Mathematics, Second Cycle
1 ali 2 year
first and second
Course director:
Hours per week – 1. semester:
Hours per week – 2. semester:
Content (Syllabus outline)

Historical introduction: basis of calendar, eclipses, size and distances of the Earth, Moon and Sun, distances in the Solar system, rotational period of the Earth, leap second.
Positional astronomy: concept of celestial sphere, spherical trigonometry, calculation of altitude and azimuth, culmination, time above horizon, sidereal time, effects of atmospheric refraction, aberration, precession, parallax and proper motion.
Solar apparent motion: coordinates, mean and true Solar time, illumination, occurence of seasons.
Astronomical telescopes: lens, mirror, combining the two elements, types of telescopes, light collecting power, image scale, image brightness, depth of field, magnification, telescope mounts.
Digital detectors: their size, image presentation, photometric filters.
Astronomical magnitudes: apparent and absolute magnitude, basics of reduction of photometric observations.
Basics of astronomical spectroscopy: spectrograph, measurable quantities.
The Sun as a typical star: mass of the Earth and Sun, their average density. Solar luminosity, effective temperature, surface gravity and rotational acceleration.
Structure of Solar-like stars: hydrostatic equilibrium, dynamical time-scale, central pressure and temperature, justification of calculation with ideal gas, polytropic model, virial theorem, thermal time-scale, optical opacity, free path of photons, energy transport with radiation and convection.
Ages of stars: the case of the Earth and the Sun, nuclear fusion, its stability and timescale, dependence of luminosity on mass for Solar-like stars, Eddington luminosity.
Evolution of stars: formation and Jeans mass, giant phase, final stages of evolution, dependence of evolution on mass.
Observation of stellar evolution: Hertzsprung-Russell diagram, star clusters, distance measurement, spectra of chemical elements in stellar atmospheres, their dependence on temperature, chemical composition, radial velocity and gravity, eclipsing spectroscopic binaries, observations of final stages of stellar evolution.
Interstellar medium: absorption in gas and dust, types of nebulae, observable properties.


H. Karttunen et al.: Fundamental Astronomy, Fifth Edition, Springer, 2007.
R.M. Green: Spherical astronomy, Cambridge University Press, 1993.
F. H. Shu, The Physical Universe. University Science Books, 1982.
A. Čadež: Fizika zvezd, DMFA, 1984.
Gordon Walker: Astronomical observations: an optical perspective. Cambridge University Press, 1987.
T. Zwitter: Pot skozi vesolje, Modrijan, 2002.
Presekova zvezdna karta, DMFA, 2000, Spikina vrtljiva zvezdna karta.
Naše nebo, astronomske efemeride, DMFA, 2012-.

Objectives and competences

Mastering of basics of astronomical observations, phenomenology of objects and processes in the Universe and understanding of the Universe using laws of physics. This connects to a wider picture of the world we live in.

Intended learning outcomes

Knowledge and understanding: Understanding of the basics of the physical picture of the Universe, its foundations, and acknowledging its present limitations.
Application: Basic knowledge of astronomy and astrophysics, experience of the universality of physics, experience of inventive measurements in difficult conditions.
Reflection: The Universe contains most diverse environments, but it can be understood with physics and mathematics as we know it.
Transferable skills: Critical evaluation of information, examples of manipulation of digital data, experience in the use of aparatus of mathematics and physics to solve open problems.

Learning and teaching methods

Lectures, computational and practical exercises, astro-lab reports.


Written exam, presentation of astro-lab report
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

ŽERJAL, Maruška, ZWITTER, Tomaž, MATIJEVIČ, Gal, et al. Chromospherically active stars in the RAdial Velocity Experiment (RAVE) Survey : I. The catalog. The Astrophysical journal, ISSN 0004-637X, 2013, vol. 776, issue 2, article id. 127, str. 1-12. [COBISS-SI-ID 418945]
KOS, Janez, ZWITTER, Tomaž. Properties of diffuse interstellar bands at different physical conditions of the interstellar medium. The Astrophysical journal, ISSN 0004-637X, 2013, vol. 774, issue 1, article id. 72, str. 1-16. [COBISS-SI-ID 417409]
MATIJEVIČ, Gal, ZWITTER, Tomaž, et al. Exploring the morphology of RAVE stellar spectra. The Astrophysical journal, supplement series, ISSN 0067-0049, 2012, letn. 200, št. 2, str. 1-14. [COBISS-SI-ID 393601]
BREDDELS, Maarten A., ZWITTER, Tomaž, et al. Distance determination for RAVE stars using stellar models. Astronomy & astrophysics, ISSN 0004-6361, 2010, let. 511, št. A90, str. 1-16. [COBISS-SI-ID 344961]
ZWITTER, Tomaž, RE FIORENTIN, Paola, MATIJEVIČ, Gal, VIDRIH, Simon, et al. The radial velocity experiment (RAVE): second data release. The Astronomical journal, ISSN 0004-6256, 2008, let. 136, št. 1, str. 421-451. [COBISS-SI-ID 309377]
PRŠA, Andrej, ZWITTER, Tomaž. A computational guide to physics of eclipsing binaries. I. Demonstrations and perspectives. The Astrophysical journal, ISSN 0004-637X, 2005, let. 628, št. 1/1, str. 426-438. [COBISS-SI-ID 239489]
ZWITTER, Tomaž, CASTELLI, Fiorella, MUNARI, Ulisse. An extensive library of synthetic spectra covering the far red, RAVE and GAIA wavelength ranges. Astronomy & astrophysics, ISSN 0004-6361, 2004, let. 417, št. 3, str. 1055-1062. [COBISS-SI-ID 220801]
MUNARI, Ulisse, ZWITTER, Tomaž. Equivalent width of Na I and K I lines and reddening. Astronomy & astrophysics, ISSN 0004-6361, 1997, let. 318, št. 1, str. 269-274. [COBISS-SI-ID 87681]
D'ODORICO, Sandro, ZWITTER, Tomaž. Evidence that the compact object in SS433 is a neutron star and not a black hole. Nature, ISSN 0028-0836. [Print ed.], 1991, let. 353, str. 329-331. [COBISS-SI-ID 64129]