. Their significance for the study of 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 pp 1).
22. Star clusters, the physical state of the interstellar medium (P. 27, paragraph 2, P. 28).
23. The 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 Quest.
2. Definition of geographic latitude.
3. Determination of the declination of the luminary by latitude and height.
4. Calculation of the size of the luminary by parallax.
5. Conditions for the visibility of the Moon (Venus, Mars) according to the school astronomical calendar.
6. Calculation of the period of revolution 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 together 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 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 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 "height of the star in the upper climax"). The height of the celestial pole above the horizon is equal to the latitude of the place of observation. It is possible to determine the latitude of the place of observation by the height of the luminary at the upper climax ( 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 zero 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 longitudes:

l m - l Gr \u003d t m - t Gr

The local time is the solar time at that location 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 this zone. The date change line runs in the east (Bering Strait).

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

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 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 ashen 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 cones of shadow and cones of penumbra. 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 Earth, it can be seen simultaneously wherever the Moon is above the horizon. The phase of a 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, refracted 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 transmits mainly red ones into the cone. That is why the Moon, during a large phase of the eclipse, is painted in a reddish light, and does not disappear altogether. Lunar eclipses occur 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 spot diameter does not exceed 250 km. When the Moon moves in its orbit, its shadow moves across the Earth from west to east, drawing a successively narrow band of total eclipse. Where the Moon's penumbra 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 either slightly larger, or slightly less than the solar one, or equal to it. In the first case, the total eclipse of the Sun lasts up to 7 minutes 40 s, in the second, the Moon does not completely cover the Sun at all, and in the third, only one instant.

Solar eclipses in a year can be from 2 to 5, in the latter case, certainly private.

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 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. On September 22, the polar night begins.

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

In addition to optical telescopes, there are radio telescopes, which are devices that detect cosmic radiation. A 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 allows you 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 star.

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

Ticket number 7. Spectral analysis is the most important tool for the study of the universe. Spectral analysis is a method by which the chemical composition of celestial bodies, their temperature, size, structure, distance to them and the speed of their 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. The intensity of the spectrum can be used to 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 magnitude of a star, and then using the formulas:

M = m + 5 + 5lg p

lg L = 0.4(5 - M)

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

Using the Doppler formula

The creation of modern space stations, reusable spacecraft, as well as the launch of spacecraft to the planets (Vega, Mars, Luna, Voyager, Hermes) made it possible to install telescopes on them, through which these luminaries can be observed close no atmospheric interference.

Ticket number 8. The beginning of the space age was laid by the works of the Russian scientist K. E. Tsiolkovsky. He suggested 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 idea. The first artificial satellite of the Earth was launched on October 4, 1957, the first flight around the Moon with taking photographs - 1959, the first manned flight into space - April 12, 1961 The first flight of Americans to the Moon - 1964, the launch of spacecraft and space stations .

1. Scientific goals:

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

1. Military purposes (protection against nuclear attack);
2. Telecommunications (satellite communication carried out with the help of 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 its foci.

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

Third law. The squares of the sidereal periods of the planets are related as the 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 the astronomical unit (AU) of distances.

Ticket number 10. Plan:

1. List all the 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. Specify 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 rarefied dust shell. The huge temperature differences on 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 of the surface;
3. Presence of tectonic activity.

Planet satellites:

1. Mars (2 small satellites: Phobos and Deimos);
2. Jupiter (16 satellites, the most famous 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 Enck;
• comet Hyakutaka;

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 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 planets are approximately the same age (about 5.5 billion years). According to the theory of the emergence of the solar system by Academician O. Yu. Schmidt, the Earth and 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 clusters 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 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) 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 have 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 in the center it is 100 times greater.

Under the action of gravitational attraction forces directed towards the center of the Sun, a huge pressure is created in its bowels, 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 velocities 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" about 1000 km in size on average. Granulation is a consequence of the movement of gases in a zone located along the photosphere. At times, in certain areas of the photosphere, the dark gaps between spots increase, and large dark spots form. Observing sunspots through a telescope, Galileo noticed that they move 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 non-permanent formations, most often appear in groups. Around the spots, almost imperceptible light formations are sometimes visible, which are called torches. The main feature of spots and torches is the presence of magnetic fields with an induction reaching 0.4-0.5 T.

Ticket number 14. 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 hadrons heavy particles). These radiations are almost entirely delayed by the Earth's atmosphere. That is why the Earth's atmosphere should be kept in a normal state. Periodically appearing ozone holes pass the radiation of the Sun, which reaches the earth's surface and adversely affects 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 the change in solar activity of the Sun affects the following factors:

• 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 a person's 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, one-year parallax is used instead of horizontal.

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

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

p - annual parallax.

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

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

By measuring the annual parallax, one can reliably determine the distance to stars that are no further than 100 parsecs or 300 ly. 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, medium stars, normal stars, giant stars and supergiant stars. Dwarf stars are a satellite of the star Sirius; medium - Sun, Capella (Auriga); normal (t \u003d 10 thousand K) - have dimensions between the Sun and Capella; giant stars - Antares, Arcturus; supergiants - Betelgeuse, Aldebaran.

By color, the 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 white and blue stars have a luminosity 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 is known, 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 stars. Most stars are in a stationary state, that is, they do not explode. Some stars explode (the so-called new and supernovae). Why are stars generally in balance? The force of nuclear explosions in stationary stars is balanced by the force of gravity, which is why these stars maintain balance.

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

e \u003d sТ 4 s - coefficient, s \u003d 5.67 * 10 -8 W / m 2 to 4

e is the 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 is determined, which accounts for the maximum radiation:

l max T = b b - Wien's constant

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

Ticket number 18. Plan:

1. cepheid
2. new stars
3. supernovae

Ticket number 19. Plan:

1. Visually double, multiple
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 patterns in this variety of stars, in their apparent chaos? Such patterns, despite the different luminosities, temperatures and sizes of stars, exist.

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 regularity L » R 5.2 is true.
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 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, burning out, turn into red giants. They synthesize 2C + He ® C 2 He. As the helium burns out, the star shrinks and turns into a white dwarf. A white dwarf eventually turns into a very dense star, which consists of only neutrons. Reducing the size of the star leads to its very rapid rotation. This star seems to pulsate, radiating 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 the so-called "black holes" turn into, 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 a part of our Galaxy. Stars up to magnitude 21 can be seen with modern telescopes. 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 the “bifurcation”, which is caused by interstellar dust that covers the stars of the Galaxy from us.

population of the galaxy.

There are many red giants and short-period Cepheids in the core of the Galaxy. There are many supergiants and classical Cepheids in the branches further from the center. 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. The rotation of the solar system can be used to determine the approximate mass of the Galaxy - 2 * 10 11 m of the Earth. Stars are considered to be stationary, but in fact the stars are moving. But since we are far removed from them, this movement can only be observed for thousands of years.

Ticket number 22. In our Galaxy, in addition to single stars, there are stars that combine 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. Open clusters are several parsecs in size. Open star clusters consist 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 magnitude (from -5 to +5 units).

The Russian astronomer V. Ya. Struve discovered that interstellar absorption of light exists. It is the 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 of the 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 by giant stars is sufficient for the formation of new stars. Gaseous nebulae form a layer in the Galaxy with a thickness of 200 parsecs. 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, there are sources of bremsstrahlung (X-ray) radio emission (quasars) in the Galaxy.

Ticket number 23. William Herschel in the 17th century put 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 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 redshift in the spectra of galaxies. This shift is greater, the farther away from us the galaxy. In other words, the farther the galaxy, the greater its speed of removal from us.

V removal = D * H H - Hubble constant, D - offset 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. Elliptical galaxies - in the constellation Taurus, a spiral galaxy - ours, the Andromeda nebula, an irregular galaxy - in the Magellanic Clouds. In addition to visible galaxies, stellar systems contain so-called radio galaxies, that is, powerful sources of radio emission. In place of these radio galaxies, small luminous objects were found, the redshift of which is so large that they are obviously billions of light years away from us. They are 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 over 30,000 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 size and number of objects, the metagalaxy is infinite; it has neither beginning nor 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, given 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 of space, new star systems arise and, given 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. The local time.

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 mean sun) at any given moment is the same. Therefore, on the entire geographic meridian, local time (stellar or solar) is the same at the same moment.

If the difference between the geographical longitudes of two places is D l, then in a more eastern place the hour angle of any star will be on D l greater than the hour angle of the same luminary in a more westerly location. Therefore, the difference of any local times on two meridians at the same physical moment is always equal to the difference in the longitudes of these meridians, expressed in hours (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 hours and considered positive east of Greenwich.

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

3. standard time. In everyday life, using both local mean solar time and universal time is inconvenient. The first because there are, in principle, as many local time counting 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 the meridians on which these events or phenomena took place.

The sequence of events marked by universal time is easily established, but the large difference between universal time and the local time of meridians, which are far from Greenwich Mean Time, creates inconvenience when using universal time in everyday life.

In 1884, it was proposed belt counting system of average time, the essence of which is as follows. Time is only kept on 24 major geographic meridians located from each other in longitude exactly 15 ° (or 1 h), approximately in the middle of each time zone. Time zones called the areas of the earth's surface into which it is conditionally divided by lines running from its north pole to the south and spaced approximately 7 °.5 from the main meridians. These lines, or boundaries of time zones, follow exactly the geographical meridians only in the open seas and oceans and in uninhabited places on land. For the rest of their length, they go along state, administrative, economic or geographical boundaries, retreating 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 exactly 15 ° east of Greenwich, the second - 30 °, the third - 45 °, etc. until the 23 time zone, the main meridian of which has an east longitude from Greenwich 345 ° (or west longitude 15°).

Standard timeT p is the local mean solar time, measured on the main meridian of a given time zone. It keeps track of time for the entire territory lying in a given time zone.

Standard time of this zone P is related to universal time by the obvious relation

T n = T 0 +n h .

(1.29)

It is also quite obvious that the difference between the standard 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 rationally distribute electricity used for lighting enterprises and residential premises, and to make the most complete use of daylight in the summer months of the year, in many countries (including our republic), the hour hands of clocks running in standard time are moved forward by 1 hour or half an hour. The so-called summer time. In the fall, the clock is again set to standard time.

DST connection T l any point with its standard time T p and with universal time T 0 is given by the following relations:

(1.30)