Week 14 - Final test, graded assesment

Week 13 - Galaxies

14. 5. 2018

Lecture

Read the learning text here (PPS PDF) page 59 - 63.

Exercise

Week 12 - Final stages of the star evolution - white dwarfs, neutron stars, black holes

7. 5. 2018

Lecture

Read the learning text here (PPS PDF) page 40 - 58.

Exercise

1. From table at page 47 from lecture text try estimate, if the matter in core of star M = 25 M_Sun could be estimated as perfect gas.

2. From Table of parametres of compact object change the input parametres and calculate data for similar objects.
3. See configuration of pulsar on demonstrations.wolfram.com/Pulsars/.
4. Find out from Wikipedia - magnetars what is magnetar, how difers from neutron stars and find out its most important parameters.
5. Calculate the density of energy in magnetic field in magnetar and compare it with density of the energy for water by normal conditions (assume magnetic flux density for magnetar as B = 10 T).

Week 11 - HR diagram - evolution of stars

30. 4. 2018

Lecture

Read the learning text here (PPS PDF) page 32 - 39.

Exercise

Compare parameter of Sun from Wikipedia web page with the Model of polythropic star (see exercise from the previous week).

From the dimensional analysis prove that the star is stable for polythropic parameter γ > 4/3.

Week 10 - HR diagram - evolution of stars

23. 4. 2018

Lecture

Read the learning text here (PPS PDF) page 23 - 31 and answer folowing questions:

1. What is red giant?
2. What is branch of stars as yellow hypergiant and how are their main characteristics?

Exercise

Derivate the simplest possible set of equations for polythropic star equlibirium, based on sheet equilibrium from gravity and pressure, mathematically closed by polythropic equation.

If some time left, You can compare parameter of Sun from Wikipedia web page with the Model of polythropic star.

Week 9 - Statistics of stars, HR diagram

16. 4. 2018

Read the learning text here (PPS PDF) page 19 - 22:

Exercise

Derivate the Jeans' criterion for colaps of cloud to the star.

From Model of polythropic star:

1. Find out the radius of star with central pressure of 1×10¹⁵ Pa.
2. Compare polythropic model with parametres of Sun (ρ₀ = 148 g/cm³, T₀ = 15.5×10⁶ K, R = 6.96×10⁸ m, from standard model Turck-Chiéze et al. 1988, You cold also use the Wikipedia web page for keywor "Sun").

Week 8 - Statistics of stars, HR diagram

9. 4. 2018

Read the learning text here (PPS PDF) page 11 - 18:

Exercise

From HR-diagram hr_diagram.xlsx find out:

1. From which spectral classes are the closest stars from Sun?
2. From Which spectral classes are the most distant stars from Sun?
3. How differs the statistics of stars on the sky from statistics in volume cube in surround part of Galaxy?
4. Find out the most brightest stars and find some info about them from APOD.
5. From APOD find the last published HR diagram and read the description under the picture. From how many stars it is?
6. In alpha.wolfram.com find position of Sun, Sirius, Betelgeuse, Rigel and Polaris in HR diagram.

Week 7 - public holyday (Easter)

2. 4. 2018

Teaching is canceled this day.

Week 6 - Spectra in astrophysics, black body radiation

26. 3. 2018

Lecture

Read the learning text here (PDF) from page 1 to 12 and answer the following questions:

1. What is the black body radiation?
2. Describe the origin of the absorption lines in spectra.
3. By which discovery contributed Josef von Fraunhofer to the knowledge in physics and when?
4. What can be determined from the thickness of the spectral lines? What are the mechanismus of generating severe types of spectras? Describe the physical mechanismus.
5. Which informations are possible to regonize from spectras?

Exercise

1. See the demonstratin "Stellar Luminosity" http://demonstrations.wolfram.com/StellarLuminosity/ and read the descritption.
2. See the demonstratin "" http://demonstrations.wolfram.com/BlackbodySpectrum/ and read the descritption. (Question will be set during the exercise).
3. Hydrogen spectrum could be calculated from Rydberg constant. Found out from Rydberg constant Wikipedia page how to caltulated the spectral lines and calculate the H-alpha line. Compare your result with the h-alpha line on Wikipedie. Last value of Rydberg constant You could find on the NIST web page, calculate its relative uncertainty.

Week 5 - Astronomical objects on the sky

19. 3. 2018

Lecture

Read the learning text here (PDF) page 26 - 32 and answer the following questions:

1. What kind of object You can observe on the sky?
2. Which are the main categories of bodies of Solar System according new classification valid from 2006?
3. Name and explain the charakteristics of every of categories of previous point.
4. Name and explain kinds of Nebulae (dark, emission, reflexion, planetary, supernova remnants)
5. What are Galaxies?
6. What are Clusters of stars?

1. See video Star size comparison at APOD and note, which is the most known giant star and how big it is.
   
2. See picture of Betelgeuse (and other picture here and the oldiest picture from 1996) and answer the question: is that real optical picture? Which only stars are visible direct with optical instruments?
   
3. See picture of colour of stars in Orion constellation and answer the question: how depends colour of stars on their temperature?
   
4. Find on web APOD information about Sedna an find: a) What kind of object it is? When it was discovered? Compare some of parameters of Sedna and Pluto (diameter, density, ...).
   
5. Find from Asteroid belt Wikipedia page, in which resonance ratio and with which planet could the object from this belt be.
   

Week 4 - Time and time scales in astronomy

12. 3. 2018

Attention:
From 4^th week the teaching hours of the astrophysics was changed:
Time:Monday 6 p.m.
Length: Theoretically possible 2×90 minutes i.e. with the end 9 p.m. o'clock. But because it is too late in the evenning, we try compromise as 60 minutes lecture + 5 minutes break + 55 minutes exercise with the end at 8 p.m. But it also depends on You (degree of tirednsess, interest in discussed topics, ...).
Room: T2:C2-84 You'll find on the ground floor, from entrance turn to the left, pass the first and the second elevators and You are at the the c2 block, where the room is located on the right hand.

Lecture

Read the learning text here (PDF) from page 16 to 25 and answer the following questions:

1. What are the most important time scales used in astronomy? Characterize them.
2. What is the time scale, that is always uniform? By what measurement metods is obtained?
3. What of two scales are depending on the rotation of the Earth and how they deffer from each other?
4. What is leap second and what is the reason for it?
5. What astro-geodetic techniques are used to measure of the rotation and axis orientation of the Earth? (More also here http://hpiers.obspm.fr/eop-pc/index.php?index=techniques&lang=en)

Exercise

• Estimate the difference between lengths of the synodical and siderial days respectivelly. You can use as hint the wikipedia pages

From Wikipedia or from http://www.leapsecond.com/ find

• How much leap seconds differs the TAI from UTC now?
• When was the last one?

From Earth rotation and axis orientation data center http://hpiers.obspm.fr/eop-pc/ find out:

• How differs UTC and UT1 right now in ms?
• When was the last one?
• Find aout the last known value of mean angular velocity of the Earth and calculate from this value the periode in h:mm:ss. Why it differs form 24:00:00?
  (Hint: Look for "Useful constant in menu or click direct here: http://hpiers.obspm.fr/eop-pc/index.php?index=constants&lang=en)

Week 3 - Apparent and absolute magnitude

8. 3. 2018

Lecture

Read the learning text here (PDF) page 10 - 15 and answer the following questions:

1. What is the difference between the apparent and the absolute magnitude?
2. What magnitude has the brightest object on the sky?
3. What is the value of the magnitude for the faintest object on the sky (by the best conditions) that could be seen by the naked eye?

Exercise

From the stars catalog stars.xlsx (or stars.xls or stars.csv) find answers to following questions:

• Which is the brightest star and what of magnitude it has?
• What number of stars is with the magnitude of <0, between 0 a 1 and between 1 a 2?
• What number of stars is to the distance ten pc?
• Estimate the magnitude of all of the visible stars, i.e., of the stars to the magnitude of 6 (not from the catalogue, where is the full statistics only to the magnitude of 4 but from extrapolation how the number of stars increases with the rise of the magnitude.

• Find from the Hipparchus Wikipedia page what number of stars was in first Hipparchus's catalogue.
• The Sun has the apparent magnitude m = -26,74. The power of the Sun (in electromagnetic radition) is 4×10²⁶ W. Calculate from the definition formula for magnitude the reference intensity I_0.
• Calculate the total power of Sun from solar constant I = 1367 W/m² and astronomical unit 1 AU in meters (use data from alpha.wolfram.com).
• The faintest object seen by naked eye (D = 7 mm) are thouse with apparent magnitude of 6. Calculate apparent magnitude of objects seen through binocular (D = 70 mm) and astronomical telescope (D = 700 mm).

Week 2 - Units of the length

1. 3. 2018

Lecture

Read the learning text here (PDF) page 6 - 9 and answer the following questions:

1. What are the basic units of the length in astronomy?
2. What is parallax?
3. What is the relationship between the distance of the star and its parallax?

Exercise

• AU: Find the value of the Astronomical Unit in meters, find out if it is exactly equal to the mean distance Earth-Sun, use the server. alpha.wolfram.com (hint: use AU, au with small case letters is interpreted as the atomic mass unit). Why possibly are the both of values (1 AU vs. mean distance Earth-Sun) different?
• Geometry of ellipse: Find out, how could be constructed the ellipse, how are the long and short ellipse parameters and eccentricity and numerical eccentricity definad and what is the relationship between them. Calculate the main ellipse parameters and from them perihelium and aphelion distances for Earth, if You know, that numerical eccentricity is &eps; = 1/60, answer, how could be this parameter taken experimentally. Which parameter of ellipse coresponds with r_mean?
• Light year: Find the value of the 1 l.y. and find out for which year is defined. (Julian, 365.25 days, Gregorian, 365.2425 days, sidereal (hint: in Wolfram Alpha set the question "sidereal year") or by other?
  (Hint: "light year" or "ly", for the result in days set "in days")
• Parsec: Find out the value of the Parsec in meters, in kilometers, in Astronomical Units, and in l.y. Find the value of Parsec in kilometers in the precision of 8 digits (hint: ad the term "... in 8 digits").
• Parallaxa Find the parallax and find the distance in AU and in pc for the nearest star except for the Sun. (Hint: in Wolfram Alpha set "Parallax of Proxima Centauri".)

Week 1 - introduction, the relationship between astronomy and astrophysics

22. 2. 2018

Lecture

Read the learning text here (PPS PDF) page 4 - 5 and answer the following questions:

1. What is the difference between astronomy and astrophysics?
2. Who was the first astrophysicist, what experiment he made and when?