The Paradoxical Universe

8/21/2019 The Paradoxical Universe

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The

ParadoxicalUniverse250 Problems in Astronomy

V. V. Ivanov, A. V. Krivov, P. A. Denissenkov

Edited By- Udbhav Singh
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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Saint-Petersburg State University

Explanations, councils and the manual

This training management is formally addressed to the students of low-order it is course

the astronomical departments of universities, that study its first astronomical course - the

course of general astronomy. But the authors hope that on these electronic pages

interesting for themselves they will find everything, coma road astronomy - from the

qualified amateurs to the astronomers - professionals. As the basis of benefit is assumed

the many-year experience of teaching by the authors of the course of general astronomy for

the students - the astronomers of the first course of St. Petersburg university. Was

included also certain additional, only more complex material.

Tasks are anticipated by the list of values of the thoroughly selected most important

astronomical and physical quantities. This list, named by usthe "universe in the numbers",

is planned as the "numerical portrait" of the universe at all its structural levels - from the

atomic nucleus to the metagalaxy. Student, who attentively studied the numbers, their

analyzed, comparable with each other, etc., will obtain excellent idea about how the peace

surrounding us is arranged. We recommend to always have a copy of the "universe in the

numbers" with itself - in the briefcase, on the working table, in the computer. But are still

better the data by the "universe in the numbers" to learn by heart. Having a minimum of

constants near at hand, and those more holding them in the memory, it is possible with theease to make different estimations, and estimation - important tool of scientific research. In

many instances, when it does not be required precise or special information, the "universe

in the numbers" will completely replace thick reference book, for example, the known book

of Allen "astrophysical values"[ 1 ] or the encyclopedia "physics of space"[ 6 ] , although, of

course, and without them sometimes not to manage. Subsequently we assume the numbers,

which entered the "universe in the numbers", known and we do not indicate them in the

formulations of tasks.

The tasks (sometimes, faster, questions for the reflections) and their detailed solutions

compose major portion of this teaching aid. They are frequently accompanied by extensive

commentaries and additions, which are the important component element of benefit andmake its not only with the assignment book, but also with the book for reading - by

something like the reader. However, the aspect of the tasks - standard (frequently

somewhat reformulated), undertaken from the known benefits (for example , [ 3 ]),

majorities belongs to the authors.

Special support is made to the tasks of estimated nature, whose solution develops in

students the skill to make simple and efficient estimators and thus rapidly and without the
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cumbersome calculations to obtain correct idea about the diverse astronomical objects and

the phenomena, which then, if this is necessary, they can be investigated more accurately

and fully. We tried to follow known motto the "purpose of calculations - not the number,

but understanding". Even microcalculator is not necessary during the solution of almost all

problems. The authors know according to the experience of teaching that to instruction in

accurate calculations with the high accuracy both on the average and in the higher school isgiven considerably more attention, than to the ordinal estimations or to estimate

calculations with one significant place. Many student- freshmen, using the calculator (and

all the more computer), diligently extract from the indicator (or the display screen) the

long tail of the significant places and propose thisas the answer. Let us give a characteristic

example. On one of first practical training to students it is proposed to estimate the mass of

air in the audience. The question excitedly is posed from the places: and are such the

dimensions of audience? Answer: you will estimate "to the view". And even after this

frequently is given an answer of the type: 438.75kg instead of of correct, matched with the

accuracy of initial data, answer: near polutonny.

Solution of many problems actually is reduced to combine several numbers of the"universe in the numbers" in one - two simple formulas, brought out at the lectures, and to

obtain the required answer. The task can serve as typical illustration: to estimate the mass

of the earth's atmosphere. The answer in an obvious manner is obtained, for example, from

radius of the earth, the height of homogeneous atmosphere and air density on the earth's

surface (all three numbers in the "universe in the numbers" are). It is possible, it goes

without saying, to solve problem and differently (as?).

Let us give three useful advice. The first - to produce calculations with the reasonable

accuracy - we already discussed. Second council - in the solution of one problem

consecutively using one and the same system of units. It is possible to consider cgs system de

facto standard in astronomy; use, for example, it. In this case it is possible not to follow thedimensionality of the intermediate results: it is clear, in what units will come out the

answer (if mass - that in the grams). The third council - is more ideological, than technical:

do not forget to evaluate everythingthat you make and which in you is obtained, from the

positions of the common sense. And intermediate results, and final answer compulsorily

must be comprehended and estimated, they are plausible. Commonplace council? But

students continue to pass the solved tasks with the following answers to instructors: a

radius of the Moon = 2.54parsecs; the mass of the Earth = 5 .10-5grams; the number of

stars in our galaxy =732 (all examples real). The authors of assignment book, checking

tests, see such answers each yr! Truly, the collection of such results could compose the

alternative "universe in the numbers" - the "universe in the number1s from the point of

view of student, which does not follow to commonplace councils"...

We relate to the proposed tasks as to the means, which makes it possible to develop the

habits of logical thinking, creative relation to the problem, the fantasy. For this purpose we

frequently propose tasks with a question "why?", and also namerenno by the "illegible"

("neshkol'nymi") formulations, which contrast with the standard "it is given - to find". As

an example let us give the following task: "to estimate the time, for which a change in the

outlines of constellations will become noticeable by rule of thumb". It is possible to discuss


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as follows. It is clear that a change in the outlines of constellations is caused by the

presence in the stars of proper motions. Star drift? ?(into ugl.sek./god) it is connected with

its tangential velocity?Vt (in km/s) and with distance to star R in the parsecs by known

formula?: Vt= 4.74 R ?. It is obvious that the stars, which determine the outlines of

constellations, be among bright, and it means, on the average, the closest to us. Therefore it

is possible to consider that the distances to the stars comprise order of tens of parsecs.What?Vt, then, after recalling the typical three-dimensional speeds of stars in the galaxy, it

is possible to accept?Vt ~of 10km/s. Substituting these values into the formula, we do find

?~0.2? ugl.sek./god. Further, completely it is possible to consider that the constellation by

noticeable means does change when the determining its form stars do displace on?1o=

3600". We immediately conclude that the desired time interval is about 20000, and it is

better to say, tens of thousands of years this is - correct result. See another, even simpler

approach in the task.

But even when the formulation of task is maximally clear and its solution, it would seem,

does not require special creation, in student the possibility to appear initiative remains.Thus, in task about mass mentioned above of the Earth's atmosphere simple calculation

does give the answer: ~5. 1021g. but not are more interesting whether, without being

limited to this (correct) answer, to compare the obtained number with some others?

Natural to take the mass of Earth itself for the comparison: ~6. 1027g. We can say as the

answer: the "mass of the earth's atmosphere - one millionth of the mass of the Earth". What

answer is better?

Some tasks have the increased difficulty, and their solution will be hardly accessible to

student- freshmen. They are noted by asterisk (*), and separately difficult - by two

asterisks (**). All such tasks are original and nonstandard. Their start, as we hope, willmake this benefit interesting to the wider circle of the readers, and the students of low-

order it is course, after becoming acquainted with the solutions, they will enlarge their

horizon. We already said that partly this benefit is planned not only as assignment book,

but simultaneously and as its kind reader.


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Contents

Problems

1.

First acquaintance2. Kinematics of the sky

3. Tools

4.

Kinematics of the solar system

5.

The universal gravitation

6. Earth, the Moon the planet

7.

The stellar magnitude

8. Emission

9. Spectra of the sun and stars

10.

Sun

11.

Fundamental characteristics of the stars12.Physics of the stars

13.Dual and variable stars

14.

The interstellar medium

15.Galaxy

16.Beyond the limits of the galaxy

17.

New tasks

Solutions

1.

First acquaintance2.

Kinematics of the sky

3.

Tools

4. Kinematics of the solar system

5. The universal gravitation

6.

Earth, the Moon the planet

7.

Solutions to chapter 7 not available in English

8. Emission

9.

Spectra of the sun and stars

10.Sun

11.

Fundamental characteristics of the stars12.

Physics of the stars

13.

Dual and variable stars

14.The interstellar medium

15.Galaxy

16.

Beyond the limits of the galaxy


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1. First acquaintance

1.1of the substance of the Earth made a wire length from the Earth to

a) of the sun; b) Cen; c) of the Andromeda nebula. To estimate the diameters of these

wires ( V.V.Sobolev).

1.2You will estimate how many stars in our galaxy and how many galaxies in the entire

universe are fallen to one person.

1.3As you do think what more - stars in the galaxy or gnats on the Earth?

1.4universe are entirely small: stars in the entire universe as much of, atoms as in the drop

of water! Prover'te.

1.5Which is more: the Coulomb force of the attraction of electron to the proton in

hydrogen atom or the Newtonian attracting force of two cosmonauts, who are exchanged

handshake in open space?

1.6Which the depth of that potential pit, in which we do live?

1.7Which distance modulus Saint Petersburg - Moscow (in the stellar magnitude)?

1.8is evident whether the sun by naked eye from the Pleiades?

1.9That is greater - the angular dimension of the disk of the Moon or Andromeda nebula?

1.10Why it is at night dark?

2. Kinematics of the sky

2.1After awaking on 21 March, you unexpectedly revealed that they were transferred by some

miracle in the uninhabited atoll. Shines the sun, on you - only bathing suit. You will be able in

the hour - other to say, in what hemisphere you are located - northern or southern?
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2.2After awaking from the lethargic sleep, you revealed that you are located in the uninhabited

atoll, which lies accurately on the equator. Shines the sun, on you - only bathing suit. Will be

able you in the hour - to other to say that now you have house in Petersburg - winter or summer?

2.3 After awaking, you unexpectedly revealed yourselves among the primitive people. How you

would begin to convince them, that the Earth - this is sphere and that it does revolve around itsaxis?

2.4In what direction - from left to right or from right to left - is moved because of the precessionthe spring equinox point?

2.5 are such minimum and maximum midday altitude of sun in your city?

2.6 In which hour will today visit the sun?

2.7 On 22 March the sun visited to later than the day before. Where you - in Armavire or

in Arzamase?

Indication: sin = sin 231/2o= 0.40.

2.8 What fraction of the total number of stars on this latitude never does go? Stars to considerevenly distributed in the celestial sphere.

2.9 Is visible the Moon into the June plenilune at the North Pole?

2.10 Why in summer the Moon in the plenilune is always dim and yellowish and is visible lowabove the horizon (in our latitudes), and in winter, on the contrary, it is bright and does rise

highly?

2.11 Which the greatest and smallest height of the upper culmination of the Moon in your city?

2.12 is it possible in Russia to somewhere see the Moon in the zenith?

2.13 Moon is visible in last fourth. To what on the average are equal the radial velocities of stars,find on the sky not far from it?

On 2.14 7 February the Moon was in last fourth. To what did be equal its right ascension?

2.15constellation of Orion has equatorial coordinates near , ~0o, and the constellation

of southern crown - , ~-40o. Are such the visibility conditions of these constellations in

Petersburg now? What they will be in 13 000 years?

On 2.16 22 June on the solar disk from the right side is visible damage. What these are -

beginning or the end of the eclipse?
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2.17 today occurred the solar eclipse. It means, the angular distance of the sun from the node of

moon's orbit is less than 17o. You will explain, why.

Indication: the angle of the slope of lunar orbit to the plane of ecliptic .

2.18 v which to hour (Moscow time) today will begin true noon in that place, where you arelocated?

2.19 sun is located in the upper culmination in universal time. To find length (by equation oftime to disregard).

2.20 Earth - spheroid with compression by 1/300. A) To determine, on how much in the twenty-

four hours will leave forward pendulum hours at the terrestrial pole in comparison with the

analogous hours at the equator. b) On how much should be lengthened pendulum it is hour at the

pole, so that the hours you dispatch so?

Centrifugal force not to consider.

2.21 It is known that the duration of twenty-four hours increases by seconds in 1000years. Therefore in 1000 years of indication it is hour, synchronized in the direction of therotation of the Earth taking into account its age-long retarding, they will differ from the

indications of atomic hour, synchronized with a constant initial velocity of the rotation of the

Earth. To it is how much? (EXPLOSIVES. Vityazev)

3. Tools

3.1 to estimate the safe speed of the motion of the controlled from the Earth Mars rover,

equipped with the television camera, which "sees" only on 10 m.

3.2 Where on the Earth it is necessary to place telescope so that its German mounting would be

simultaneous and azimuthal?

3.3 will be sufficient one disk in order to write down the entire the information about the

celestial sphere, which humanity was located up to the moment of the invention of telescope?(Sun, the Moon, planet and comet - not on account.)

3.4 Which smallest linear dimension of the formations on the Moon, which can be distinguished

by the naked eye?

3.5 satellite does fly above the earth's surface at the height of 200 km which minimum size ofthe details on the Earth, which can be from it photographed?
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Indication: the size of the disk of the vibration of star because of the influence of the earth's

atmosphere comprises .

3.6beyond the orbit of Neptune, at heliocentric distances from 30 to 50 AU, is located thatopened in 1992. Kuiper's belt, which consists of the small bodies of the type of comets and

asteroids. At the beginning of 1996 in the belt are discovered 32 objects; in 1996 it is opened 7more. It is assumed that there there are tens of thousands of bodies of larger than 100 km they are

such the approximately minimal sizes of the bodies of Kuiper's belts, which can be revealed withthe aid of the khabblovskogo space telescope?

3.7 To estimate the photon flow (number of fotonov/(sm s)), that is necessary from: A) thesuns; b) Cen; c) of star .

Indication: flow from the source of zero stellar magnitude composes approximatelyfotonov/(sm s).

3.8 how many photons do fall in 1 second on the mirror of the largest in the world telescope ofcake (D = of 10m) from Vegi and from the star ?

4. Kinematics of the solar system

4.1 as in the task , you again among the primitive people. Continuing to sow reasonable, good,

eternal, you explained by them, as the solar system was arranged, but they revealed to horrortheir that distance from the sun and the periods of revolution of Venus and Jupiter you forgot.

What observations you should be produced in order to determine their values?

4.2 na how much approximately degrees was displaced Pluto along its orbit from the time of its

discovery?

4.3period of revolution of Neptune around the sun is 165 years. Will be in the sun visible disk,

if we look at it from Neptune by the naked eye, or it will be point target?

4.4 to depict in the projection on the plane of ecliptic the orbit of celestial body, which has the

elements: AU, e = 0 . For the comparison on the same drawing and onthe same scale to depict the orbit of the Earth.

4.5How angular distance of the Earth from the sun in the elongation with the observation fromJupiter?

4.6 At what greatest angular distance from the sun there is visible Jupiter with Cen?
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4.7 sidereal period of the axial rotation of the sun (at the equator) of --- of 25 days. To what is

equal the synodic period of its rotation with the observation with A) mercury; b) the Earth; c) of

Pluto?

4.8 You will estimate the characteristic transit time of Venus on the solar disk. How it is moved

along the disk with the observation from middle latitudes of the northern hemisphere of --- fromright to left or from left to right?

4.9 diameter of Pluto composes 2300 km, distances from the sun (to the end of the currentmillenium) of --- 30 AU. You will estimate zone width on the earth's surface, in which it is

possible to observe coating star with Pluto, and its duration.

4.10 astronomers of future produce the radar of the asteroid, which moves along the circular

orbit by radius 5/3 AU. By how many times more powerful pulse they must send in the

connection, than in the opposition in order to register the signal of identical force reflected? Tohow many stellar magnitude this asteroid brighter in the opposition than in the connection?

5. The universal gravitation

5.1 which would become with the solar system, if the mass of the sun did instantly decreasedoubly?

5.2 as would change the orbit of the Earth, if the mass of the sun suddenly was doubled?

5.3 why in all without the exception of the bodies of the solar system, from the sun to the

asteroids and the satellites of planets inclusively, the minimum times of their circling do have

one and the same order of magnitude?

5.4 speed of the motion of comet in the perihelion three times as great than in the aphelion. To

what is equal eccentricity of its orbit?

5.5 as does depend the linear speed of the motion of planet along the circular orbit on a radius of

orbit R? No matter how unexpectedly, a question refers straight to the famous problem of the

"concealed mass" in the galaxies

5.6 to determine the semimajor axis, the revolution period, eccentricity and perihelion distance

of comet, which at a distance of 1 AU from the sun has a speed, directed perpendicularly to

radius-vector, also, along the value ten times less than the speed of the Earth.
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5.7 satellite "Molniya"; in the perigee it is separated from the center of the earth by 7000 km, in

the apogee - on 46000 km you will calculate circling time of satellite around the Earth and

eccentricity of its orbit.

5.8 you will estimate the time of the overflight of automatic spacecraft from the Earth to Mars

on the semi-ellipse, in the perihelion which is concerned the orbit of the Earth, and in theaphelion - the orbit of Mars (Hohmann ellipse). Semimajor axis of the orbit of Mars to accept

equal to 1.5 AU.

5.9 Geliostatsionarnoy is called the circular orbit, which lies at the equatorial plane of the sun,

with the revolution period, equal to the sidereal period of the axial rotation of the sun. To find its

semimajor axis.

5.10 which the minimum speed of a drop in the meteorite on the Moon?

5.11 what must be the rate of accretion to Jupiter (in the masses of Jupiter per year) so that its

bolometric luminosity would grow doubly?

5.12 when people intended to land on the Moon, actively was discussed a question, it was not

covered with the thick layer of dust, in which it is possible to sink. Then in students this question

arose: how long must on the Earth work vacuum cleaner, so that the isolated energy would besufficient for its delivery to the Moon?

5.13 which limit of size of the asteroid, from which still it is possible to jump into space?

5.14 it is improbable, but the fact: from the friction against air the satellite, which flies in the

rarefied layers of the atmosphere, is not impeded, but it is accelerated! To understand, as so it

can be, after proving that energy, which the satellite expends on overcoming of air resistance,exactly is equal to an increase (positive) in its kinetic energy.

5.15 how must be distance to the Moon, so that in its orbit in the solar system would be points of

inflection? To consider that the Moon dvizhetsya strictly in the plane of ecliptic, and its orbit

relative to the Earth - circular.

5.16 spacecraft investigates neutron star. At what approximately distance from it tidal forces yetwill not create the danger in the health of cosmonaut?

5.17 several years ago in the solar system is opened the new class of the objects of --- dual

asteroids. You will roughly estimate the greatest possible distance from the 100-kilometerasteroid to its satellite - the asteroid of smaller size.

5.18 surface, on which the attracting forces to the Earth and to the sun are equal, is called the

sphere of the attraction of the Earth relative to the sun. Is the sphere of attraction actually sphere?

With what mass of the Earth the sphere of attraction would be plane?
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5.19 raised stone to height Rabove the surface of the planet of radius Rand mass Mand let go

there with the zero speed. From dimensional considerations to show that the time of its free fall

on the surface of planet exists

where --- dimensionless coefficient (order of one). Without attempting to find accurately, to

obtain the following estimation:

5.20 Task- parody to the fantastic subjects about the starry wars.

Reconnaissance reported, that the nuclear-powered submarine of enemy must float at the north

pole for 10 minutes exactly at noon on our time. DAN order it to destroy. For this to the pole inthe morning arrived our submarine, from onboard of which was vertically upward neglected the

combat missile. In the very short time (count - instantly) rocket collected the speed, equal to thefirst space, after which its engines were opened. Our submarine here was immersed and swam

away. After a certain time - exactly at noon as prevented the reconnaissance, on the surface

appeared enemy submarine. But it did not pass even five minutes after its emersion, as it was

destroyed by rocket fallen to it from space.

How much did show the hours of the commander of our valiant submarine, when it did return

command "launching!"?

6. Earth, the Moon the planet

6.1 to what is equal the temperature of the surface of the Moon at sunflower point?

6.2 with the building of lunar observatory muddler- astronaut at hot noon spilled to the lain on

the soil thick iron sheet the bucket of remarkable white- white whiting (albedo A=0.99). It was

revealed after a certain time that to work, costing on this sheet, is completely impossible. Howyou do think, why?

6.3 let us assume that around the star with the temperature and the average densitydvizhetsya the planet. Let it not have an atmosphere, it is inverted to the star by one side and has

the same albedo A, as on the Moon. To what is equal the period of revolution of this planet along

the orbit, if temperature on its surface is the same as on the Moon? How does depend
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temperature on the planetary disc on the zenith distance of star? It is considered that also the star,

and planet emit as blackbody.

6.4 is there sufficient whether the kinetic kinetic energy of the Earth along the orbit in order to

ionize the mass of hydrogen, equal to the mass of the Earth?

6.5 what fraction of the mass of the Earth is fallen to its atmosphere?

6.6 with a good approximation (by what?) it is possible to consider that the sun illuminates the

Earth by parallel light beams. As then to explain the picture, which you for sure repeatedly

observed: from under the cloud, which closes the sun, do go the clearly divergent rays?

6.7the earth's atmosphere has optical thickness along the normal (at the wavelength

). Visualize that the mass of the atmosphere grew 5. With what will see the cloudlesssky of peterburzhets at noon and in midnight? But that if the mass of the atmosphere does

decrease 5?

6.8 with a smooth increase in the mass of the atmosphere from zero skies would be in the

daytime first black, then everything would become brighter, then again by less bright and finally

would begin the dark. At what optical thickness is reached the maximum of the brightness ofsky?

6.9 sky from the morning to the evening is tightened by the overcast, but the disciplined

astronomer honestly works --- on its solar telescope it it attempts to be occupied by the

determination of the chemical composition of the sun. How you do think, can this something

leave?

6.10 sun arises from behind the sea horizon. One person admires rise from deck of ship, andanother of --- from the mountain peak with a height of 4 km on the located in ocean volcanicisland (let us say, from the observatory of Mauna Kea in Hawaii). In which of the observers the

solar disk will be more brightly, also, into how much approximately once?

6.11 everyone knows that on the rise and with the sunset is red. To show that this in a sense

illusion, in fact it infrared. More precisely saying, to show that the maximum in the energy

distribution in the spectrum of the direct radiation of the sun, recorded at the moments of rise andsunset, lies at the IR range. To consider that 1) in the exoatmospheric spectrum of the sun the

energy distribution blackbody with the maximum at the wavelength and 2)

extinction of light in the atmosphere is caused by molecular scattering.

Note. The calculator will be required for the solution of this problem. The solution is sufficiently

long.

7. The stellar magnitude
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7.1 to largest ground-based telescopes (in particular, to two largest in the world 10- metertelescopes of cake) are accessible stars . By how many times they are weaker than stars,

hardly distinguished by the naked eye?

7.2 the variable ocet (peace of whale) in the maximum has visual luster , in the minimum

of --- . In how much approximately once do change its luminosity in the visible region?

7.3 difference in the stellar magnitude of two stars of identical luminosity is equal . By how

many times one of them is further another?

7.4 where it is brighter than --- in the daytime on Pluto or on the lunar night on the Earth?

7.5 of the substance of the Moon into the plenilune made millions of identical spherical

satellites, after leaving them approximately in the same place, but so that they would not

overshade each other. Which the stellar magnitude of the received cluster? Stellar magnitude offull moon is known to you.

7.6binary star has components and . To find the summary stellar magnitude of dual.

7.7 Zatmenno - binary system has identical components. On how many stellar magnitude do

change the luster of system at the moment of the total eclipse of one component of another?

7.8 v star cluster Nof the stars of stellar magnitude meach. To find the summary stellar

magnitude of accumulation.

7.9before the sky of approximately 6000 stars is brighter than the 6th stellar magnitude.Considering, that in all stars identical luminosity and that they are distributed in the spaceevenly, to estimate, it is how much before the sky of stars of brighter than mof -1 stellar

magnitude.

7.10 * on what approximately distance it is necessary to place 100 - watt lamp so that it would

look like the star of 0-1 stellar magnitude?

7.11 * is it possible from the Moon with the naked eye to see cities on the Earth?

7.12 * one of four Galilean satellites of Jupiter --- Europe --- has a radius of 1600 km and it is

completely covered with ice. You will estimate the stellar magnitude of Europe at that moment,when Jupiter nearest of all to the Earth.

7.13 to show that with a small change in the distance to the luminous object ( ) itsvisible stellar magnitude changes on
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7.14 the stellar magnitude of planet in the opposition to 3.43mis less than in the connection.

What this after planet?

7.15 how long did pass from the connection to the opposition of planet, if its stellar magnitude

in this time did decrease by 0.85m?

7.16 you will estimate the maximum distance (in PK), from which the sun by the also evidently

naked eye.

7.17 as you do think, there will be the sun in the number of one - two ten brightest stars for the

observer, who lives in environments Cen?

7.18 are accessible to the largest telescopes of the stars, similar to the sun, in the Andromeda

nebula?

7.19 to estimate the absolute bolometric stellar magnitude of the working vacuum cleaner.

8. Emission

8.1 * the very good estimation of blackbody intensity in the maximum of Planckian curveis obtained, if we use ourselves the approximation of wine. You will explain, why this so, and

give estimation of error. How far beyond maximum, i.e., in the region , still it is

possible to use the approximation of wine? How in the maximum it does grow with T?

8.2 * you will examine the family of Planckian curves in the scale of the wavelengths, whichcorrespond to the different values of the temperature (see any course of general physics). They

do not intersect, those, which correspond to higher temperature, lying above (prove!), and

maximum in them is located to the left (Wein's displacement law). In this case maximum in these

Planckian curves the "sharper", the higher the temperature. Why this thus? But as does changewith an increase in the temperature the form of Planckian curves in the frequency scale?

8.3 ** to obtain the following exponential approximation of the dependence of blackbody

intensity on the temperature in the environment :

where
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It is hence clearly evident that upon transfer into the short-wave part of the spectrum the

sensitivity to variations in the temperature becomes stronger of --- the very important

property of the Planck function.

8.4 * why the medium energy of one blackbody photon is not equal ? To find it.

8.5 * to show that photon concentration in the equilibrium field of emission with temperature

Tis equal .

8.6 upon what transfer of electron in hydrogen atom is formed the lying at the red part of the

spectrum line )?

Indication: to consider known the maximum wavelength of the photon, even capable of ionizing

hydrogen atom from the ground state: .

8.7 are possible the ground observations of the line of interstellar hydrogen H (passage ofelectron from the 11th to the 10th level)?

8.8 to estimate the wavelength of the recombination radio link of hydrogen H .

8.9 * to prove that the recombination radio links of hydrogen , , are equidistant in the

frequency.

8.10 is capable whether emission of ionizing hydrogen atoms, which are located on the

second level?

8.11 * why in the spectrum of the solar chromosphere the evidently much larger number of lines

of a Balmer series, than in the spectra of white dwarfs?

9. Spectra of the sun and stars

9.1 to estimate the minimum width of Fraunhofer lines.

9.2 star of class B0V have a period of axial rotation . To find the characteristic widths of lines

in the spectrum of this star in the visible region of the spectrum (in the angstroms).
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9.3 * lines Hand Kof ionizovannogo calcium of --- the strongest in the visible part of the

spectrum suns. (their equivalent widths of --- 14 and 19 , respectively.) The strongest of the

hydrogen lines of --- these are Balmer lines and (their equivalent widths they are close

they are about 4 ). Why lines Hand Kare considerably stronger than hydrogen lines, althoughhydrogen of --- fundamental component of solar atmosphere, and calcium of --- the minorconstituent?

9.4 ** the prevailing detail of the spectra of the stars of class A0 in the optical part of the

spectrum of --- large Balmer jump on . Is great whether the darkening of the disks of

these stars to the edge na and on ?

but9.5 ** energy distribution in the spectrum of sun (G2V) is close to the blackbody

with k. why in the spectrum Of vegi (A0V) it in no way similarly to the Planckian s

k?

9.6 ** the atmosphere of the sun can be considered gray. This means that the emission of allwavelengths (in the visible part of the spectrum) is weakened by it equally. Why then the

darkening of solar disk to the edge with the decrease of wavelength does become more?

9.7 ** as is known, the fundamental component the atmosphere suns of --- these are hydrogenand helium. The number of atoms of all other elements, together, --- so-called "metals" of --- is

from the number of hydrogen atoms. How will change the mass of solar atmosphere, i.e.,those it is layer, from where emission does come to us directly, if the content of "metals"

decreased 10 times?

10. Sun

10.1 ** as does be born daylight? It is more precise: which that concrete elementary atomic

process, proceeding in the atmosphere of the sun, with which are emitted the photons, receivedby us as sunlight?

10.2 visualize improbable: the gigantic spot, which shut entire solar disk, developed in the sun.

It will become in the daytime darker than on the lunar night?

10.3prove that the gravitational pole of the Sun not is capable of holding the electrons of thesolar corona.

10.4 ** the brightness of crown from the brightness of the sun. It shines due to the

scattering of light of the sun on the free electrons. To estimate the mass of crown.
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The Paradoxical Universe

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