1. The local time.

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

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

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

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

3. standard time. IN Everyday life use both local mean solar time and universal time uncomfortable. The first because there are, in principle, as many local time counting 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 the meridians on which these events or phenomena took place.

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

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

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

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

T n = T 0 +n h .

(1.29)

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

4. Summer time. In order to more rationally distribute electricity used for lighting enterprises and residential premises, and to make the most of daylight in the summer months of the year 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 clock is again set to standard time.

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

(1.30)

1. The theoretical resolution of the telescope:

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

2. Telescope magnification:

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

3. The height of the luminaries at the climax:

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

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

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

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

the height of the luminaries at the lower climax:

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

4. Astronomical refraction:

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

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

sidereal time:

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

mean solar time (local mean time):

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

world time:

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

standard time:

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

maternity time:

or

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

for upper planets:

for the lower planets:

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

7. Kepler's third law:

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

8. Law of gravity:

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

9. Kepler's third generalized law:

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

for the system Sun and two planets:

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

for systems Sun and planet, planet and satellite:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

16. Luminary radius:

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

20. Stefan-Boltzmann law:

ε=σT 4 , where ε is the energy radiated per unit time from a unit surface, T is the temperature (in kelvins), and σ is the Stefan-Boltzmann constant.

21. Wine's Law:

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

22. Hubble's law:

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

1.2 Some important concepts and formulas from general astronomy

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

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

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

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

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

, (1.2)

(1.3)

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

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

The brilliance of a star, estimated by the eye, is called visual. It corresponds to a stellar magnitude, denoted by m u . or m visas. . The brilliance of stars, estimated by their image diameter and the degree of blackening on a photographic plate (photographic effect), is called photographic. It corresponds to the photographic magnitude m pg or m phot. The difference C \u003d m pg - m ph, depending on the color of the star, is called the color index.

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

Theoretical information about eclipsing variable stars

2.1 History of discovery and classification of eclipsing variable stars

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

The Algol light curve shown in Fig. one

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

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

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

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

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

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

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

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

In addition to stars like Algol, b Lyra and W Ursa Major, there are rarer objects that are also classified as eclipsing variable stars. These are ellipsoidal stars that rotate around an axis. A change in disk area causes small changes in brightness.

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

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

From the sea of ​​information in which we are drowning, apart from self-destruction, there is another way out. Experts with a broad enough mind can create up-to-date summaries or summaries that briefly summarize key facts from a given area. We present an attempt by Sergei Popov to make such a collection of the most important information on astrophysics.

S. Popov. Photo by I. Yarovaya

Contrary to popular belief, school teaching of astronomy was not up to par in the USSR either. Officially, the subject was in the curriculum, but in reality, astronomy was not taught in all schools. Often, even if the lessons were held, teachers used them for additional classes in their core subjects (mainly physics). And in very few cases, the teaching was of sufficient quality to have time to form an adequate picture of the world among schoolchildren. In addition, astrophysics has been one of the most rapidly developing sciences over the past decades; the knowledge of astrophysics that adults received at school 30-40 years ago is significantly outdated. We add that now there is almost no astronomy in schools at all. As a result, for the most part, people have a rather vague idea of ​​\u200b\u200bhow the world works on a scale larger than the orbits of the planets in the solar system.

Spiral galaxy NGC 4414

Cluster of galaxies in the constellation Coma Berenices

Planet around the star Fomalhaut

In such a situation, I think it would be wise to do 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 stated in one lecture or fit into one small 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 on astrophysics that would fit on one standard A4 page (about 3000 characters with spaces). At the same time, of course, it is assumed that a person knows that the Earth revolves around the Sun, understands why eclipses and the change of seasons occur. That is, absolutely “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 that is on the list can be stated in about an hour lecture (or in 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 with large strokes” should help, in which all the main points that reveal the basic properties of the structure of the Universe are captured.

All images were taken by the Hubble Space Telescope and taken from 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 remnants, interstellar gas, dust and dark matter. The distances between stars in the galaxy are usually a few light years.

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

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

4. The sun is evolving. Its age is less than 5 billion years. In about 5 billion years, it will run out of hydrogen in its core. The Sun will become a red giant and then a white dwarf. Massive stars explode at the end of their lives, leaving 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 part of the universe. They are surrounded by small satellites. The galaxy is about 100,000 light years across. 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 over 1,000 exoplanets. Apparently, many stars have planets, but only a small part can be suitable for life.

7. The world as we know it has a finite age of 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, evolving. In the course of expansion from a dense hot state, the universe cooled and became less dense, ordinary particles appeared. Then there were stars, galaxies.

8. Due to the finiteness of the speed of light and the finite age of the observable universe, only a finite region of space is available to us for observation, but the physical world does not end at this boundary. At great distances, due to the finiteness of the 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 of which we are made) 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 the formation of stars, ordinary matter mainly existed in the form of hydrogen (the most common element) and helium.

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

ASTRONOMY 11 CLASS TICKETS

TICKET #1

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

The Earth makes complex movements: it rotates around its axis (T=24 hours), moves around the Sun (T=1 year), rotates together with the Galaxy (T=200 thousand years). This shows that all observations made from the Earth differ in apparent trajectories. The planets move across the sky from east to west (direct movement), then from west to east (reverse movement). Moments of direction change are called stops. If you put this path on the map, you get a loop. The size of the loop is the smaller, the greater the distance between the planet and the Earth. 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, thanks to the movement of the Earth, one can observe the loop-like movement of the planets. The relative positions of the planets relative to the Sun and the Earth are called planetary configurations.

Planet configurations, diff. geometric the positions 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 ill. V - inner planet, I- outer planet, E - Earth, S - The sun. When the internal the planet lies in a straight line with the sun, it is in connection. K.p. EV 1S and ESV 2 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). I 5 ES, is called elongation. For internal planets max, elongation occurs when EV 8 S is 90°; for external planets can elongate 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 makes a revolution around the Sun in its orbit is called the sidereal (stellar) period of revolution - T, the period of time between two identical configurations - the synodic period - S.

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

for inner planets

for outer planets

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

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

Calculation of the distance to the galaxy based on Hubble's law.

H = 50 km/sec*Mpc – Hubble constant

TICKET #2

Principles of determining geographical coordinates from astronomical observations.

There are 2 geographic coordinates: geographic latitude and geographic longitude. Astronomy as a practical science allows you to find these coordinates. The height of the celestial pole above the horizon is equal to the geographical latitude of the place of observation. Approximate geographic latitude can be determined by measuring the height of the North Star, because. it is about 1 0 from the north celestial pole. It is possible to determine the latitude of the place of observation by the height of the luminary at the upper climax ( climax- the moment of passage of the luminary through the meridian) according to the formula:

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

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

T λ 1 - T λ 2 \u003d λ 1 - λ 2 Thus, having learned the time difference at two points, the longitude of one of which is known, one can determine the longitude of the other point.

The local time is the solar time at that location on Earth. At each point, local time is different, so people live according to standard time, that is, according to the time of the middle meridian of this zone. The date change line runs in the east (Bering Strait).

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

L - luminosity (Lc = 1)

R - radius (Rc = 1)

T - Temperature (Tc = 6000)

TICKET #3

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

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

Eclipse, an astronomical phenomenon, in which one celestial body completely or partially covers another, or the shadow of one body falls on others. 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 the central shadow and the penumbra surrounding it. Under favorable conditions, 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 those of the Sun. Solar 3. can occur if the line connecting the centers of the Sun and the Moon crosses the earth's surface. The diameters of the lunar shadow when falling to the Earth can reach several. hundreds of kilometers. The observer sees that the dark lunar disk has not completely covered the Sun, leaving its edge open in the form of a bright ring. This is the so-called. annular solar 3. If the angular dimensions of the Moon are greater than 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 the full solar 3. The Earth rotates around its axis, the Moon - around the Earth, and the Earth - around the Sun, the lunar shadow quickly slides over the earth's surface from the point where it fell on it to another, where it leaves it, and draws on the Earth * a strip of full or ring 3. Private 3. can be observed when the Moon blocks only part of the Sun. 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. do not occur on every new moon or full moon. Comparison of the prediction 3. with observations makes it possible to refine the theory of the motion of the moon. Since the geometry of the system is almost exactly repeated every 18 years 10 days, 3. occur with this period, called saros. 3. Registrations from ancient times make it possible to test the effect of tides on the lunar orbit.

Determining the coordinates of stars on a star map.

TICKET #4

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

Consider the annual movement of the Sun in the celestial sphere. The Earth makes a complete revolution around the Sun in a year, in one day the Sun moves along the ecliptic from west to east by about 1 °, and in 3 months - by 90 °. However, on 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, during the year, the location of the daily parallel of the Sun also changes. Consider the average latitudes of the northern hemisphere.

During the passage of the vernal equinox by the Sun (α = 0 h), at the end of March, the declination of the Sun is 0 °, therefore on this day the Sun is practically on the celestial equator, it rises in the east, rises at the upper culmination to a height 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 a day, and below it for half, i.e. day equals night, which is reflected in the name "equinox". At the moment of equinox, the tangent to the ecliptic at the location of the Sun is inclined to the equator 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 every day everything most of The daily parallel of the Sun is above the horizon. The sun rises earlier, rises higher in the upper climax and sets later. The points of sunrise and sunset are shifting north every day, and the day is lengthening.

However, the angle of inclination of the tangent to the ecliptic at the location of the Sun decreases every day, and with it the rate of increase in declination also decreases. Finally, at the end of June, the Sun reaches the northernmost point of the ecliptic (α = 6 h, δ = +e). By this moment it rises in the upper climax to a height 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 stops at the upper culmination, and the midday Sun, as it were, "stops" in its movement to the north. Hence the name "summer solstice".

After that, the declination of the Sun begins to decrease - very slowly at first, and then faster and faster. It rises later every day, 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 again sets in, now the autumn one. Again, the rate of change of the Sun's declination reaches its maximum, and it rapidly shifts to the south. The night becomes longer than a day, and every day the height of the Sun in the upper climax 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 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 the scattering of light by the earth's atmosphere, the sky continues to be bright for some time after sunset. This period is called twilight. Civil twilight (-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 sinks less than 18° below the horizon, and summer nights become bright due to astronomical twilight. Similarly, at φ > 54°.5 on the summer solstice, the height of the Sun 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). Further north, at φ > 58°.5, civil twilight no longer stops in summer (here is St. Petersburg with its famous "white nights").

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. Further north, the Sun does not set below the horizon for some time in summer - the polar day sets in, and in winter - it does not rise - the polar night.

Now consider more southern latitudes. As already mentioned, south of the 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 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 time of the summer solstice at one of the points at this latitude, the Sun is exactly at its zenith. Finally, at the equator, the daily parallels of the Sun are always divided by the horizon into two equal parts, that is, the day there is always equal to the night, and the Sun is at its zenith during the equinoxes.

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

Aiming at a given object and focusing the telescope .

TICKET #5

1. Principle of operation and purpose of the telescope.

Telescope, an astronomical instrument for observing the heavenly bodies. A well-designed telescope is capable of collecting electromagnetic radiation in various ranges of the spectrum. In astronomy, an optical telescope is designed to magnify an image and collect light from weak sources, especially those invisible to the naked eye, because compared to it, it is able to collect more light and provide high angular resolution, so more details can be seen in the enlarged image. A refractor telescope uses a large lens to collect and focus light as an objective, and the image is viewed through an eyepiece consisting of one or more lenses. The main problem in the design of refracting telescopes is chromatic aberration (color fringing around the image created by a simple lens due to the fact that light of different wavelengths is focused at different distances.). It can be eliminated using a combination of convex and concave lenses, but lenses larger than a certain size limit (about 1 meter in diameter) cannot be made. Therefore, at present, preference is given to reflecting telescopes, in which a mirror is used as an objective. The first reflecting telescope was invented by Newton according to his scheme, called Newton's system. Now there are several methods for observing an image: Newton, Cassegrain systems (the focus position is convenient for recording and analyzing light using other devices, such as a photometer or spectrometer), kude (the scheme is very convenient when bulky equipment is required for light analysis), Maksutov ( 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, widespread different types radio telescopes (with a parabolic mirror: fixed and full-rotating; type RATAN-600; in-phase; radio interferometers). There are also telescopes for detecting x-rays and gamma rays. Since the latter is absorbed by the Earth's atmosphere, X-ray telescopes are usually mounted on satellites or airborne probes. Gamma-ray astronomy uses telescopes located on satellites.

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

T s \u003d 1 year

a z = 1 astronomical unit

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

TICKET #6

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

First, the distance to some accessible point is determined. This distance is called the basis. The angle at which the basis 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 the fact that a powerful short-term impulse is sent to a celestial body, and then the reflected signal is received. 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 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. By this method, the distances to the Moon, Venus, Mercury, Mars, and Jupiter have been refined.

Laser location of the moon. Soon after the invention of powerful sources of light radiation - optical quantum generators (lasers) - experiments began to be carried out on laser location of the moon. The laser location 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 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 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 earthly observer - the angular radius of the luminary r and the distance to the luminary D.

Taking into account p 0 - the horizontal parallax of the star 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 #7

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

Decomposition electromagnetic radiation by wavelengths in order to study them is called spectroscopy. Spectrum analysis is the main method for studying astronomical objects used in astrophysics. The study of spectra provides information on temperature, velocity, 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. The intensity of the spectrum can be used to determine the temperature of stars and other bodies:

l max T = b, b is Wien's 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:. The shift of the lines in the spectrum of the star relative to the comparison spectrum to the red side indicates that the star is moving away from us, the 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 companion 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 radiating gas has no relative motion, the spectral lines emitted by individual atoms will shift relative to the laboratory value due to erratic thermal motion. For the total mass of the gas, this will be expressed in the 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 radiating gas can be judged from the width of the spectral line. In 1896, the Dutch physicist Zeeman discovered the effect of splitting the lines of the spectrum in a strong magnetic field. With 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 appears in a star.

The earth's atmosphere delays part of the radiation coming from space. Visible light passing through it is also distorted: the movement of air blurs the image of celestial bodies, and the stars twinkle, although in fact their brightness is unchanged. Therefore, since the middle of the 20th century, astronomers began to conduct observations from space. Out-of-atmosphere telescopes collect and analyze x-ray, 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 mixes with the IR of the planet itself. Therefore, it is preferable to take infrared telescopes into space. X-ray radiation reveals regions in the Universe where energy is especially 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 from the optics over a wide range of temperatures. Gamma-ray astronomy makes it possible to detect sources of electron-positron annihilation, i.e. high energy sources.

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

h - the height of the luminary

TICKET #8

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

The main problems of modern astronomy:

There is no solution to many particular problems of cosmogony:

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

In stellar astronomy:

· There is no detailed model of the Sun capable of accurately explaining all of its observed properties (in particular, the flux of neutrinos from the nucleus).

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

In galactic and extragalactic astronomy:

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

· There is no unified theory of galaxy formation;

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

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

· Do nearby stars have terrestrial planets and do they have biospheres (do they have life)?

What processes contribute to the formation of stars?

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

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

Where and when did galaxies form?

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

TICKET #9

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

The three laws of planetary motion relative to the Sun were empirically derived 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 in an ellipse with the Sun at one of its foci ( e = c / a, where from is the distance from the center of the ellipse to its focus, but- big semi-axle, e - eccentricity ellipse. The larger e, the more the ellipse differs from the circle. If from= 0 (foci coincide with the center), then e = 0 and the ellipse turns into a circle with a radius but).

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

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

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

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

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

Velocity 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 system of circulating bodies is of great importance. In a generalized form, this law is usually formulated as follows: the squares of the periods T 1 and T 2 of the revolution of two bodies around the Sun, multiplied by the sum of the masses of each body (M 1 and M 2, respectively) and the Sun (M s), are related as cubes of the semi-major axes a 1 and a 2 of their orbits: . In this case, the interaction between the bodies M 1 and M 2 is not taken into account. If we neglect the masses of these bodies in comparison with the mass of the Sun, then we get the formulation of the third law given by Kepler himself: Kepler's third law can also be expressed as the relationship between the period T of the orbit of a body with mass M and the semi-major 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 according to specified coordinates.

TICKET #10

Terrestrial planets: Mercury, Mars, Venus, Earth, Pluto. They are small in size and mass, the average density of these planets is several times greater than the density of water. They slowly rotate around their axes. They have few satellites. The terrestrial planets have solid surfaces. The similarity of the terrestrial planets does not exclude a significant difference. For example, Venus, unlike other planets, rotates in the opposite direction 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 D planets: 4870 km Atmospheric properties: There is practically no atmosphere, helium and hydrogen from the Sun, sodium released by the superheated surface of the planet. Surface: pitted 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 D planets: 12100 km Atmospheric composition: Mainly carbon dioxide with admixtures of nitrogen and oxygen, clouds of condensate of sulfuric and hydrofluoric acid. Surface: Stony desert, relatively smooth, although there are some craters Features: Pressure near the surface is 90 times higher than the earth's, reverse rotation along the orbit, strong greenhouse effect (T=475 0 С).

Earth . R orbits: 1 AU (150,000,000 km) R planets: 6400 km The composition of the atmosphere: 78% nitrogen, 21% oxygen and carbon dioxide. Surface: The most varied. Features: A lot of water, the conditions necessary for the origin and existence of life. There is 1 satellite - the Moon.

Mars. Weight: 6.4*1023 kg R orbits: 1.52 AU (228 million km) D planets: 6670 km Atmospheric composition: Carbon dioxide with impurities. Surface: Craters, Mariner Valley, Mount Olympus - the highest in the system Features: A lot of water in the polar caps, presumably before the climate was suitable for carbon-based organic life, and the evolution of the Martian climate 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 orbits: 29.65-49.28 AU

D planets: 2324/1212 km

Atmospheric composition: Thin layer of methane

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

Giant planets: Jupiter, Saturn, Uranus, Neptune.

They have large sizes and masses (the mass of Jupiter > the mass of the Earth by 318 times, by volume - by 1320 times). The 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). A feature of the giant planets is rings consisting of particles and blocks. These planets do not have solid surfaces, their density is low, they consist mainly of hydrogen and helium. The gaseous hydrogen of 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 causes 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 planets: 143,760 km at the equator Composition: Hydrogen with helium impurities. Satellites: There is a lot of water on Europa, 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 orbits: 9.5 AU D planets: 120,420 km Composition: Hydrogen and helium. Moons: Titan is larger than Mercury and has an atmosphere. Features: Beautiful rings, low density, many satellites, poles magnetic field almost coincide with the axis of rotation.
Uranus Weight: 8.5*1025kg R orbit: 19.2 AU D planets: 51,300 km Ingredients: Methane, ammonia. Satellites: Miranda has a very difficult terrain. Features: The axis of rotation is directed to 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 planets: 49500 km Ingredients: Methane, ammonia, hydrogen atmosphere.. Moons: Triton has a nitrogen atmosphere, water. Features: Radiates 2.7 times more absorbed energy.

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

TICKET #11

Distinctive features of the Moon and satellites of the planets.

moon is the only natural satellite of the Earth. The surface of the Moon is highly inhomogeneous. The main large-scale formations - seas, mountains, craters and bright rays, perhaps - are emissions of matter. The seas, dark, smooth plains, are depressions filled with solidified lava. The diameters of the largest of them exceed 1000 km. Dr. three types of formations are most likely the result of the bombardment of the lunar surface in the early stages of the existence of the solar system. The bombardment lasted for several hundreds of millions of years, and the debris settled on the surface of the moon and planets. Fragments of asteroids with a diameter of 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 instruments. apparatuses of the Apollo series recorded the seismic activity of the moon, the so-called. l shock. Samples of lunar soil brought to Earth by astronauts showed that the age of L. 4.3 billion years, probably the same as the Earth, consists of the same chemical. elements as the Earth, with the same approximate ratio. There is no and probably never was an atmosphere on L., and there is no reason to assert that life ever existed there. According to the latest theories, L. was formed as a result of collisions of planetesimals the size of Mars and the young Earth. The temperature of the lunar surface reaches 100°C on a lunar day and drops to -200°C on a lunar night. On L. there is no erosion, for the claim. slow destruction of rocks due to alternating thermal expansion and contraction and random sudden local catastrophes due to meteor impacts.

The mass of L. is accurately measured by studying the orbits of her arts, 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 diameter of the Earth. 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 L. is equal to the period of revolution around the Earth, so that, except for the effects of libration, it always turns one side towards it. Wed the density is 3330 kg/m 3 , a value very close to the density of the main rocks lying under 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 closest celestial body to Earth. If the Earth and the Moon were point masses or rigid spheres, the density of which changes only with distance from the center, and there were no other celestial bodies, then the Moon's orbit around the Earth would be an unchanging ellipse. However, the Sun and, to a much lesser extent, the planets exert gravity. influence on the orbit, causing a perturbation of its orbital elements; therefore, the semi-major axis, eccentricity, and inclination are continuously subjected to cyclic perturbations, oscillating about average values.

Natural satellites, a natural body orbiting a planet. More than 70 moons 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 geol. history; some have an atmosphere. All other satellites have dimensions comparable to asteroids, i.e. from 10 to 1500 km. They may be composed of rock or ice, varying in shape from nearly spherical to irregular, and the surface is either ancient with numerous craters or altered by subsurface activity. The sizes of the orbits range from less than two to several hundred radii of the planet, the period of revolution is from several hours to more than a year. It is believed that some satellites were captured by the gravitational pull of the planet. They have irregular orbits and sometimes turn in the direction opposite to the orbital movement of the planet around the Sun (the so-called reverse movement). 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 the gas and dust cloud surrounding the parent planet, similar to the formation of planets in the protosolar nebula. S.e. smaller than a few. hundreds of kilometers have irregular shape and probably formed during the destructive collisions of larger bodies. In ext. areas of the solar system, they often circulate near the rings. Orbital elements ext. The SE, especially the eccentricities, are subject to strong perturbations caused by the Sun. Several pairs and even triples S.e. have circulation periods related by a simple relation. For example, Jupiter's moon Europa has a period almost equal to half that of Ganymede. This phenomenon is called resonance.

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

TICKET #12

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

Comet, the celestial body of the solar system, consisting of particles of ice and dust, moving along highly elongated orbits, 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 gas and dust shell that surrounds the comet's head as it approaches the Sun. This "atmosphere", continuously blown away by the solar wind, is replenished by gas and dust escaping from the nucleus. The diameter of the comet reaches 100 thousand km The escape velocity of gas and dust is several kilometers per second relative to the nucleus, and they dissipate in interplanetary space partly through the comet's tail.) and tail (The gas and dust flow formed under the action of light pressure and interaction with the solar wind from the space of the atmosphere of a comet. In most comets, X. appears when they approach the Sun at a distance of less than 2 AU X. is always directed from the Sun. Gaseous X. is formed by ionized molecules ejected from the nucleus, under the influence of solar radiation has a bluish color, distinct boundaries, typical width 1 million km, length - tens of millions of kilometers. The structure of X. can noticeably change over several years. hours. The speed of individual molecules varies 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 K. 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 the core K. 1-100 billion kg, diameter 200-1200 m, density 200 kg / m 3 ("/5 the density of water). There are voids in the cores. These are unstable formations, consisting of one third of ice and two thirds of the dust in. Ice is mainly water, but there are impurities of other compounds. With each return to the Sun, the ice melts, gas molecules leave the core and drags particles of dust and ice with them, while a spherical shell forms around the core - coma, a long plasma tail directed away from the Sun and a dust tail.The amount of energy lost depends on the amount of dust covering the core and the distance from the Sun at perihelion. Halley's Comet at close range, confirmed many theories of the structure of K.

K. are usually named after their discoverers with an indication of the year when they were last observed. Subdivided into short-term 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. Enke. These K. were captured by gravity. Jupiter's field and began to rotate in relatively small orbits. A typical one has a perihelion distance of 1.5 AU. and completely collapses after 5 thousand revolutions, giving rise to a meteor shower. Astronomers observed the decay of K. West in 1976 and K. * Biel. On the contrary, the circulation periods are long-periodic. C. can reach 10 thousand, or even 1 million years, and their aphelia can be at one-third of the distance to the nearest stars. At the present time, about 140 short-period and 800 long-period ones are known, and every year about 30 new K. Our knowledge of these objects is incomplete, because they are detected only when they approach the Sun at a distance of about 2.5 AU It is assumed that about a trillion K turns around the Sun.

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

A. are also grouped according to the elements of the orbits, forming the so-called. the Hirayama family. Most A. has a circulation period of approx. 8 o'clock All A. with a radius of less than 120 km have an irregular shape, orbits are subject to gravity. influence of Jupiter. As a result, there are gaps in the distribution of A. along the semi-major axes of the orbits, called Kirkwood hatches. A. falling into these hatches would have periods that are multiples of the orbital period of Jupiter. The asteroid orbits in these hatches are highly 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 contracts, it forms a disk of matter around the star. Part of the matter of this disk falls back onto the star, obeying the force of gravity. The gas and dust that remain in the disk are gradually cooled. When the temperature drops low enough, the material of the disk begins to gather into small clumps - pockets of condensation. This is how planetesimals are created. During the formation of the solar system, some of the planetesimals collapsed as a result of collisions, while others merged to form planets. In the outer part of the solar system, large planetary cores formed, which were able to hold on to some 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 was the beginning of the formation of "gas giants" - Jupiter, Saturn, Uranus and Neptune. They probably developed their own mini-discs of gas and dust, which eventually formed moons and rings. Finally, in the inner solar system, solid matter forms Mercury, Venus, Earth, and Mars.

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

TICKET #13

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

The 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 type 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 pressure that can withstand the force of gravity, which is 27 times greater on the surface of the Sun (photosphere) than on Earth. Such a high temperature arises due to thermonuclear reactions of the conversion of hydrogen into helium (proton-proton reaction) (energy output from the surface of the photosphere 3.8 * 10 26 W). The sun is a spherically symmetrical body in balance. Depending on the change in physical conditions, the Sun can be divided into several concentric layers, gradually turning into each other. Almost all of the Sun's energy is generated in the central region - core, where the nuclear 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 huge 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 the X-ray decreases, and it becomes visible light. However, neutrinos produced in nuclear reactions, freely leave the Sun and, in principle, provide direct information about the core. The discrepancy between the observed and theoretically predicted neutrino flux has given rise to serious controversy about internal structure Sun. Over the last 15% of the radius, there is a convective zone. Convective motions also play a role in the transport of magnetic fields generated by currents in its rotating inner layers, which manifests itself as solar activity, the strongest fields are observed in sunspots. Outside the photosphere is the solar atmosphere, in which the temperature reaches a minimum value of 4200 K, and then increases again due to the dissipation of shock waves generated by subphotospheric convection in the chromosphere, where it sharply increases to a value of 2 * 10 6 K, characteristic of the corona. The high temperature of the latter leads to a continuous outflow of plasma matter into interplanetary space in the form of the solar wind. In some areas, the magnetic field strength can quickly and strongly increase. This process is accompanied by a whole complex of phenomena of 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 masses and 110 Earth radii, respectively; 1.3 million such bodies as the Earth can fit in the Sun. The rotation of the Sun causes the movement of its surface formations, such as sunspots, in the photosphere and the layers above it. The average rotation period is 25.4 days, and at the equator it is 25 days, and at the poles - 41 days. The rotation is due to the compression of the solar disk, which is 0.005%.

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

TICKET #14

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

Solar activity is a consequence of the convection of the middle layers of the star. The reason for this phenomenon lies in the fact that the amount of energy coming from the nucleus is much greater than that removed by thermal conduction. 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 the present time they are considered areas of the photosphere with a temperature of 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 lighter fibrous penumbra. The flow of gas from shade to penumbra is called the Evershed effect (V=2km/s). Number of S.p. and their appearance change over the course of an 11-year solar activity cycle, or sunspot cycle, which is described by Spörer's law and graphically illustrated by the Maunder butterfly diagram (movement of spots in 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 magnet. polarity during the 22-year cycle of solar activity. But naib, a striking example of long-term variation, is the minimum. Maunder (1645-1715), when S.p. were absent. Although it is generally accepted that variations in the number of S.p. determined by the diffusion of the magnetic field from the rotating solar interior, the process is not yet fully understood. The strong magnetic field of sunspots affects the Earth's field, causing radio interference and auroras. there are several irrefutable short-term effects, the assertion of the existence of long-term. the relationship between climate and the number of S.p., especially the 11-year cycle, is very controversial, due to the difficulties in meeting the conditions that are necessary when conducting an accurate statistical analysis of data.

sunny wind Outflow of high-temperature plasma (electrons, protons, neutrons and hadrons) of the solar corona, radiation of intense radio spectrum waves, X-rays into the surrounding space. Forms the so-called. the 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 form. S.V. ionizes the upper layers of the atmosphere, due to which the ozone layer is formed, causes auroras and an increase in the 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 the greatest number of sunspots, radiation and prominences. It has long been established that the change in solar activity of the Sun affects the following factors:

* the epidemiological situation on Earth;

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

* on the number of road and rail accidents.

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

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

TICKET #15

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

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

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

a is the semi-major axis of the Earth's orbit,

p is the annual parallax.

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

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

By measuring the annual parallax, one can reliably determine the distance to stars that are no further than 100 parsecs or 300 ly. years.

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

Determination of the conditions for the visibility of the moon according to the "School astronomical calendar".

TICKET #16

The main physical characteristics of stars, the relationship of these characteristics. Conditions for the equilibrium of stars.

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

Luminosity- the energy emitted by a star or other celestial body per unit of time. Usually given in units of solar luminosity, expressed as lg (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 magnitudes for the Sun (Mc = +4 .83). Also determined by the formula L=4πR 2 σT 4 . Stars are known, the luminosity of which is many times greater than the luminosity of the Sun. The luminosity of Aldebaran is 160, and Rigel is 80,000 times greater than that of 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 power of the star's radiation. A faint star close to Earth may look brighter than a distant bright star because the radiation flux received from it decreases inversely with the square of the distance. Visible Z.v. - the brilliance of a star, which the observer sees when looking at the sky. Absolute Z.v. - a measure of true brightness, represents the level of brightness of a star, which it would have, being at a distance of 10 pc. Hipparchus invented a system of visible Z.v. in the 2nd century BC. The stars were assigned numbers according to their apparent brightness; the brightest stars were 1st magnitude, and the faintest were 6th. All R. 19th century this system has been modified. Modern scale Z.v. was established by determining Z.v. representative sample of stars near the north. poles of the world (northern polar row). According to them, Z.v. all other stars. This is a logarithmic scale, on which 1st magnitude stars are 100 times brighter than 6th magnitude stars. As the measurement accuracy increased, tenths had to be introduced. The brightest stars are brighter than 1st magnitude, and some even have negative magnitudes.

stellar mass - a parameter directly determined only for components of binary 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 dependence. Masses greater than 40 solar masses and less than 0.1 solar masses are very rare. The masses of most stars are less than the mass of 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 the Kelvin-Helmholtz compression. Such objects are called brown dwarfs.

Mass-luminosity ratio, found in 1924 by Eddington, the relationship between the luminosity L and the stellar mass M. The ratio has the form L / Lc \u003d (M / Mc) a, where Lc and Mc are the luminosity and mass of the Sun, respectively, the value but usually lies in the range of 3-5. The ratio 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 it is also valid for supergiants and giants, although their mass is difficult to measure directly. The ratio is not applicable to white dwarfs, because increases their luminosity.

temperature stellar is the temperature of some region of the star. It is one of the most important physical characteristics of any object. However, due to the fact that the temperature of different regions of the star is different, and also due to the fact that temperature is a thermodynamic quantity that depends on the flux of electromagnetic radiation and the presence of various atoms, ions and nuclei in a certain region of the stellar atmosphere, all these differences are united into the effective temperature, which is closely related to the radiation of the star in the photosphere. Effective temperature, a parameter characterizing the total amount of energy emitted by a star per unit area of ​​its surface. This is an unambiguous method for describing stellar temperature. This. is determined through the temperature of a completely black body, which, according to the Stefan-Boltzmann law, would radiate the same power per unit surface area as a 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 makes it possible, using the Wien displacement law (λ max = 0.29/T), to determine by which wavelength there is a maximum of stellar radiation, and hence 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, strength of the magnetic field and chemical. composition.

Spectral classes, the classification of stars according to their spectra (first of all, according to the intensities of the spectral lines), first introduced by the Italian. astronomer Secchi. Introduced letter designations, to-rye were modified as knowledge of the internal was expanded. the structure of the stars. The color of a star depends on the temperature of its surface, therefore, in modern. spectral classification Draper (Harvard) S.K. arranged in descending order of temperature:

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

Equilibrium conditions: as is known, stars are the only natural objects within which uncontrolled thermonuclear fusion reactions occur, which are accompanied by the release of a large amount of energy and determine the temperature of stars. Most stars are in a stationary state, that is, they do not explode. Some stars explode (the so-called new and supernovae). Why are stars generally in balance? Strength nuclear explosions in stationary stars it is balanced by the force of gravity, which is why these stars maintain balance.

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

TICKET #17

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

Stefan-Boltzmann law, the ratio between the total radiation power of a completely black body and its temperature. The total power of a unit radiation area in W per 1 m 2 is given by the formula P \u003d σ T 4, where σ \u003d 5.67 * 10 -8 W / m 2 K 4 - Stefan-Boltzmann constant, T - absolute temperature of an absolute black body. Although the astronomer rarely radiates like a black body, their emission spectrum is often a good model of the spectrum of a real object. The dependence on temperature to the 4th power is very strong.

e is the radiation energy per unit surface of the star

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

Using the Stefan-Boltzmann formula and Wien's law, the wavelength is determined, which accounts for the maximum radiation:

l max T = b, b – Wien constant

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

2. Determination of the geographical latitude of the place of observation according to the given height of the luminary at the culmination and its declination.

H = 90 0 - +

h - the height of the luminary

TICKET #18

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

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

The most important types of physical P.Z.:

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

Eruptive(explosive) - stars with shells, young irregular variables, incl. T Tauri type stars (very young irregular stars associated with diffuse nebulae), Hubble-Seineja type 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, when exceeded, "deflation" of stellar shells. Potential supernovae.), flaring red dwarfs;

Cataclysmic - novae, supernovae, symbiotic;

X-ray double stars

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

Among the pulsating stars, Cepheids are very interesting, named after one of the first discovered variables of this type - 6 Cephei. Cepheids are stars of high luminosity and moderate temperature (yellow supergiants). In the course of evolution, they acquired a special structure: at a certain depth, a layer arose that accumulates energy coming from the bowels, and then gives it back again. A star periodically contracts as it heats up and expands as it cools. Therefore, the radiation energy is either absorbed by the stellar gas, ionizing it, or released again when, when the gas cools, the ions capture electrons, while emitting light quanta. As a result, the brightness of the Cepheid changes, as a rule, by several times with a period of several days. Cepheids play a special role in astronomy. In 1908, the American astronomer Henrietta Leavitt, who studied Cepheids in one of the nearest galaxies - the Small Magellanic Cloud, drew attention to the fact that these stars turned out to be the brighter, the longer the period of change in their brightness was. The size of the Small Magellanic Cloud is small compared to its distance, which means that the difference in apparent brightness reflects the difference in luminosity. Thanks to the period-luminosity dependence 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. It is not difficult to determine the age of each Cepheid from the period-age dependence. By selecting stars with maximum periods and studying the stellar groups they belong to, astronomers explore the youngest structures in the Galaxy. Cepheids, more than other pulsating stars, deserve the name of periodic variables. Each subsequent cycle of brightness changes usually repeats the previous one quite accurately. However, there are exceptions, the most famous of them is the North Star. It has long been discovered that it belongs to the Cepheids, although it changes the brightness in a rather insignificant range. But in recent decades, these fluctuations began to fade, and by the mid-90s. The polar star has practically ceased to pulsate.

Stars with shells, stars that continuously or at irregular intervals shed a ring of gas from the equator or a spherical shell. 3. with about. - giants or dwarf stars of spectral class B, rapidly rotating and close to the destruction limit. Shell ejection 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 about the same mass as the Sun. Many of them are in globular star clusters. As a rule, they change their brightness by one magnitude in about a day. Their properties, like those of Cepheids, are used to calculate astronomical distances.

R North 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 the eighth magnitude, and then gradually increases, returning to its previous level. Apparently, the reason for this is that this supergiant star sheds 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 obscures the star's light until the cloud dissipates into space. Stars of this type produce dense dust, which is of no small importance in regions where stars are formed.

flashing stars. Magnetic phenomena on the Sun cause sunspots and solar flares, but they cannot significantly affect the brightness of the Sun. For some stars - red dwarfs - this is not so: on them, such flashes reach enormous proportions, and as a result, light emission 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 they last only a few minutes.

Calculation of the declination of the luminary according to its height at the culmination at a certain geographical latitude.

H = 90 0 - +

h - the height of the luminary

TICKET #19

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

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

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

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

Spectral binary stars are detected by changes in their spectra. With mutual circulation, the stars periodically move either towards the Earth, or away from the Earth. The Doppler effect in the spectrum can be used to determine changes in motion.

Polarization binaries are characterized by periodic changes in the polarization of light. In such systems, stars in their orbital motion illuminate the gas and dust in the space between them, the angle of incidence of light on this substance periodically changes, while the scattered light is polarized. Precise 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 spectroscopically binary, then one 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 serve as a source of radiation in the X-ray range are called X-ray binaries. In a number of cases, a third component is observed that revolves around the center of mass of the binary system. Sometimes one of the components of a binary system (or both), in turn, may turn out to be binary stars. The close components of a binary star in a triple system can have a period of several days, while the third element can revolve around the common center of mass of a close pair with a period of hundreds or even thousands of years.

Measuring the speeds 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 binary stars, mutual gravitational forces tend to stretch each of them, to give it the shape of a pear. If gravity is strong enough, there comes a critical moment when matter begins to flow away from one star and fall onto another. Around these two stars there is a certain area in the form of a three-dimensional figure-eight, the surface of which is a critical boundary. These two pear-shaped figures, each around its own star, are called Roche lobes. If one of the stars grows so much that it fills its Roche lobe, then the 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 twists around, forming what is known as an accretion disk. If both stars have expanded so much that they have filled their Roche lobes, then a contact binary star is formed. The material from both stars mixes and merges into a ball around the two stellar cores. Since eventually all stars swell, turning into giants, and many stars are binary, interacting binary systems are not uncommon.

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

H = 90 0 - +

h - the height of the luminary

TICKET #20

The evolution of stars, its stages and final stages.

Stars form in interstellar gas and dust clouds and nebulae. The main force that “shapes” stars is gravity. Under certain conditions, a very rarefied atmosphere (interstellar gas) begins to shrink under the influence of gravitational forces. A cloud of gas condenses in the center, where the heat released during compression is retained - a protostar appears, emitting in the infrared range. The protostar heats up under the influence of matter falling on it, and nuclear fusion reactions begin with the release of energy. In this state, it is already a T Tauri variable star. The rest of the cloud dissipates. Gravitational forces then pull the hydrogen atoms toward the center, where they fuse to form helium and release energy. Increasing pressure in the center prevents further contraction. This is a stable phase of evolution. This star is a Main Sequence star. The luminosity of a star increases as its core compacts and heats up. The time a star stays in 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 regime for only a few million years. After the star has used up the hydrogen contained in its central part, major changes take place inside the star. Hydrogen begins to burn out not in the center, but in the shell, which increases in size, swells. As a result, the size of the star itself increases dramatically, and the temperature of its surface drops. It is this process that gives rise to red giants and supergiants. The final stages of the evolution of a star 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 contraction does not occur due to the basic property of electrons. There is such a degree of compression at which they begin to repel, although there is no longer any source of thermal energy. This only happens when electrons and atomic nuclei are compressed incredibly tightly, forming extremely dense matter. A white dwarf with the mass of the Sun is approximately equal in volume to the Earth. The white dwarf gradually cools, eventually turning into a dark ball of radioactive ash. Astronomers estimate that at least a tenth of all the stars in the Galaxy are white dwarfs.

If the mass of a shrinking star exceeds the mass of the Sun by more than 1.4 times, then such a star, having reached the stage of a white dwarf, will not stop there. The gravitational forces in this case are so great that the electrons are pressed into the atomic nuclei. As a result, protons turn into neutrons, capable of adhering to each other without any gaps. The density of neutron stars surpasses even the density of white dwarfs; but if the mass of the material does not exceed 3 solar masses, neutrons, like electrons, are able to prevent further compression themselves. A typical neutron star is only 10 to 15 km across, and one cubic centimeter of its 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: fast rotation and a strong magnetic field.

If the mass of a star exceeds 3 solar masses, then the final stage of its life cycle is probably a black hole. If the mass of the star, and, consequently, the gravitational force is so great, then the star is subjected to catastrophic gravitational contraction, which cannot be resisted by any stabilizing forces. The density of matter during this process tends to infinity, and the radius of the object - to zero. According to Einstein's theory of relativity, a singularity of space-time arises at the center of a black hole. The gravitational field on the surface of a shrinking star grows, so it becomes increasingly difficult for radiation and particles to leave it. In the end, such a star ends up below the event horizon, which can be visualized as a one-sided membrane that allows matter and radiation to pass only inward and nothing out. The collapsing star turns into a black hole, and it can be detected only by a sharp change in the properties of space and time around it. The radius of the event horizon is called the Schwarzschild radius.

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

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

TICKET #21

Composition, structure and dimensions of our Galaxy.

Galaxy, the 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 in its center (core) there is a powerful source of radiation. It was assumed that there is a black hole in the core, which initiates the observed powerful energy processes accompanied by radiation in the radio spectrum. (The ring of gas revolves around the black hole; hot gas escaping from its inner edge falls into the black hole, releasing energy, which we observe.) But recently a burst of visible radiation was detected in the core, and the black hole hypothesis was dropped. Parameters of the central thickening: 20,000 light-years across and 3,000 light-years thick.

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

The galactic halo is concentric with the disk and the central bulge and consists of stars that are predominantly members of globular clusters and belong to the type II population. However, most of the matter 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 speed 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 that we observe in the disk and thickening.

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 (the galactic equator) makes it possible to see disk stars from the Earth in the form of a narrow band milky way, covering the entire celestial sphere and inclined at an angle of 63 ° to the celestial equator. The center of the Galaxy lies in Sagittarius, but it is not visible in visible light due to dark nebulae of gas and dust that absorb starlight.

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

L - luminosity (Lc = 1)

R - radius (Rc = 1)

T - Temperature (Tc = 6000)

TICKET #22

star clusters. The 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, not 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 that they differ from each other only in their mass. There are two types of star clusters: open and globular. In an open cluster, each star is visible separately, they are distributed more or less evenly over some part of the sky. And 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 from 10 to 1000 stars, many more young than old, and the oldest are 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 rather 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 ones, globular clusters are spheres densely filled with stars (from 100 thousand to 1 million). A typical globular cluster is 20 to 400 light-years across.

In the densely packed centers of these clusters, the stars are in such close proximity to each other that mutual gravity binds them to each other, forming compact binary stars. Sometimes there is even a complete merger of stars; in close approach, the outer layers of the star can collapse, exposing the central core to direct viewing. In globular clusters, double stars are 100 times more common than anywhere else.

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

The substance (gas and dust) located 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 matter is relatively cold (100 K) and is detected by infrared radiation. Such clouds contain neutral hydrogen, molecular hydrogen, and other radicals that can be detected with radio telescopes. In regions near high-luminosity stars, the gas temperature can reach 1000-10000 K, and hydrogen is ionized.

The interstellar medium is very rarefied (about 1 atom per cm3). However, in dense clouds, the concentration of a substance can be 1000 times higher than the average. But even in a dense cloud, there are only a few hundred atoms per cubic centimeter. The reason why we still manage to observe interstellar matter is that we see it in a large thickness of space. The 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 permeated with cosmic ray fluxes.

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 #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. masses of the sun. The true nature of galaxies was finally explained only in the 1920s. after heated discussions. Until that time, when observed with a telescope, they looked like diffuse spots of light resembling nebulae, but only with the help of the 2.5-meter reflecting telescope of the Mount Wilson Observatory, first used in the 1920s, was it possible to obtain images of the nebulae. 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 to be able to accurately determine their distances. The Andromeda Nebula is approx. 700 kpc, i.e. it lies far beyond our Galaxy.

There are several types of galaxies, the main ones are spiral and elliptical. Attempts have been made to classify them using alphabetic and numerical schemes, such as the Hubble classification, but some galaxies do not fit into these schemes, in which case they are named after the astronomers who first identified them (for example, the Seyfert and Markarian galaxies), or give 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. Most spiral galaxies have 2 arms radiating from opposite sides of the core. As a rule, the stars in them are young. These are normal coils. There are also crossed spirals that have a central bridge of stars connecting the inner ends of the two arms. Our G. also belongs to the spiral. The masses of almost all spiral G. 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, devoid of a discernible spiral structure. Their shape can vary from almost spherical to cigar-shaped. They vary in size, from dwarfs with a mass of several million solar masses to giant ones with a mass of 10 trillion solar ones. The largest known CD-type galaxies. They have a large core, or possibly several cores moving rapidly relative to each other. Often these are quite strong radio sources. The Markarian galaxies were identified by the Soviet astronomer Veniamin Markarian in 1967. They are strong sources of radiation in the ultraviolet range. galaxies N-type have a faintly luminous core similar to a star. They are also strong radio sources and are expected to evolve into quasars. In the photo, Seyfert galaxies look like normal spirals, but with a very bright core and spectra with wide and bright emission lines, indicating the presence of a large amount of rapidly rotating hot gas in their cores. This type of galaxies was discovered by the American astronomer Karl Seifert 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 G., and some quasars. The mechanism of energy generation of radio galaxies is not yet understood.

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

TICKET #24

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

In the 20th century the 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 the millions of stars in the Milky Way. The subsequent study 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). Thus, we live in expanding universe. The recession of galaxies is reflected in the Hubble law, according to which the redshift of a galaxy is proportional to the distance to it. In addition, on the largest scale, i.e. at the level of superclusters of galaxies, the Universe has a cellular structure. Modern cosmology (the doctrine of the evolution of the Universe) is based on two postulates: the Universe is homogeneous and isotropic.

There are several models of the universe.

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

Some cosmological models are based on the "hot universe" theory 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 zero. All the energy of the Universe, all its mass was concentrated in the zero volume. The density of energy is infinite, and the density of matter is also infinite. Such a state is called singular.

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

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

Starting from the moment of time t p = R p /c = 5*10 -44 s (c is the speed of light, h is Planck's constant). Most likely, it was through t P that the gravitational interaction separated from the rest. According to theoretical calculations, during the first 10 -36 s, when the temperature of the Universe was more than 10 28 K, the energy per unit volume remained constant, and the Universe expanded at a speed much higher than 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 force separated from the electromagnetic and weak forces. The energy released as a result was the cause of the catastrophic expansion of the Universe, which in a tiny time interval of 10 - 33 s increased from the size of an atom to the size of the solar system. At the same time, elementary particles familiar to us and a slightly smaller number of antiparticles appeared. Matter and radiation were still in thermodynamic equilibrium. This era is called radiation stage of evolution. At a temperature of 5∙10 12 K, the stage 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 over antiparticles is one billionth of their number. It is from this "excessive" matter that the substance of the observable Universe mainly consists. A few seconds after the Big Bang, the stage began primary nucleosynthesis, when deuterium and helium nuclei were formed, lasting about three minutes; then the calm expansion and cooling of the Universe began.

About a million years after the explosion, the balance between matter and radiation was disturbed, atoms began to form from free protons and electrons, and radiation began to pass through matter, as through a transparent medium. It was this radiation that was called relic, its temperature was about 3000 K. At present, a background with a temperature of 2.7 K is recorded. Relic background radiation was discovered in 1965. It appeared in high degree isotropic and confirms by its existence the model of a hot expanding Universe. After primary nucleosynthesis matter began to evolve independently, due to variations in the density of matter, formed in accordance with the Heisenberg uncertainty principle during the inflationary stage, protogalaxies appeared. Where the density was slightly above average, centers of attraction were formed, regions with a lower density became more and more rarefied, as the substance left them for denser regions. This is how the practically homogeneous medium was divided into separate protogalaxies and their clusters, and after hundreds of millions of years 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 that fills it. If it is below some critical density, the expansion of the universe will continue forever. This option is called "open universe". A similar development scenario awaits a flat Universe when the density is critical. In a googol of years, all the matter in the stars will burn out, and the galaxies will plunge into darkness. Only planets, white and brown dwarfs, will remain, and collisions between them will be extremely rare.

However, even in this case, the metagalaxy is not eternal. If the theory of the grand unification of interactions is correct, in 10 40 years the protons and neutrons that make up the former stars will decay. After about 10,100 years, giant black holes will evaporate. In our world, only electrons, neutrinos and photons will remain, separated 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 is closed, and sooner or later the expansion will be replaced by a catastrophic contraction. The universe will end its life in a gravitational collapse in a sense, which is even worse.

Calculating the distance to a star from a known parallax.