Basic formulas of astronomy with explanations. Some important concepts and formulas from general astronomy. X-ray binary stars

Below is a list of words useful for astronomy. These terms were created by scientists to explain what happens in outer space.

It is useful to know these words; without understanding their definitions it is impossible to study the Universe and explain the topics of astronomy. Hopefully, the basic astronomical terms will remain in your memory.

Absolute magnitude - How bright a star would be if it were 32.6 light years from Earth.

Absolute zero - The lowest possible temperature, -273.16 degrees Celsius

Acceleration - A change in speed (speed or direction).

Skyglow - Naturally, the night sky glows due to reactions occurring in the Earth's upper atmosphere.

Albedo - The albedo of an object indicates how much light it reflects. An ideal reflector, such as a mirror, will have an albedo of 100. The Moon has an albedo of 7, the Earth has an albedo of 36.

Angstrom - A block that is used to measure the wavelength of light and other electromagnetic radiation.

Annular - Shaped like or forming a ring.

Apoaster - When two stars revolve around each other, how far apart they can be (maximum distance between the bodies).

Aphelion - During the orbital motion of an object around the Sun, when it reaches its most distant position from the Sun.

Apogee - The position of an object in the Earth's orbit when it is farthest from the Earth.

Aerolite is a stone meteorite.

Asteroid - A solid body or small planet revolving around the Sun.

Astrology - The belief that the position of stars and planets influences the events of human destinies. This has no scientific basis.

Astronomical unit - The distance from the Earth to the Sun. Usually written AU.

Astrophysics - The use of physics and chemistry in the study of astronomy.

Atmosphere - The gaseous space surrounding a planet or other space object.

Atom - The smallest particle of any element.

Aurora (Northern Lights) - Beautiful lights over the polar regions that are caused by the tension of particles from the Sun interacting with the Earth's magnetic field.

Axis - An imaginary line on which an object rotates.

Background radiation - Weak microwave radiation emanating from space in all directions. It is believed to be a remnant of the Big Bang.

Barycenter - The center of gravity of the Earth and Moon.

Binary stars - A stellar duo that actually consists of two stars orbiting each other.

Black Hole - A region of space around a very small and very massive object in which the gravitational field is so strong that even light cannot escape from it.

Fireball - A brilliant meteor that may explode during its descent through the Earth's atmosphere.

Bolometer - Radiation-sensitive detector.

Celestial Sphere - The imaginary sphere surrounding the Earth. The term is used to help astronomers explain where objects are in the sky.

Cepheids are variable stars; scientists use them to determine how distant a galaxy is or how far a cluster of stars is from us.

Charge-coupled device (CCD) - A sensitive image device that replaces photography in most branches of astronomy.

Chromosphere - Part of the solar atmosphere, it is visible during a total solar eclipse.

Circumpolar Star - A star that never sets, it can be viewed all year round.

Clusters - A group of stars or a group of galaxies that are connected by gravitational forces.

Color Index - A measure of a star's color that tells scientists how hot the star's surface is.

Coma - Nebula surrounding the nucleus of a comet.

Comet - Small, frozen masses of dust and gas orbiting the Sun.

Conjunction - A phenomenon in which a planet approaches another planet or star and moves between the other object and the body of the Earth.

Constellations - A group of stars that were given names by ancient astronomers.

Corona - The outer part of the Sun's atmosphere.

Coronagraph - A type of telescope designed to view the Corona Sun.

Cosmic rays are high-speed particles that reach the Earth from outer space.

Cosmology - The study of the Universe.

Day - The amount of time during which the Earth, rotating, rotates around its axis.

Density - Compactness of matter.

Direct motion - Objects moving around the Sun in the same direction as the Earth - they move in forward motion, unlike objects moving in the opposite direction - they move in retrograde motion.

Diurnal motion - The apparent movement of the sky from East to West caused by the Earth moving from West to East.

Ash Light - The faint glow of the Moon over the dark side of the Earth. Light is caused by reflection from the Earth.

Eclipse - When we see an object in the sky blocked by the shadow of another object or the shadow of the Earth.

Ecliptic - The path of the Sun, Moon and planets, which everyone follows in the sky.

Ecosphere - The area around a star where the temperature allows life to exist.

Electron - A negative particle that orbits an atom.

Element - A substance that cannot be broken down further. There are 92 known elements.

Equinoxes are March 21 and September 22. Twice a year, when day and night are equal in time, all over the world.

Second escape velocity - The speed required for an object to escape the grip of another object's gravity.

Exosphere - The outer part of the Earth's atmosphere.

Flares - the effect of Solar Flares. Beautiful eruptions in the outer part of the Sun's atmosphere.

Galaxy - A group of stars, gas and dust that are held together by gravity.

Gamma - Extremely short wavelength energetic electromagnetic radiation.

Geocentric - Simply means the Earth is at the center. People used to believe that the universe is geocentric; The earth for them was the center of the universe.

Geophysics - The study of the Earth using physics.

HI region - Cloud of neutral hydrogen.

NI region - Cloud of ionized hydrogen (region of hot plasma emission nebula).

Hertzsprung-Russell Diagram - A diagram that helps scientists understand different kinds stars

Hubble Constant - The relationship between the distance from an object and the speed at which it is moving away from us. Further, the object moves faster, the further away it becomes from us.

Planets that have an orbit less than the Earth's - Mercury and Venus, which lie closer to the Sun than the Earth, are called inferior planets.

Ionosphere - Region of the Earth's atmosphere.

Kelvin - The measurement of temperature is often used in astronomy. 0 degrees Kelvin is equal to -273 degrees Celsius and -459.4 degrees Fahrenheit.

Kepler's laws - 1. planets move in elliptical orbits with the Sun at one focus. 2. An imaginary line connecting the center of the planet with the center of the Sun. 3. The time required for the planet to orbit around the Sun.

Kirkwood Gaps - Regions in the asteroid belt where there are almost no asteroids. This is due to the fact that giant Jupiter changes the orbits of any object that enters these areas.

Light Year - The distance a ray of light travels in one year. This is approximately 6,000,000,000,000 (9,660,000,000,000 km) miles.

Limb - The edge of any object in outer space. The Moon zone, for example.

Local Group - A group of two dozen galaxies. This is the group to which our Galaxy belongs.

Lunation - The period between new moons. 29 days 12 hours 44 minutes.

Magnetosphere - The region around an object where the influence of the object's magnetic field can be felt.

Mass - Not the same as weight, although the mass of an object helps determine how much it will weigh.

Meteor - A shooting star is a particle of dust entering the Earth's atmosphere.

Meteorite - An object from outer space, such as a rock, that falls to Earth and lands on its surface.

Meteoroids - Any small object in outer space, such as clouds of dust or rocks.

Micrometeorites - Extremely small objects. They are so small that when they enter the Earth's atmosphere, they do not create a star effect.

The Milky Way is Our Galaxy. (The word "Galaxy" actually means Milky Way in Greek.)

Minor planet - Asteroid

Molecule - A group of atoms bound together.

Multiple stars - A group of stars that orbit each other.

Nadir - This is the point on the celestial sphere directly below the observer.

Nebula - A cloud of gas and dust.

Neutrino - A very small particle that has no mass or charge.

Neutron star - Remnants of a dead star. They are incredibly compact and spin very quickly, some spinning 100 times per second.

Novelty - A star that suddenly flares up before disappearing again - a flare many times stronger than its original brightness.

Terrestrial spheroid - A planet that is not perfectly round because it is wider in the middle and shorter from top to bottom.

Eclipse - The occultation of one celestial body by another.

Opposition - When a planet is exactly opposite the Sun, so that the Earth is between them.

Orbit - The path of one object around another.

Ozone - An area in the Earth's upper atmosphere that absorbs many of the deadly radiations coming from space.

Parallax - The shift of an object when it is viewed from two different places. For example, if you close one eye and look at your thumbnail and then switch eyes, you will see everything in the background shifting back and forth. Scientists use this to measure the distance to stars.

Parsec - 3.26 light years

Penumbra - The light part of the shadow is at the edge of the shadow.

Periastra - When two stars that orbit each other are at their closest point.

Perigee - The point in an object's orbit around the Earth when it is closest to the Earth.

Perihelion - When an object that orbits the Sun is at its closest point to the sun

Disturbances - Disturbances in the orbit of a celestial object caused by the gravitational pull of another object.

Phases - Obviously changing the shape of the Moon, Mercury and Venus due to how much of the sun faces Earth.

Photosphere - The bright surface of the Sun

Planet - An object moving around a star.

Planetary nebula - A nebula of gas surrounding a star.

Precession - The Earth behaves like a top. Its poles spin in circles causing the poles to point in different directions over time. It takes 25,800 years for the Earth to complete one precession.

Proper motion - The movement of stars across the sky as seen from Earth. Nearer stars have higher proper motion than more distant ones, as in our car - closer objects such as road signs, move faster than distant mountains and trees.

A proton is an elementary particle at the center of an atom. Protons have a positive charge.

Quasar - A very distant and very bright object.

Radiant - An area in the sky during a meteor shower.

Radio galaxies - Galaxies that are extremely powerful emitters of radio radiation.

Redshift - When an object moves away from Earth, the light from that object is stretched, making it appear redder.

Rotate - When something moves in a circle around another object, like the Moon around the Earth.

Rotation - When a rotating object has at least one fixed plane.

Saros (draconic period) is a time interval of 223 synodic months (approximately 6585.3211 days), after which eclipses of the Moon and Sun are repeated in the usual manner. Saros cycle - Period of 18 years 11.3 days in which eclipses are repeated.

Satellite - A small object in orbit. There are many electronic objects that orbit the Earth.

Twinkling - Twinkling stars. Thanks to the Earth's atmosphere.

Type - The state of the Earth's atmosphere at a certain point in time. If the sky is clear, astronomers say there is good viewing.

Selenography - Study of the surface of the Moon.

Seyfert galaxies are galaxies with small bright centers. Many galaxies are Seyfert good sources radio waves

Shooting Star - Light into the atmosphere resulting from a meteorite falling to Earth.

Sidereal Period - The period of time that an object in space takes to complete one full revolution with respect to the stars.

Solar System - A system of planets and other objects in the orbit of the star Sun.

Solar wind - A steady flow of particles from the Sun in all directions.

Solstice - June 22 and December 22. The time of year when the days are either shortest or longest, depending on where you are.

Spicules are the main elements, up to 16,000 kilometers in diameter, in the chromosphere of the Sun.

Stratosphere - The level of the Earth's atmosphere from approximately 11-64 km above sea level.

Star - A self-luminous object that shines through the energy produced in nuclear reactions within its core.

Supernova - Super bright explosion of a star. A supernova can produce the same amount of energy per second as the entire galaxy.

Sundial - Ancient instrument, used to determine time.

Sunspots - Dark spots on the surface of the Sun.

Outer planets - Planets that lie further from the Sun than Earth.

Synchronous satellite - Artificial satellite, which moves around the Earth at the same speed at which the Earth rotates, so that it is always in the same part of the Earth.

Synodic orbital period - The time it takes for an object in space to reappear at the same point, in relation to two other objects, such as the Earth and the Sun

Syzygy - The position of the Moon in its orbit, in a new or full phase.

Terminator - The line between day and night on any celestial object.

Thermocouple - An instrument used to measure very small amounts of heat.

Time dilation - When you approach the speed of light, time slows down and mass increases (there is such a theory).

Trojan asteroids - Asteroids that orbit the Sun following the orbit of Jupiter.

Troposphere - The lower part of the Earth's atmosphere.

Shade - The dark inner part of the sun's shadow.

Variable stars - Stars that fluctuate in brightness.

Zenith - It is directly above your head in the night sky.

1.2 Some important concepts and formulas from general astronomy

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

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

Magnitude m and magnitude E are related by the formula:

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

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

, (1.2)

(1.3)

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

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

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

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

Theoretical information about eclipsing variable stars

2.1 History of discovery and classification of eclipsing variable stars

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

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

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

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

From the graph of brightness changes it is clear (Fig. 1) that at Algol, immediately after reaching the main minimum (lowest brightness value), its rise begins. This means that a partial eclipse is occurring. In some cases, there may also be full eclipse, which is characterized by the preservation of the minimum brightness value of the variable in the main minimum for a certain period of time. For example, for the eclipsing variable star U Cephei, which can be observed with powerful binoculars and amateur telescopes, at the main minimum the duration of the total phase is about 6 hours.

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

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

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

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

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

In addition to stars such as Algol, b Lyrae and W Ursa Major, there are rarer objects that are also classified as eclipsing variable stars. These are ellipsoidal stars that rotate around an axis. Changing the disk area causes 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 the spectrum of our Sun has this type I. The sequence of spectra of stars, resulting from a continuous change in the temperature of their surface layers, is denoted by the following letters: O, B, A, F, G, K, M, from the hottest to...



No lines will be observed (due to the weakness of the satellite's spectrum), but the spectral lines 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 double stars, which are obviously also the periods of their revolution, are very different. The shortest known period is 2.4H (g Ursa Minor), and the longest is tens of years. For...

1. Theoretical resolution of the telescope:

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

2. Telescope magnification:

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

3. Height of the luminaries at the culmination:

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

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

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

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

height of the luminaries at the lower culmination:

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

4. Astronomical refraction:

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

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

sidereal time:

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

mean solar time (local mean time):

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

universal time:

Wherel is the longitude of the point with local mean time T m, expressed in hourly units, T 0 – universal time at this moment;

standard time:

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

maternity time:

or

6. Formulas relating the sidereal (stellar) period of revolution of the planet T with the synodic period of its revolution S:

for the upper planets:

for the lower planets:

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

7. Kepler's third law:

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

8. Law of universal gravitation:

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

9. Kepler's third generalized law:

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

for the Sun and two planets system:

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

for systems Sun and planet, planet and satellite:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

16. Radius of the luminary:

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

20. Stefan-Boltzmann law:

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

21. Law of Wine:

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

22. Hubble's law:

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

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

S. Popov. Photo by I. Yarovaya

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


Spiral galaxy NGC 4414


Cluster of galaxies in the constellation Hairs of Veronica


Planet around the star Fomalhaut

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

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


Star forming region NGC 3603


Planetary nebula NGC 6543


Supernova remnant Cassiopeia A

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

All images obtained by the Hubble Space Telescope and taken from the sites http://heritage.stsci.edu and http://hubble.nasa.gov

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

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

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

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

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

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

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

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

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

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

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