Head of the school tour of the Olympiad with astronomy with solutions. Headquarters for independent robotics from astronomy Basics of spherical and practical astronomy
". On our site you will know the theoretical part, just put it right and tell them, based on 4 main categories, for the sake of making the site easier to use. Dana razdіli hunt: the basics of spherical and practical astronomy, the basics of theoretical astronomy and celestial mechanics, the basics of astrophysics and characteristics of telescopes.
Clicking on the mouse cursor in the right part of our site on any of the children in 4 categories, you will see the theoretical part in the skin of them, as if we were happy to see you to the brightest before the middle-of-the-line view, " In short, the theoretical part is right for consolidating and expanding your knowledge in certain areas, the same point "Vidpovidi" for converting the knowledge and corrections of pardons.
You can, at first glance, the deyaki zavdannya to be old-fashioned, for that the geographic names of the lands, districts and places, which were on the site, changed in an hour, the laws of astronomy did not conceive of any snakes. Tom on our dumka, zbіrnik to take revenge on a lot corian information in theoretical parts, like revenge timeless information, available in the form of tables, graphs, diagrams and text. Our site will give you the opportunity to get started in astronomy from the beginning and to continue to work on additional tasks. Zbirnik will help you lay down the basics of astronomy and maybe you will, one day see a new star or fly to the nearest planet.
BASES OF SPHERICAL TA PRACTICAL ASTRONOMIS
The culmination was illuminated. View of the dawn sky on the winter geographic parallels
In the skin muscle earthly surface height hp poles light geographic latitudeφ ts'go miscy, i.e., hp = φ (1)
and the area of the heavenly equator and the area of the heavenly parallels were nailed to the area of the true horizon below the cut
Azimuth "href =" / text / category / azimut / "rel =" bookmark "> azimuth AB = 0 ° і hour coot tB = 0 ° = 0 year.
Small. 1. Upper culmination of light
When δ> φ, the light (M4) at the upper culm-nation overtakes the heavenly meridian to the beginning of the zenith (above the point of the winter Ν), between the zenit Z and the new pole of the light P, and this time of the day
height hв = (90 ° -δ) + φ (7)
azimuth AB = 180 °, and the hourly cut tB = 0 ° = 0 year.
At the moment of the lower culmination (Fig. 2), it flashed over the celestial meridian from the north pole to the light: do not go over the light (M1) -above the point of the night N, when the light (M2 and M3) did not go At the lower culmination the height of the light
h n = δ- (90 ° -φ) (8)
yo zenіtne vіdstan zн = 180 ° -δ-φ (9)
), At the geographic latitude φ = + 45 ° 58 "and at the northern polar line (φ = + 66 ° 33"). Shilyannya Kapeli δ = + 45 ° 58 ".
Dani: Drop (α Viznichy), δ = + 45 ° 58 ";
winter path, φ = + 23 ° 27 "; mice z φ = + 45 ° 58";
half-polar, φ = + 66 ° 33 ".
Decision: Shilyannya Kapeli δ = + 45 ° 58 "> φ of the winter path, and furthermore it is faster with formulas (6) and (3):
zv = δ-φ = + 45 ° 58 "-23 ° 27" = 22 ° 31 "N, hv = 90 ° -zv = 90 ° -22 ° 31" = + 67 ° 29 "N;
the same, azimuth AB = 180 °, and the hourly cut t in = 0 ° = 0 year.
At the geographic latitude φ = + 45 ° 58 "= δ zenitne view of the Capel zв = δ-φ = 0 °, i.e. at the upper culmination of the won is located in the zenіtі, і її height hв = + 90 °, the clock cut t в = 0 ° = 0 year, and the AB azimuth is not valid.
The values for the polar polar cola are calculated according to the formulas (4) and (3), so that the amount of the grain is δ<φ=+66°33":
zv = φ-δ = + 66 ° 33 "-45 ° 58" = 20 ° 35 "S, hv = 90 ° -zv = + 90 ° -20 ° 35" = + 69 ° 25 "S, and AB = 0 ° і tv = 0 ° = 0 year,
The calculation of the height h n і zenіth vіdstanі zn Drops in the lower culmination are carried out according to the formulas (8) and (3): on the winter path (φ = + 23 ° 27 ")
h n = δ- (90 ° -φ) = + 45 ° 58 "- (90 ° -23 ° 27") = -20 ° 35 "N,
that is, in the lower culmination of the Capella, go beyond the horizon,
zн = 90 ° -hн = 90 ° - (- 20 ° 35 ") = 110 ° 35" N, azimuth An = 180 ° і hour cut tн = 180 ° = 12year,
At geographic latitude φ = + 45 ° 58 "at the star h n = δ- (90 ° -φ) = + 45 ° 58" - (90 ° -45 ° 58 ") = + 1 ° 56" N,
that is, do not enter any more, і її zн = 90 ° -hн = 90 ° -1 ° 56 "= 88 ° 04" N, An = 180 ° і tn = 180 ° = 12year
At the polar pole (φ = + 66 ° 33 ")
h n = δ- (90 ° -φ) = + 45 ° 58 "- (90 ° -66 ° 33") = + 22 ° 31 "N, і zn = 90 ° -hн = 90 ° -22 ° 31" = 67 ° 29 "N,
that is, the star can not go beyond the horizon.
Butt 2. On some geographic parallels of the Capela Zirka (δ = + 45 ° 58 "), do not go beyond the horizon, is it not visible, and in the lower culmination pass in the nadir?
Dani: Drop, δ = + 45 ° 58 ".
Decision. For wash (10)
φ≥ + (90 ° -δ) = + (90 ° -45 ° 58 "), stars φ≥ + 44 ° 02", that is, on geographic parallel, z φ = + 44 ° 02 " її, right up to the pivnіchny pole of the Earth (φ = + 90 °), Capela є do not go in the light.
From the symmetry of the celestial sphere, it is known that in the first half of the Earth Capela does not descend from the geographic latitude from φ = -44 ° 02 "to the first geographic pole (φ = -90 °).
According to the formula (9), the lower culmination of the Drop in nadir, i.e., at zΗ = 180 ° = 180 ° -φ-δ, we go to the northern part of the Earth, to the geographic parallel from the latitude φ = -δ = -45 ° 58 ".
Zavdannya 1. The height of the pole from the light and the way of the heavenly equator to the true horizon on the earthly equator, on the original path (φ = + 23 ° 27 "), on the original polar line (φ = + 66 ° 33") and on the original geographic pole.
Zavdannya 2. Shilyannya zirki Mitsara (ζ Velikoi Vedmeditsi) one + 55 ° 11 ". At any zenith vіdstanі and at the yak height of the buvaє at the upper culmination in Pulkovo (φ = + 59 ° 46") and Dushanbe (φ = + 38 ° 33 " ?
Zavdannya 3. At any of the lowest zenith city and the most high altitude, they fly in Eupatoria (φ = + 45 ° 12 ") and Murmansk (φ = + 68 ° 59") zirki Aliot (ε of the Great Medical Academy) and Antares (and Scorpion of Ukraine), schools 56 ° 14 "і -26 ° 19"? Specify the azimuth and hour cut of the skin zirka at the moment.
Zavdannya 4. At the singing mіsci, the zirka is cautious from the view of + 32 ° 19 "to fly over the point of pivday at a height of 63 ° 42". Know the altitude and altitude of the glare at the same time at an azimuth equal to 180 °.
Zavdannya 5. Virishiti zavdannya for this zyrka for the brains of the smallest zenith view 63 ° 42 "for the first time in zenita.
Zavdannya 6. Yake, the school is guilty of the mother of the star, does it take place at the upper culmination in the zenith, and in the lower culmination - in the nadir, the point of the day and the point of the day of the day? Why is the geographic latitude of the city?
Zavdannya for independent robotics from astronomy.
Topic 1. Study of the dawn sky behind the help of a ruhomo picture:
1. Insert the crumbling card for the day and the second year.
date of caution __________________
hour of caution ___________________
2. Rehack the suzir'ya, as spaced out in the private part of the sky from the horizon to the pole of light.
_______________________________________________________________
5) Visnachiti, where will come and Suzir'ya Mala Vedmeditsya, Bootes, Orion.
Mala Vedmeditsya ___
Bootes ___
______________________________________________
7) Know the equatorial coordinates of Vega's star.
Vega (α Lyri)
Straight convergence a = _________
Shilyannya δ = _________
8) Specify the suzir'ya, in which there is an object with coordinates:
a = 0 years 41 khilina, δ = +410
9. Know the position of the Sontsya on the calendar of the year, because of the triviality of the day. An hour right off the bat and the call of Sontsya
Skid ____________
Zakhid _____________
10. The hour of the transfer of the Sontsya at the moment of the upper culmination.
________________
11. Does any architectural suzir have a Sonce before the hour of the upper culmination?
12. Visually sign your zodiac
Date of birth ___________________________
suzir'ya __________________
Topic 2. Budova Sonyachnoy system.
Who has the similarity and intelligence of the planets of the terrestrial group and the planets of giants. Store at the table view:
2. Viber the planet for the simplified option in the list:
| Mercury | ||||
Store additional information about the planet of the Sleeping System for an option, based on food:
How does the planet come from?
Yaku masu maє qya planet?
Yake the planet's encampment in the Sonyachny system?
How much is a planetary ric and a little sidereal dob?
How many sidereal finishes fit into one planetary ric?
The average triviality of human life on Earth is 70 earthly rock, how can a human being live on the whole planet?
What details can you see on the surface of the planet?
If you are on the planet, who can you see?
Skіlki at the planet satellites and yaks?
3.Pick up to a clear description of the planet you need:
| Mercury | most massive |
|
| The orbit is heavily healed up to the area of the ecliptic |
||
| Nimesha of the planets of gigants |
||
| Rіk approximately dorіvnyu to two earthly rocks |
||
| Nyblijca to Sonc |
||
| Beyond the size, close to the Earth |
||
| Most of the average scholarship |
||
| Wrap around, lie on the boat |
||
| MA system of malovnichykh dumplings |
Topic 3. Characteristics of spikes.
The choice is up to the option.
Indicate the position of the light on the spectrum-light diagram.
| temperature | parallax | proficiency | lightness, | Hour of life t, rock_v | see |
|||
Required formulas:
Average proficiency:
lightness: 
Life Hour:
Come to see: 
Topic 4. Theory of walking and evolving to all.
Name the galaxy in which it is alive:
Classify our galaxy according to the Hubble systems:
Paint schematically the Budova of our galaxy, write the main elements. Visnite the position of Sontsya.
Yak are called companions of our galaxy?
How many an hour is it necessary, how can the light penetrate across our Galaxy in її diameter?
Yaki ob'єkti є storage parts of galaxies?
Classify the objects of our galaxy by photos:
Yaki ob'ykti є warehouse parts to Vsesvita?
Vsesvit
How galaxies become the population of the Mistsevo group?
Who is active in galaxies?
What are the quasars and on some of the places in the Earth there is a stench?
Describe how to be featured in photographs: 
Chi infused the cosmological expansion of the Metagalaxy to the view of the Earth ...
Before Misyats; □
To the center of the Galaxy; □
Before the galaxy M31 in the Andromeda region; □
To the center of the mіtssevskaya collection of galaxies □
Name three possible options for the development of Vsesvita from Fridman's theory.
List of Literature
Main:
Klimishin I.A., "Astronomy-11". - Kiev, 2003 p.
Gomulina N. "Vidkrita Astronomy 2.6" CD - Physicon 2005 p.
The working man is making astronomy / N.O. Gladushina, V.V. Kosenko. - Luhansk: Navchalna Kniga, 2004 .-- 82 p.
Dodatkova:
Vorontsov-Velyaminov B.A.
"Astronomy" Pidruchnik for the 10th grade of the middle school. (View. N'fifteen). - Moscow "Education", 1983.
Perelman Y. I. "Tsikava Astronomy" 7 types. - M, 1954.
Dagayev M. M. "Zbirnik zavdan z astronomy". - Moscow, 1980.
Apply the task of astronomy
§ 1. Zirka Vega is located at 26.4 St. rock from the earth. How many rockets flew before a rocket with a continuous speed of 30 km / s?
The speed of the rocket is 10 0 0 0 times less, less the speed of light, so the cosmonaut will fly to Bizha 10 000 times more.
solution:
§ 2. Your information is two times less than your age. Look at Sontsya's height above the horizon.
solution:
Visota Soncya h vimіryuєl kutom across the area of the horizon and directly onto the lumen. 3 rectangular tricot, de cathetes є L (Dovzhina tіnі) і N (your zrіst), we know
§ 3. How long does it take to start in Simferopol at the time of Kiev?
solution:
charge
To charge the monthly hour in Simferopol, the Kiev hour. The hinges of all years in Europe should be transferred 1 year ahead, then the Kiev hour is transferred to the 44th hour of the month in Simferopol.
§ 4. The asteroid Amur collapses along the ellipse with an eccentricity of 0.43. How many asteroids can be trapped in the Earth, when the period is wrapped around Sontsya to 2.66 rock?
solution:
The asteroid can fly to the Earth, if it will fly into orbitEarth, to be seen at perihelion rmin =< 1 а. o .
With the help of Kepler's third law, the orbit of the asteroid is very much larger:
de a 2 1 a. o .- great growth of the Earth's orbit; T 2 = 1 рік-period
Wrapping the Earth:
Small. P. 1.
View.
Asteroid Cupid DOES NOT fly over the Earth's orbit;
§ 5. The geostationary companion is guilty of turning around on the ground above the surface of the Earth, hanging over one point Earth?
Rozi LZ (X - H LIL
1. Beyond Kepler's third law visually great pivvis orbit companion:
de a 2 = 3 80,000 km - great growth of the orbit of Misyatsya; 7і, = 1 dobu - period of wrapping of the companion near the Earth; T "2 = 27.3 dB - the period of the wrapping around the Earth.
a1 = 41900 km.
View. Geostationary companions are wrapped from the approach to the highway in the area of Ekvatora at a height of 35,500 km.
§ 6. How can the cosmonaut from the surface of Misyats hit the Black Sea with an indelible eye?
Rosv "yazannya:
Visnachaєmo kut, before yakim from Misyatsya you can see the Chorne Sea. From the rectangular tricycle, in yaky legs є go up to Misyats and the diameter of the Black Sea, viznachaєmo kut:
View.
As soon as it is day in Ukraine, then from Misyatsya the Black Sea can be pocketed, for that the cusp diameter is larger than the size of the building.
§ 8. On the surface of a planet of the earth's group, will the cosmonaut's carriage be the least?
solution:
P = mg; g = GM / R 2,
de G - gravitatsіyna became; M - masa of the planet, R - radius of the planet. Naymensha vaga will be on the surface of this planetfall. formulas g = GM / R viznachaєmo, on Mercury # = 3.78 m / s2, on Venus # = 8.6 m / s2, on Mars # = 3.72 m / s2, on Earth # = 9.78 m / s2.
View.
Vaga will be employed on Mars 2.6 times less than on Earth.
§ 12. If, in any case, I will charge you more sleepy energy in your apartment? Look at the vipadk: А. Вікно visit for pivday; B. Log in to the window.
solution:
A. The amount of sleepy energy, if we take away one surface for one hour, can be calculated according to the additional offensive formula:
E = qcosi
de q - sleepy post_yna; i - kut fall of dormouse exchanges.
The wall is roasted perpendicular to the horizon, so the charge for the fall of the sleepy promenade will be less. Otzhe, it’s not marvelous, I’ll charge more energy in your apartment from Sontsya.
B. If you know how to go to the link, then sleepy exchanges do not affect your room.
§ 13. Viznachte radius zirki Vega, yak viprominyu 55 times more energy, nizh Sonce. The temperature of the surface should become 1 1000 K. Yaky viglyad would be too small to see the light on our sky, as if it was on the place of the Sontsya?
solution:
The radius of the star is based on the additional formula (13.11):
de Dr, = 6 9 5 202 km - Radius Soncya;
Surface temperature Sontsya.
View.
Zirka Vega has a radius 2 times more, lower than Sonts, and in our sky there is little more than a blue disk with a 1 ° cut diameter. Yakbi Vega had become a substitute for Sontsya, then the Earth would have lost 55 times more energy, less now, and the temperature on the surface would be 1000 ° C. In such a rank, the mind on our planet would become unsuitable for any forms of life.
I know how fast I am with the brochure "Didactic material in astronomy", written by G.I. Malakhovo and EK Straut and released by the "Enlightenment" in 1984. 75.
For the visualization of the formulas, I will use the LaTeX2gif service, as in the RSS library jsMath it is not possible to draw the formulas.
Zavdannya 1 (Option 1)
Umova: Planetary fog in the middle of Liri has a diameter of 83 "and is located at 660 pc. What are the linear dimensions of nebulae in astronomical units?
Decision: Assigned in mind the parameters of the knitted, and forgive the relationship:
1 pc = 206265 a.s., according to:
Zavdannya 2 (Option 2)
Umova: Parallax zirki Procyon 0.28 ". Get up to the star of Betelgeuse 652 St. rock. Yak from the zirki zirok and how far away are you from us?
Decision: Parallax and getting knitted, forgive the spouses:
The distance between D 2 and D 1 is known, and it is acceptable that Betelgeuse is about 56 times the distance of Procyon.
Zavdannya 3 (Option 3)
Umova: Has a little bit of Venus's cusp diameter changed, how is it possible to travel from the Earth, as a result of the fact that the planet has moved from the smallest to the maximum? Orbit of Venus with a radius of 0.7 a.o.
Decision: We know Venus's cusp diameter for the minimum and maximum dimensions in astronomical units and far and simple settings:
Otrimuєmo vidpovіd: changed by 5.6 times.
Zavdannya 4 (Option 4)
Umova: How big the size of our Galaxy will be (the diameter of which will be 3 x 10 4 pc) is it possible to be in the galaxy M 31 (Andromeda fog) at 6 x 10 5 pc?
Decision: Viraz, scho pov'yu linіynі rozmіri ob'єkta, yogo parallax and kutovі rozmіri already in the solution of the first plant. Quickly and quickly, having slightly modified it, apparently needed a value from the mind:
Zavdannya 5 (Option 5)
Umova: Construction of the eye 2 '. What size can an astronaut be able to grow on the surface of Misyatsya, flowing over it at a height of 75 km?
Decision: The zavdannya is similar to the first and the fourth:
As a matter of fact, the cosmonaut can take out the details of the surface with a size of 45 meters.
Zavdannya 6 (Option 6)
Umova: In some cases, the Sonce is larger than Misyatsya, where the same diameter is the same, and the horizontal parallaxes are usually equal to 8.8 "and 57 '?
Decision: The most common task is to determine the size of the light according to its parallax. The formula for the parallax sound has been repeatedly consumed by the food. As a result of the rapid repetition of the part, the following is recognized: 
We will recognize that Sonce is 400 times bigger than Misyatsya.
zavdannya 1
The focal point of the telescope lens is 900 mm, and the focal point of the vicious eyepiece is 25 mm. Check out the telescope.
Decision:
The improvement of the telescope will start from the date of the F- focus on the asset, f- focal point of the eyepiece. In such a rank, the increase of the telescope in stock 
once.
as follows: 36 times.
zavdannya 2
Translate into the old world of Krasnoyarsk (l = 92 ° 52 ¢ skidnoї dovgoti).
Decision:
Visiting from the weekend of the year miri kuta and degree:
24 h = 360 °, 1 h = 15 °, 1 hv = 15 ¢, 1 h = 15², and 1 ° = 4 hv, і vrakhovuchi, scho 92 ° 52 ¢ = 92.87 °, we can see:
1 h 92.87 ° / 15 ° = 6.19 h = 6 h 11 min. s.d.
as follows: 6 h 11 min s.d.
zavdannya 3
Yake skhilennya zirki, which culminates at a height of 63 ° in Krasnoyarsk, the geographic latitude of which road is 56 ° Mon.
Decision:
Vikoristovuchi spіvіdnoshennya, sho tinkling the whistle at the upper culmination, culminates on the day off zenіtu, h, Vіdmіna svіtila δ and the latitude of the mission φ , h = δ + (90 ° - φ ), Otrimaєmo:
δ = h + φ - 90 ° = 63 ° + 56 ° - 90 ° = 29 °.
as follows: 29 °.
zavdannya 4
If in Грінвічі 10 years 17 hv 14 s, in the deyakom point іsceviy hour dorіvnyuє 12 years 43 hv 21 s. What do you want for a point?
Decision:
The midnight hour is the middle sleepy hour, and the Greenwich hour is the all-round hour. Having quickened the sleepers, the middle sleepy hour is ringing T m, all-round hour T 0 i dovgotu l, I turn in the years of the world: T m = T 0 +l, Otrimaєmo:
l = T m - T 0 = 12 h 43 x 21 s. - 10 hours 17 hours 14 seconds = 2 years 26 hours 07 seconds.
as follows: 2year 26 hv 07 s.
zavdannya 5
In every hour, the moments of maximum visibility of Venus from the Earth are repeated, when the period of time is 224.70 dB?
Decision:
Venus is the lower (inner) planet. The configuration of the planet, when you see the maximum visibility of the inner planet from the Earth, is called the upper ones. And the hour between the last one-day configurations of the planet is called the synodic period S... It is necessary for that to know the synodical period of Venus's wrapping. Having shrunk to the synodic ruch for the lower (inner) planets, de T- sidereal, for the dawn period of the planet's wrapping, TÅ - sidereal period of the Earth's wrapping (zoryaniy rik), equal 365.26 average sleepy dibs, we know:
= 583.91 add.
as follows: 583.91 add.
zavdannya 6
The early period of Jupiter's wrapping around Sontsya becomes close to 12 years. What is the middle view of Jupiter from Sontsya?
Decision:
The middle view of the planet from the Sontsya road is great during the economic orbit a... According to Kepler's third law, the planet collapses to the Earth, T 2 = 1 рік, and the orbital size is great a 2 = 1 a.r. Having submitted the numerical values, the residual is known:
as follows: close to 5 a.o.
zavdannya 7
Visually start from the Earth to Mars at the moment of its prototype, if the horizontal parallax is 18².
Decision:
3 formulas for the designation of geocentric views 
, de ρ
- horizontal parallax of the beam, RÅ = 6378 km is the middle radius of the Earth, but it is significant to reach Mars at the moment of prototype:
»73 × 10 6 km. Increased values by the value of astronomical units, can be measured as 73 × 10 6 km / 149.6 × 10 6 km "0.5 AO.
as follows: 73 × 10 6 km "0.5 AO
zavdannya 8
Horizontal parallax Sontsya dorivnyuє 8.8². Is Jupiter located at each end of the Earth (in the a.o.), if the horizontal parallax is 1.5²?
Decision:
formulas it can be seen that the geocentric appearance of one wing D 1 wrapped proportionally to horizontal parallax ρ
1, tobto. An analogous proportion can be recorded for the second light at any type of building D 2 and horizontal parallax ρ
2 :. Have grown one sp_vv_dnoshennya on іnshe, otrimaєmo. This rank, I know from mind the tasks, is that the horizontal parallax Sontsya dorivnyuє 8.8², with which it is located at 1 AO. from the Earth, you can easily know how to see Jupiter behind the horizontal parallax of the planet at the moment:
= 5.9 a.r.
as follows: 5.9 a.d.
zavdannya 9
Start the line radius of Mars, as soon as the hour of the great prototype becomes 12.5², and the horizontal parallax is 23.4².
Decision:
Linear radius illuminated R It is possible to see the value from the speed, r - kutoviy radius of light, r 0 - the horizontal parallax, R Å - radius of the Earth, equal 6378 km. Having submitted the values for the mind and tasks, we can recognize: 
= 3407 km.
as follows: 3407 km.
zavdannya 10
At the time of the development of Pluto's mass is less than the mass of the Earth, as soon as it seems, it is 19.64 × 10 3 km to go to the th companion Charon, and the period of the companion's turn around is 6.4 dobu. The distance from the Earth to the Earth becomes 3.84 × 10 5 km, and the period of wrapping is 27.3 dB.
Decision:
For the purpose of establishing the mass of heavenly bodies, it is necessary to speed up the third most important Kepler's law: 
... So yak masi planets M 1 і М 2 Significantly less, nіzh masi іхніх supporters m 1 i m 2, then masses of supporters can be zehtuvati. One can rewrite Kepler's law in an offensive view: 
, de a 1 - great pivvis of the orbit companion of the first planet with Masoy M 1, T 1 - period of wrapping around the companion of the first planet, a 2 - great pivvis of the orbit of another planet's companion with Masoy M 2, T 2 - the period of wrapping up the companion of another planet.
Having submitted a summary of the meanings of the tasks, we can recognize:
= 0,0024.
as follows: 0.0024 times.
zavdannya 11
The space probe "Huygens" September 14, 2005 landed on Saturn's companion Titan. From what line can rivers and seas be formed on Titan?
vkazivka: The distance from Sontsya to Saturn becomes 9.54 a.o. I think the health of the Earth and Titan is the same, and the average temperature on the surface of the Earth is 16 ° C.
Decision:
Energy, possessed by the Earth and by Titan, is wrapped in proportional squares of the places in Sontsya r... A part of the energy is brought up, a part of it is glimpsed and seen on the surface of the heating. Vazhayuchi, that the building of the cich of heavenly bodies is the same, then the amount of energy used to heat the cich til will be the same. The temperature of the surface of Titanium is estimated in the vicinity of absolutely black heat, so that if there is a bit of energy, then you can use a little bit of energy to heat it up. According to the Stefan-Boltzmann law of energy, which is a single surface at one hour, the proportions of the fourth step of the absolute temperature of the floor. In such a rank, for energy, how to worship the Earth can be written 
, de r h - go from Sontsya to Earth, T w-average temperature on the surface of the Earth, and Titan - 
, de r c - go from Sontsya to Saturn with his companion Titan, T T is the average temperature on the surface of Titan. Taking the vіdnoshennya, otrimaєmo: 
, stars 
94 ° K = (94 ° K - 273 ° K) = -179 ° C. At such low sea temperatures on Titan, it is possible to accumulate with a gas, for example, methane or ethane.
as follows: For gas, for example, methane or ethane, as the temperature on Titanium is -179 ° C.
zavdannya 12
Yaku can see the magnitude of his son, why should he be spared from the closest glimpse? Get close to getting close to 270,000 a.o.
Decision:
Skoristyaєmosya formula Pogson: 
, de I 1 i I 2 - yaskravost_ dzherel, m 1 i m 2 - їх zoryanі values are obvious. So, as it is wrapped in proportion to the square of appearance to dzherel, then you can write 
... Logarithmіng tsei vislіv, otrimaєmo 
... Seemingly, the magnitude of the Sontsya from the Earth is visible (from the r 1 = 1 a.a.) m 1 = -26.8. It is necessary to know the value of Sontsya visible to Zoryan m 2 from vіdstanі r 2 = 270,000 a.s. Having submitted the values at the viraz, we can see:
, Zvidsi ≈ 0.4 m.
as follows: 0.4 m.
zavdannya 13
The richesky parallax of Sirius (a Great Dog) becomes 0.377². Why is it possible to get to the city of light in parsecs and light rock?
Decision:
From the start to the stars in parsecs, the start of the meeting starts, de π - the parallax of the star. Tom = 2.65 pc. So 1 pc = 3.26 sv. m, then the rise to Sirius in the light rocks becomes 2.65 pc · 3.26 sv. m = 8.64 sv. m
as follows: 2.63 pc or 8.64 sv m
zavdannya 14
Apparently, the magnitude of the star of the Sirius road is -1.46 m, and it becomes 2.65 pc. Look for the absolute zoryan value of the zyrka price.
Decision:
Absolute zoryana value M tied with a visible zoryan magnitude m i go to the show r in parsecs to such persons: 
... The qiu formula can be derived from the Pogson formula 
, Knowing, that the absolute zoryana value is the zoryana value, the zorya value is small, and the value has passed to the standard vidstani r 0 = 10 pc. For the whole, it is possible to rewrite the formula of Pogson in viglyadі 
, de I- the brightness of the light on the Earth from the beginning r, a I 0 - quality from the office r 0 = 10 pc. So, as the visible brightness of the glimpse is changing, it is wrapped in proportion to the square of the distance to it, that is, then 
... Logarithmiruya, we will recognize: abo abo .
Having submitted the values of the minds of the tasks in the center, it is recognized:
as follows: M= 1.42 m.
zavdannya 15
In the sky of the Zirka Arcturus (a Bootes) is more behind the Sonce, as the light of Arcturus is 100 times more than the Sleepyhead, and the temperature is 4500 ° K?
Decision:
light of the star L- I will turn the energy into a light at one hour, you can see it, de S- area of the surface of the star, ε - energy, as viprominuє zirkoy from one area of the surface, which is based on the Stefan-Boltzmann law, de σ is the step of Stefan-Boltzmann, T- absolute temperature of the surface of the glass. In this rank, you can write: R- radius star. For Sonts, you can write an analogous viraz: 
, de L s - the luminosity of the Sontsya, R h - radius Soncya, T h - temperature of the surface of the Sontsya. Having raised one hanging on the inshe, we can make it:
For it is possible to write down the sp_v_dnoshennya with the following rank: 
... Accepted for Sontsya R s = 1 i L s = 1, otrimaєmo 
... After submitting the values of the tasks, we know the radius of the star in the radii of Sontsya (for example, the development of the star is more or less Sontsya):
≈ 18 times
as follows: 18 times
zavdannya 16
In the spinal galaxies in the Trikutnik suspicion, the cepheideas are slowed down over a period of 13 days, while the visible value is 19.6 m. Visit the galaxy in light rock.
vkazivka: The absolute value of the cepheid with the specified period of time M= - 4.6 m.
Decision:
wіth spіvvіdnoshennya , I call the absolute zoryan value M with the apparent dawn magnitude m i go to the show r, Venturing in parsecs, otrimaєmo: = 
... Zvidsi r ≈ 690,000 pc = 690,000 pc · 3.26 sv. m ≈2 250,000 sv. l.
as follows: approx. 2,250,000 St. l.
zavdannya 17
Quasar maє chervoniy zsuv z= 0.1. Visit the quasar.
Decision:
Written Hubble's law :, de v- exchanging the visibility of the galaxy (quasar), r- get to her, H- Hubble post. From the side, according to the Doppler effect, exchanging the speed of a rugged object 
, H - light intensity, λ 0 - additional amount of line in the spectrum for an unstable jerel, λ - additional amount of line in a spectrum for a loose jerel, - red wickedness. And so, like the doppler warrant in the spectra of galaxies, like the Doppler warrant, which is tied to all of them, Hubble's law is often written down in the spectra of galaxies :. Vislovi went to the quasar r and having submitted the values for the mind and tasks, we can recognize:
≈ 430 Mpc = 430 Mpc 3.26 sv. m ≈ 1.4 billion light l.
as follows: 1.4 billion St. l