1. Theoretical resolution of the telescope:

Where λ – average light wavelength (5.5·10 -7 m), D– diameter of the telescope lens, or , where D– diameter of the telescope lens in millimeters.

2. Telescope magnification:

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

3. Height of the luminaries at the culmination:

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

, Where j– latitude of the observation site, d– declination of the luminary;

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

, Where j– latitude of the observation site, d– declination of the luminary;

height of the luminaries at the lower culmination:

, 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 arcseconds (at a temperature of +10°C and atmospheric pressure 760 mm. rt. Art.):

, Where z– zenith distance of the luminary (for z<70°).

sidereal time:

Where a- the right ascension of a star, t– its hour angle;

mean solar time (local mean time):

T m = T  + h, Where T– true solar time, h– equation of time;

universal time:

Wherel is the longitude of the point with local mean time T m, expressed in hourly units, 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 revolution of the planet T with the synodic period of its revolution S:

for the upper planets:

for the lower planets:

, Where TÅ – sidereal period of the Earth’s revolution around the Sun.

7. Kepler's third law:

, Where T 1 And T 2– periods of revolution of the planets, a 1 and a 2 – semimajor axes of their orbit.

8. Law universal gravity:

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

9. Kepler's third generalized law:

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

for the Sun and two planets system:

, Where T 1 And T 2– sidereal (stellar) periods of revolution of the planets, M– mass of the Sun, m 1 And m 2– masses of planets, a 1 and a 2 – semimajor axes of planetary orbits;

for systems Sun and planet, planet and satellite:

, Where M– mass of the Sun; m 1 – mass of the planet; m 2 – mass of the planet’s satellite; T 1 and a 1– the period of revolution of the planet around the Sun and the semimajor axis of its orbit; T 2 and a 2– the period of revolution of the satellite around the planet and the semimajor axis of its orbit;

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

10. Linear speed of body motion in a parabolic orbit (parabolic speed):

, Where G M– mass of the central body, r– radius vector of a selected point of a parabolic orbit.

11. Linear speed of movement of a body along an elliptical orbit at a selected point:

, Where G– gravitational constant, M– mass of the central body, r– radius vector of a selected point of the elliptical orbit, a– semimajor axis of the elliptical orbit.

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

, Where G– gravitational constant, M– mass of the central body, R– orbital radius, v p – parabolic speed.

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

, Where c– distance from the focus to the center of the orbit, a– semimajor axis of the orbit, b– semi-minor axis of the orbit.

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

Where r P – distances from the focus, where the central celestial body is located, to the periapsis, r A – distances from the focus, where the central celestial body is located, to the apocenter, a– semimajor axis of the orbit, e– orbital eccentricity.

15. Distance to the star (within the Solar System):

, Where R ρ 0 – horizontal parallax of the luminary, expressed in arcseconds,

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

16. Radius of the luminary:

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

20. Stefan-Boltzmann law:

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

21. Law of Wine:

Where λ max – wavelength at which the maximum radiation of a completely black body occurs (in centimeters), T– absolute temperature in Kelvin.

22. Hubble's law:

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

TICKETS FOR ASTRONOMY 11TH GRADE

TICKET No. 1

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

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. The planets move across the sky, either from east to west (direct motion), or from west to east (retrograde motion). Moments of change of direction are called stops. If you plot this path on a map, you get a loop. The larger the distance between the planet and the Earth, the smaller the loop is. The planets are divided into lower and upper (lower - inside the earth's orbit: Mercury, Venus; upper: Mars, Jupiter, Saturn, Uranus, Neptune and Pluto). All these planets revolve in the same way as the Earth around the Sun, but due to the movement of the Earth, loop-like motion of the planets can be observed. The relative positions of the planets relative to the Sun and Earth are called planetary configurations.

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

The period during which the planet orbits around the Sun is called the sidereal (stellar) period of revolution - T, the period of time between two identical configurations is called the synodic period - S.

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

for inner planets

for outer planets

S – sidereal period (relative to stars), T – synodic period (between phases), Т = 1 year.

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

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

H = 50 km/sec*Mpc – Hubble Constant

TICKET No. 2

Principles of determining geographic coordinates from astronomical observations.

There are 2 geographical coordinates: geographic latitude and geographic longitude. Astronomy how practical science allows you to find these coordinates. The height of the celestial pole above the horizon is equal to the geographic latitude of the observation site. Approximately geographical latitude can be determined by measuring the altitude of the North Star, because it is approximately 1 0 away from the north celestial pole. 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:

j = d ± (90 – h), depending on whether it culminates south or north of the zenith. h – height of the star, d – declination, j – 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:

T λ 1 – T λ 2 = λ 1 – λ 2 Thus, having found out the time difference at two points, the longitude of one of which is known, you can determine the longitude of the other point.

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).

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

L – luminosity (Lc = 1)

R – radius (Rc = 1)

T – Temperature (Tc = 6000)

TICKET No. 3

Reasons for changing phases of the moon. Conditions for the occurrence and frequency of solar and lunar eclipses.

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

Eclipse , astronomical phenomenon, in which one celestial body completely or partially covers another, or the shadow of one body falls on another. Solar 3. occur when the Earth falls into the shadow cast by the Moon, and lunar - when the Moon falls into the shadow of the Earth. The shadow of the Moon during solar 3. consists of a central shadow and a penumbra surrounding it. Under favorable conditions, a full lunar 3. can last 1 hour. 45 min. If the Moon does not completely enter the shadow, then an observer on the night side of the Earth will see a partial lunar 3. The angular diameters of the Sun and the Moon are almost the same, so the total solar 3. lasts only a few. minutes. When the Moon is at its apogee, its angular dimensions are slightly smaller than the Sun. Solar 3. can occur if the line connecting the centers of the Sun and Moon crosses the earth's surface. The diameters of the lunar shadow when falling on Earth can reach several. hundreds of kilometers. The observer sees that the dark lunar disk did not completely cover the Sun, leaving its edge open in the form of a bright ring. This is the so-called annular solar 3. If the angular dimensions of the Moon are greater than those of the Sun, then the observer in the vicinity of the point of intersection of the line connecting their centers with the earth's surface will see a full solar 3. Because The Earth rotates around its axis, the Moon around the Earth, and the Earth around the Sun, the lunar shadow quickly slides across earth's surface from the point where it fell on it to the other where it leaves it, and draws a strip of complete or circular 3. on the Earth. Partial 3. can be observed when the Moon blocks only part of the Sun. The time, duration and pattern of solar or lunar 3. depend on the geometry of the Earth-Moon-Sun system. Due to the inclination of the lunar orbit relative to the *ecliptic, solar and lunar 3. events do not occur on every new or full moon. Comparison of prediction 3. with observations allows us to clarify the theory of the movement of the Moon. Since the geometry of the system repeats itself almost exactly every 18 years 10 days, 3. occur with this period, called saros. Registrations 3. have been used since ancient times to test the effects of tides on the lunar orbit.

Determining the coordinates of stars using a star map.

TICKET No. 4

Features of the daily movement of the Sun at different geographical latitudes at different times of the year.

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

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

After the spring equinox, the declination of the Sun increases rapidly, so that every day more and more of the daily parallel of the Sun appears above the horizon. The sun rises earlier, rises higher and higher at its climax, and sets later. The sunrise and sunset points shift north every day, and the day lengthens.

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

After this, the declination of the Sun begins to decrease - very slowly at first, and then more and more quickly. Every day it rises later, sets earlier, the points of sunrise and sunset move back to the south.

By the end of September, the Sun reaches the second point of intersection of the ecliptic with the equator (α = 12 hours), and the equinox occurs again, this time in autumn. Again, the rate of change in the Sun's declination reaches a maximum, and it quickly moves south. The night is getting longer than a day, and every day the height of the Sun at the upper culmination decreases.

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

And then everything starts all over again - the declination of the Sun increases, the height at the upper culmination increases, the day lengthens, the points of sunrise and sunset shift to the north.

Due to light scattering earth's atmosphere the sky continues to remain light for some time after sunset. This period is called twilight. Civil twilight differs depending on the depth of the Sun's immersion below the horizon (-8° -12°) and astronomical (h>-18°), after which the brightness of the night sky remains approximately constant.

In summer, at d = +e, the height of the Sun at the lower culmination is h = φ + e - 90°. Therefore, north of latitude ~ 48°.5 at the summer solstice, the Sun at its lower culmination plunges below the horizon by less than 18°, and summer nights become light due to astronomical twilight. Similarly, at φ > 54°.5 on the summer solstice, the height of the Sun is h > -12° - navigational twilight lasts all night (Moscow falls into this zone, where it does not get dark for three months a year - from early May to early August). Even further north, at φ > 58°.5, civil twilight no longer stops in the summer (St. Petersburg with its famous “white nights” is located here).

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

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

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

Pointing at a given object and focusing the telescope .

TICKET No. 5

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

Telescope, an astronomical instrument for observing celestial bodies. A well-designed telescope is capable of collecting electromagnetic radiation in various spectral ranges. In astronomy, an optical telescope is used to magnify images and collect light from faint sources, especially those invisible to the naked eye, because In comparison, it is able to collect more light and provide high angular resolution, so more detail can be seen in an enlarged image. A refracting telescope uses a large lens as an objective to collect and focus light, and the image is viewed using an eyepiece made of one or more lenses. A major problem in the design of refracting telescopes is chromatic aberration (the fringing of color around the image created by a simple lens as light of different wavelengths is focused at different distances). This can be eliminated by using a combination of convex and concave lenses, but lenses larger than a certain size limit (about 1 meter in diameter) cannot be manufactured. Therefore, preference is currently given to reflecting telescopes that use a mirror as a lens. The first reflecting telescope was invented by Newton according to his design, called Newton's system. Now there are several methods for observing images: the Newton system, Cassegrain (the focus position is convenient for recording and analyzing light using other instruments, such as a photometer or spectrometer), Kude (the circuit is very convenient when bulky equipment is required for light analysis), Maksutov ( the so-called meniscus), Schmidt (used when it is necessary to make large-scale surveys of the sky).

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

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

T s = 1 year

a s = 1 astronomical unit

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

TICKET No. 6

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

First, the distance to some accessible point is determined. This distance is called the basis. The angle at which the base is visible from an inaccessible place is called parallax. Horizontal parallax is 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.

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

Radar observations make it possible to determine with great accuracy the distances to the celestial bodies of the Solar System. This method was used to clarify the distances to the Moon, Venus, Mercury, Mars, and Jupiter.

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

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

To determine the size of the bodies of the Solar System, you can measure the angle at which they are visible to an observer on earth - the angular radius of the star r and the distance to the star D.

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

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

L – luminosity (Lc = 1)

R – radius (Rc = 1)

T – Temperature (Tc = 6000)

TICKET No. 7

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

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

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

The earth's atmosphere blocks some of the radiation coming from space. Visible light, passing through it, is also distorted: the movement of air blurs the image of celestial bodies, and the stars flicker, although in fact their brightness is unchanged. Therefore, from the middle of the 20th century, astronomers began making observations from space. Outside the atmosphere, telescopes collect and analyze x-rays, ultraviolet, infrared and gamma rays. The first three can only be studied outside the atmosphere, while the latter partially reaches the Earth's surface, but is mixed with the IR of the planet itself. Therefore, it is preferable to take infrared telescopes into space. X-ray radiation reveals areas in the Universe where energy is particularly rapidly released (for example, black holes), as well as objects invisible in other rays, such as pulsars. Infrared telescopes make it possible to study thermal sources hidden to optics over a wide temperature range. Gamma-ray astronomy makes it possible to detect sources of electron-positron annihilation, i.e. sources of great energy.

2. Determination of the declination of the Sun for a given day using a star chart and calculation of its height at noon.

h – height of the luminary

TICKET No. 8

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

The main problems of modern astronomy:

There is no solution to many particular problems of cosmogony:

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

In stellar astronomy:

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

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

In galactic and extragalactic astronomy:

· The problem of hidden mass has not been solved, which consists in the fact that the gravitational field of galaxies and galaxy clusters is several times stronger than what the observed matter can provide. It is likely that most of the matter in the Universe is still hidden from astronomers;

· No unified theory galaxy formation;

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

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

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

· What processes contribute to the onset of star formation?

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

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

· Where and when did galaxies form?

· Will the Universe expand forever, or will its expansion give way to collapse?

TICKET No. 9

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

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

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

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

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

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

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

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

Speed ​​at aphelion:.

Kepler discovered his laws empirically. Newton derived Kepler's laws from the law of universal gravitation. To determine the masses of celestial bodies, Newton’s generalization of Kepler’s third law to any systems of orbiting bodies is important. In a generalized form, this law is usually formulated as follows: the squares of the periods T 1 and T 2 of revolution of two bodies around the Sun, multiplied by the sum of the masses of each body (M 1 and M 2, respectively) and the Sun (M s), are related as the cubes of the semi-major axes a 1 and a 2 of their orbits: . In this case, the interaction between bodies M 1 and M 2 is not taken into account. If we neglect the masses of these bodies in comparison with the mass of the Sun, we obtain the formulation of the third law given by Kepler himself: Kepler’s third law can also be expressed as the dependence between the orbital period T of a body with mass M and the semimajor axis of the orbit a: . Kepler's third law can be used to determine the mass of binary stars.

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

TICKET No. 10

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

Mercury. Weight: 3*10 23 kg (0.055 earth) R orbit: 0.387 AU Planet D: 4870 km Properties of the atmosphere: There is practically no atmosphere, helium and hydrogen from the Sun, sodium released by the overheated surface of the planet. Surface: Pockmarked with craters, There is a depression 1300 km in diameter called the Caloris Basin. Features: A day lasts two years.

Venus. Weight: 4.78*10 24 kg R orbit: 0.723 AU Planet D: 12100 km Composition of the atmosphere: Mainly carbon dioxide with admixtures of nitrogen and oxygen, clouds of condensate of sulfuric and hydrofluoric acid. Surface: Rocky desert, relatively smooth, but there are some craters Features: Surface pressure 90 times > Earth's, reverse orbital rotation, strong Greenhouse effect(T=475 0 C).

Earth . R orbit: 1 AU (150,000,000 km) R planet: 6400 km Atmospheric composition: 78% nitrogen, 21% oxygen and carbon dioxide. Surface: Most varied. Features: Lots of water, conditions necessary for the origin and existence of life. There is 1 satellite - the Moon.

Mars. Weight: 6.4*1023 kg R orbit: 1.52 AU (228 million km) Planet D: 6670 km Atmospheric composition: Carbon dioxide with impurities. Surface: Craters, Valles Marineris, Mount Olympus - the highest in the system Features: A lot of water in the polar caps, presumably the climate was previously suitable for organic life on a carbon basis, and the evolution of the climate of Mars is reversible. There are 2 satellites - Phobos and Deimos. Phobos is slowly falling towards Mars.

Pluto/Charon.

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

R orbit: 29.65-49.28 AU

Planet D: 2324/1212 km

Atmospheric composition: Thin layer of methane

Features: Double planet, possibly planetesemal, orbit does not lie in the plane of other orbits. Pluto and Charon always face each other with the same side

Giant planets: Jupiter, Saturn, Uranus, Neptune.

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

Jupiter Weight: 1.9*10 27 kg R orbit: 5.2 AU D planet: 143,760 km at the equator Composition: Hydrogen with helium impurities. Satellites: Europa has a lot of water, Ganymede with ice, Io with a sulfur volcano. Features: The Great Red Spot, almost a star, 10% of the radiation is its own, pulls the Moon away from us (2 meters per year).	Saturn. Weight: 5.68* 10 26 R orbit: 9.5 AU Planet D: 120,420 km Composition: Hydrogen and helium. Moons: Titan is larger than Mercury and has an atmosphere. Features: Beautiful rings, low density, many satellites, magnetic field poles almost coincide with the rotation axis.
Uranus Weight:8.5*1025kg R orbit: 19.2 AU Planet D: 51,300 km Composition: Methane, ammonia. Satellites: Miranda has a very complex terrain. Features: The axis of rotation is directed towards the Sun, does not radiate its own energy, the largest angle of deviation of the magnetic axis from the axis of rotation.	Neptune. Weight: 1*10 26 kg R orbit: 30 AU D planet: 49500 km Composition: Methane, ammonia, hydrogen atmosphere.. Satellites: Triton has a nitrogen atmosphere, water. Features: Emits 2.7 times more absorbed energy.

Installation of a model of the celestial sphere for a given latitude and its orientation along the sides of the horizon.

TICKET No. 11

Distinctive features of the Moon and planetary satellites.

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

The mass of L. is accurately measured by studying the orbits of its arts and satellites and is related to the mass of the Earth as 1/81.3; Its diameter of 3476 km is 1/3.6 of the Earth's diameter. L. has the shape of an ellipsoid, although the three mutually perpendicular diameters differ by no more than a kilometer. The period of rotation of the planet is equal to the period of revolution around the Earth, so that, apart from the effects of libration, it is always turned to one side. Wed. the density is 3330 kg/m 3, a value very close to the density of the main rocks underlying the earth's crust, and the gravitational force on the surface of the Moon is 1/6 of the Earth's. The Moon is the celestial body closest to Earth. If the Earth and Moon were point masses or rigid spheres, the density of which varies only with distance from the center, and there were no other celestial bodies, then the Moon's orbit around the Earth would be a constant ellipse. However, the Sun and, to a much lesser extent, the planets exert gravitational forces. influence on the planet, causing disturbance of its orbital elements, so the semimajor axis, eccentricity and inclination are continuously subject to cyclic disturbances, oscillating around the average values.

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

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

TICKET No. 12

Comets and asteroids. Fundamentals of modern ideas about the origin of the Solar system.

Comet, a celestial body of the Solar System, consisting of particles of ice and dust, moving in highly elongated orbits, which means that at a distance from the Sun they look like faintly luminous oval-shaped spots. As it approaches the Sun, a coma forms around this nucleus (an almost spherical shell of gas and dust that surrounds the head of a comet as it approaches the Sun. This “atmosphere,” continuously blown away by the solar wind, is replenished with gas and dust escaping from the nucleus. The diameter of the comet reaches 100 thousand km. The escape velocity of gas and dust is several kilometers per second relative to the nucleus, and they are scattered in interplanetary space partially through the tail of the comet.) and tail (A flow of gas and dust formed under the influence of light pressure and interaction with the solar wind from dissipating in interplanetary space of the comet's atmosphere. In most comets, X. appears when they approach the Sun at a distance of less than 2 AU. X. is always directed away from the Sun. Gas X. is formed by ionized molecules ejected from the nucleus, under the influence of solar radiation it has a bluish color, distinct boundaries, a typical width of 1 million km, length - tens of millions of kilometers.The structure of X. can change noticeably over several periods. hours. The speed of individual molecules ranges from 10 to 100 km/sec. Dust X. is more diffuse and curved, and its curvature depends on the mass of dust particles. Dust is continuously released from the core and is carried away by the gas flow.). The center, part of the planet, is called the core and is an icy body - the remains of huge accumulations of icy planetesimals formed during the formation of the Solar System. Now they are concentrated on the periphery - in the Oort-Epic cloud. The average mass of a K core is 1-100 billion kg, diameter 200-1200 m, density 200 kg/m3 ("/5 the density of water). The cores have voids. These are fragile formations, consisting of one third ice and two thirds from dust matter. The ice is mainly water, but there are admixtures of other compounds. With each return to the Sun, the ice melts, gas molecules leave the core and carry along particles of dust and ice, while a spherical shell is formed around the core - a coma, a long plasma tail directed away from the Sun and a dust tail. The amount of matter lost depends on the amount of dust covering the core and the distance from the Sun at perihelion. Data obtained from observations spacecraft"Giotto" behind Halley's comet from close range, confirmed by many. theories of the structure of K.

K. are usually named after their discoverers, indicating the year when they were last observed. They are divided into short-period. and long-term Short period K. revolve around the Sun with a period of several. years, on Wed. OK. 8 years; the shortest period - a little more than 3 years - has K. Encke. These K. were captured by gravity. field of Jupiter and began to rotate in relatively small orbits. A typical one has a perihelion distance of 1.5 AU. and is completely destroyed after 5 thousand revolutions, giving rise to a meteor shower. Astronomers observed the decay of K. West in 1976 and K. *Biela. On the contrary, circulation periods are long-period. K. can reach 10 thousand, or even 1 million years, and their aphelion can be at 1/3 of the distance to the nearest stars. At present, about 140 short-period and 800 long-period K. are known, and every year opens about 30 new K. Our knowledge of these objects is incomplete, because they are detected only when they approach the Sun at a distance of about 2.5 AU. It is estimated that about a trillion K orbit the Sun.

Asteroid(asteroid), a small planet, which has a nearly circular orbit, lying near the ecliptic plane between the orbits of Mars and Jupiter. Newly discovered A. are assigned a serial number after determining their orbit, which is sufficiently accurate so that the A. “does not get lost.” In 1796 the French. Astronomer Joseph Jérôme Lalande proposed to start searching for the “missing” planet between Mars and Jupiter, predicted by Bode’s rule. IN New Year's Eve 1801 Italian Astronomer Giuseppe Piazzi discovered Ceres while making observations to compile a star catalogue. German scientist Carl Gauss calculated its orbit. To date, about 3,500 asteroids are known. The radii of Ceres, Pallas and Vesta are 512, 304 and 290 km, respectively, the others are smaller. According to estimates in Chap. the belt is approx. 100 million A., their total mass appears to be about 1/2200 of the mass originally present in this area. The emergence of modern A., perhaps, is associated with the destruction of the planet (traditionally called Phaethon, the modern name is Olbers’s planet) as a result of a collision with another body. The surfaces of observed objects consist of metals and rocks. Depending on their composition, asteroids are divided into types (C, S, M, U). Type U composition has not been identified.

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

When a protostar collapses, it forms a disk of material surrounding the star. Part of the matter from this disk falls back onto the star, obeying the force of gravity. The gas and dust that remain in the disk gradually cools. When the temperature drops low enough, the substance of the disk begins to gather into small clumps - pockets of condensation. This is how planetesimals arise. During the formation of the Solar System, some planetesimals were destroyed as a result of collisions, while others came together to form planets. Large planetary cores formed in the outer part of the Solar System, which were able to retain a certain amount of gas in the form of a primary cloud. Heavier particles were held by the attraction of the Sun and, under the influence of tidal forces, could not form into planets for a long time. This marked the beginning of the formation of the “gas giants” - Jupiter, Saturn, Uranus and Neptune. They likely developed their own mini-disks of gas and dust, from which they eventually formed moons and rings. Finally, in the inner solar system, Mercury, Venus, Earth and Mars form from solid matter.

Determination of visibility conditions for the planet Venus according to the “School Astronomical Calendar”.

TICKET No. 13

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

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

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

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

TICKET No. 14

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

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

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

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

The last maximum solar activity was in 2001. Maximum solar activity means greatest number spots, radiation and prominences. It has long been established that changes in solar activity The sun affects the following factors:

* epidemiological situation on Earth;

* quantity of different types natural Disasters(typhoons, earthquakes, floods, etc.);

* on the number of automobile and railway 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.

2. Determination of visibility conditions for the planet Jupiter according to the “School Astronomical Calendar”.

TICKET No. 15

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

The parallax method is used to measure the distance to solar system bodies. 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 (p) 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 is the semimajor axis of the 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 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, you can reliably determine the distance to stars located no further than 100 parsecs or 300 light years away. years.

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

Determination of the visibility conditions of the Moon according to the “School Astronomical Calendar”.

TICKET No. 16

Basic physical characteristics of stars, the relationship between these characteristics. Conditions for the equilibrium of stars.

Basic physical characteristics of stars: luminosity, absolute and apparent magnitudes, mass, temperature, size, spectrum.

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

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

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

Mass-luminosity relationship, found in 1924 by Eddington, the relationship between luminosity L and stellar mass M. The relationship has the form L/Lc = (M/Mc) a, where Lc and Mc are the luminosity and mass of the Sun, respectively, the value A usually lies in the range of 3-5. The relationship follows from the fact that the observed properties of normal stars are determined mainly by their mass. This relationship for dwarf stars agrees well with observations. It is believed that this is also true for supergiants and giants, although their mass is difficult to directly measure. The relation does not apply to white dwarfs, because increases their luminosity.

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

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

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

Spectral classes, classification of stars according to their spectra (primarily according to the intensities of spectral lines), first introduced by Italian. astronomer Secchi. Introduced letter designations, which were modified as knowledge about internal processes expanded. structure of stars. The color of a star depends on the temperature of its surface, so in modern times. spectral classification Draper (Harvard) S.k. arranged in descending order of temperature:

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

Equilibrium conditions: as 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.

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

TICKET No. 17

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

Stefan-Boltzmann law, the relationship between the total radiation power of a black body and its temperature. The total power of a unit radiation area in W per 1 m2 is given by the formula Р = σ Т 4, Where σ = 5.67*10 -8 W/m 2 K 4 - Stefan-Boltzmann constant, T - absolute temperature of an absolute black body. Although astronomers rarely emit objects like a black body, their emission spectrum is often a good model of the real object's spectrum. The dependence on temperature to the 4th power is very strong.

e – radiation energy per unit surface of the star

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

Using the Stefan-Boltzmann formula and Wien's law, 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

2. Definition geographical latitude observation locations based on the given height of the luminary at its culmination and its declination.

H = 90 0 - +

h – height of the luminary

TICKET No. 18

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

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

The most important types of physical P.Z.:

Pulsating – Cepheids, Mira Ceti type stars, semi-regular and irregular red giants;

Eruptive(explosive) – stars with shells, young irregular variables, incl. T Tauri stars (very young irregular stars associated with diffuse nebulae), Hubble–Sanage supergiants (Hot supergiants of high luminosity, the brightest objects in galaxies. They are unstable and are likely sources of radiation near the Eddington luminosity limit, above which "blowing away" the shells of stars. Potential supernovae.), flaring red dwarfs;

Cataclysmic – novae, supernovae, symbiotic;

X-ray binary stars

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

Among the pulsating stars, the Cepheids are very interesting, named after one of the first discovered variables of this type - 6 Cephei. Cepheids are stars of high luminosity and moderate temperature (yellow supergiants). In the course of evolution, they acquired a special structure: at a certain depth, a layer appeared that accumulates energy coming from the depths, and then releases it again. The star periodically contracts as it heats up and expands as it cools down. Therefore, the radiation energy is either absorbed by the stellar gas, ionizing it, or released again when, as the gas cools, the ions capture electrons, emitting light quanta. As a result, the brightness of the Cepheid changes, as a rule, several times with a period of several days. Cepheids play a special role in astronomy. In 1908, American astronomer Henrietta Leavitt, who studied Cepheids in one of the nearby galaxies, the Small Magellanic Cloud, noticed that these stars turned out to be brighter the longer the period of change in their brightness. The Small Magellanic Cloud's size is small compared to its distance, meaning differences in apparent brightness reflect differences in luminosity. Thanks to the period-luminosity relationship found by Leavitt, it is easy to calculate the distance to each Cepheid by measuring its average brightness and period of variability. And since supergiants are clearly visible, Cepheids can be used to determine distances even to relatively distant galaxies, in which they are observed. There is a second reason for the special role of Cepheids. In the 60s Soviet astronomer Yuri Nikolaevich Efremov found that the longer the Cepheid period, the younger this star. Using the period-age relationship, it is not difficult to determine the age of each Cepheid. By selecting stars with maximum periods and studying the stellar groups they belong to, astronomers are exploring the youngest structures in the Galaxy. Cepheids, more than other pulsating stars, deserve the name periodic variables. Each subsequent cycle of brightness changes usually very accurately repeats the previous one. However, there are exceptions, the most famous of them being the North Star. It has long been discovered that it belongs to the Cepheids, although it changes its brightness within rather insignificant limits. But in recent decades, these fluctuations began to fade, and by the mid-90s. The North Star has practically stopped pulsating.

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

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

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

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

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

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

H = 90 0 - +

h – height of the luminary

TICKET No. 19

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

Double star, a pair of stars bound into one system by gravitational forces and revolving around a common center of gravity. The stars that make up a binary star are called its components. Double stars are very common and are divided into several types.

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

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

Spectral binary stars are detected by changes in their spectra. During mutual rotation, the stars periodically move either towards the Earth or away from the Earth. Changes in motion can be determined by the Doppler effect in the spectrum.

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

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

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

Calculation of the height of the luminary at its culmination based on a known declination for a given geographic latitude.

H = 90 0 - +

h – height of the luminary

TICKET No. 20

The evolution of stars, its stages and final stages.

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

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

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

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

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

TICKET No. 21

Composition, structure and size of our Galaxy.

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

The central bulge consists of old population type II stars (red giants), located very densely, and at its center (core) there is a powerful source of radiation. It was assumed that there is a black hole in the core, initiating the observed powerful energy processes accompanied by radiation in the radio spectrum. (The gas ring rotates around the black hole; hot gas, escaping from its inner edge, falls onto the black hole, releasing energy that we observe.) But recently a flash of visible radiation was detected in the core and the black hole hypothesis was no longer necessary. The parameters of the central thickening are 20,000 light-years across and 3,000 light-years thick.

The Galaxy's disk, containing young population type I stars (young blue supergiants), interstellar matter, open star clusters and 4 spiral arms, is 100,000 light-years in diameter and only 3,000 light-years thick. The galaxy rotates, its inner parts move through their orbits much faster than the outer parts. The Sun completes a revolution around the core every 200 million years. The spiral arms undergo a continuous process of star formation.

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

The Sun is located at a distance of 2/3 from the center of the disk in the Orion Arm. Its localization in the plane of the disk (galactic equator) allows the stars of the disk to be seen from Earth as narrow strip Milky Way, covering the entire celestial sphere and inclined at an angle of 63° to the celestial equator. The galactic center lies in Sagittarius, but it is not visible in visible light due to dark nebulae of gas and dust that absorb starlight.

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

L – luminosity (Lc = 1)

R – radius (Rc = 1)

T – Temperature (Tc = 6000)

TICKET No. 22

Star clusters. Physical state of the interstellar medium.

Star clusters are groups of stars located relatively close to each other and connected by a common movement in space. Apparently, almost all stars are born in groups, rather than individually. Therefore, star clusters are a very common thing. Astronomers love to study star clusters because all the stars in a cluster formed at about the same time and at about the same distance from us. Any noticeable differences in brightness between such stars are true differences. It is especially useful to study star clusters from the point of view of the dependence of their properties on mass - after all, the age of these stars and their distance from the Earth are approximately the same, so they differ from each other only in their mass. There are two types of star clusters: open and globular. In an open cluster, each star is visible separately; they are distributed more or less evenly over some part of the sky. Globular clusters, on the contrary, are like a sphere so densely filled with stars that in its center individual stars are indistinguishable.

Open clusters contain between 10 and 1,000 stars, many more young than old, with the oldest hardly more than 100 million years old. The fact is that in older clusters the stars gradually move away from each other until they mix with the main set of stars. Although gravity holds open clusters together to some extent, they are still quite fragile, and the gravity of another object can tear them apart.

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

In contrast to open clusters, globular clusters are spheres densely filled with stars (from 100 thousand to 1 million). The size of a typical globular cluster is between 20 and 400 light years across.

In the densely packed centers of these clusters, the stars are so close to each other that mutual gravity binds them together, forming compact binary stars. Sometimes even a complete merger of stars occurs; When approaching closely, the outer layers of the star can collapse, exposing the central core to direct view. Binary stars are 100 times more common in globular clusters than elsewhere.

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

The matter (gas and dust) found in the space between stars is called the interstellar medium. Most of it is concentrated in the spiral arms of the Milky Way and makes up 10% of its mass. In some areas the material is relatively cold (100 K) and is detectable by infrared radiation. Such clouds contain neutral hydrogen, molecular hydrogen and other radicals, the presence of which can be detected using radio telescopes. In areas near high-luminosity stars, gas temperatures can reach 1000-10000 K, and hydrogen is ionized.

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

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

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

TICKET No. 23

The main types of galaxies and their distinctive features.

Galaxies, systems of stars, dust and gas with a total mass of 1 million to 10 trillion. mass of the Sun. The true nature of galaxies was only finally explained in the 1920s. after heated discussions. Until this time, when observed through a telescope, they looked like diffuse spots of light, reminiscent of nebulae, but only with the help of the 2.5-meter reflecting telescope at Mount Wilson Observatory, first used in the 1920s, were it possible to obtain images of the separation. stars in the Andromeda nebula and prove that it is a galaxy. The same telescope was used by Hubble to measure the periods of Cepheids in the Andromeda nebula. These variable stars have been studied well enough that the distances to them can be accurately determined. The distance to the Andromeda nebula is approx. 700 kpc, i.e. it lies far beyond our Galaxy.

There are several types of galaxies, the main ones being spiral and elliptical. Attempts have been made to classify them using alphabetic and numerical schemes, such as the Hubble classification, but some galaxies do not fit into these schemes, in which case they are named after the astronomers who first identified them (for example, the Seyfert and Markarian galaxies), or given alphabetic designations of classification schemes (for example, N-type and CD-type galaxies). Galaxies that do not have a distinct shape are classified as irregular. The origin and evolution of galaxies are not yet fully understood. Spiral galaxies are the best studied. These include objects that have a bright core from which spiral arms of gas, dust and stars emanate. Majority spiral galaxies have 2 arms emanating from opposite sides of the core. As a rule, the stars in them are young. These are normal spirals. There are also crossed spirals, which have a central bridge of stars connecting the inner ends of the two arms. Our G. also belongs to the spiral type. The masses of almost all spiral gases lie in the range from 1 to 300 billion solar masses. About three-quarters of all galaxies in the Universe are elliptical. They have an elliptical shape, lacking a discernible spiral structure. Their shape can vary from almost spherical to cigar-shaped. They are very diverse in size - from dwarf ones with a mass of several million solar masses to giant ones with a mass of 10 trillion solar masses. The largest known - CD-type galaxies. They have a large core, or perhaps several cores, moving rapidly relative to each other. These are often quite strong radio sources. Markarian galaxies were identified by Soviet astronomer Veniamin Markarian in 1967. They are strong sources of radiation in the ultraviolet range. Galaxies N-type have a star-like, faintly luminous core. They are also strong radio sources and are thought to evolve into quasars. In the photo, Seyfert galaxies look like normal spirals, but with a very bright core and spectra with broad and bright emission lines, indicating the presence of large amounts of rapidly rotating hot gas in their cores. This type of Galaxies was discovered by the American astronomer Carl Seyfert in 1943. Galaxies that are observed optically and at the same time are strong radio sources are called radio galaxies. These include Seyfert Galaxies, cD- and N-type galaxies, and some quasars. The energy generation mechanism of radio galaxies is not yet understood.

Determination of visibility conditions for the planet Saturn according to the “School Astronomical Calendar”.

TICKET No. 24

Fundamentals of modern ideas about the structure and evolution of the Universe.

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

There are several models of the Universe.

In the Einstein-de Sitter model, the expansion of the Universe continues indefinitely; in the static model, the Universe does not expand or evolve; in a pulsating Universe, cycles of expansion and contraction are repeated. However, the static model is the least likely; not only the Hubble law, but also the background discovered in 1965 speaks against it. cosmic microwave background radiation(i.e. radiation from the primary expanding hot four-dimensional sphere).

Some cosmological models are based on the theory of a “hot universe”, outlined below.

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

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

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

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

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

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

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

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

Calculating the distance to a star using a known parallax.

1. Local time.

Time measured on a given geographical 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) is at any moment the same. Therefore, throughout the entire geographic meridian, local time (sidereal or solar) is the same at the same moment.

If the difference geographical longitudes there are two places D l, then in more eastern place the hour angle of any luminary will be at D l greater than the hour angle of the same star in a more western location. Therefore, the difference in 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 hourly measure (in time units):

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 hourly units and considered positive east of Greenwich.

In astronomical calendars, the moments of most phenomena are indicated in universal time. T 0 . Moments of these phenomena 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 is because there are, in principle, as many local time systems as there are geographical meridians, i.e. countless. Therefore, in order to establish the sequence of events or phenomena noted in local time, it is absolutely necessary to know, in addition to the moments, also the difference in longitudes of those meridians on which these events or phenomena took place.

The sequence of events marked by universal time is easy to establish, but the large difference between universal time and the local time of meridians located at considerable distances from Greenwich creates inconvenience when using universal time in everyday life.

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

Standard timeT p is the local mean solar time measured at the prime meridian of a given time zone. It is used to keep track of time throughout the entire territory lying in a given time zone.

Standard time of this zone P connected with universal time by an obvious relationship

Tn = T 0 +n h .

(1.29)

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

4. Summer time. In order to more rationally distribute electricity used for lighting enterprises and residential premises, and make the most complete use of daylight in summer months Years in many countries (including our republic) the hour hands of clocks running according to standard time are moved forward by 1 hour or half an hour. The so-called summer time. In the fall, the clocks are again set to standard time.

Daylight saving time 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)

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 create such a collection of the most important information on astrophysics.

S. Popov. Photo by I. Yarovaya

Contrary to popular belief, school teaching 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 few 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 past 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 reasonable to make a “Very Short Course in 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 the 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 obtained by the Hubble Space Telescope 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. That's how it changes these days chemical composition universe.

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. Most of the chemical elements that we encounter in life (and that we are made of) originated in 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. The nature of dark energy is unclear.