Course Description:

(A) Objectives: The course will introduce basic concepts of Positional astronomy, observa- tional techniques, signal properties with a few examples of observations of celestial sources.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Positional astronomy: Night sky, celestial sphere, ancient astronomy, motion of planets, moon and comets, constellation and nakshtras, sidereal time, calendars, precession, proper motion and parallax, eclipses and transits, Astrometry, distance ladder, application of Stellarium software (7 lectures)
2. Measurements: Observations, brightness, intensity, flux, luminosity, magnitude scale, Photometry, spectroscopy (Doppler shift, spectral resolution, FWHM, convolution), filters, Atmospheric transmission windows on Earth, atmospheric seeing and extinction, effect of ionosphere (6 lectures)
3. Signal properties: - Signal & noise, wave and shot noise, sampling, VCZ theorem, coherence, Hanbury brown - Twiss effect, bunching of photons (4 lectures)
4. Celestial objects (observational): Multi-wavelength observations of - solar system objects, exo-planets, stars (color-magnitude, HR diagram), Galaxies, large-scale structures. (4 lectures)

Course description and contents:

This course helps describe various astronomical observations, primarily within the Solar System, employing relatively simple mechanical models. An introduction to galactic dynamics will also be given. The distribution is given below in terms of 50 minute lectures.

1. Introduction to the Solar System, stars and galaxies – 1 lecture
2. The 1- and 2- body problems: Kepler’s laws, Newton’s law of gravitation, Equations of motion, Mean and eccentric anomalies, Barycentric orbits, Orbital elements, Applications, e.g. Hohmann transfer – 4 lectures
3. Introduction to galactic dynamics: Collisionless N-body system (Coulomb logarithm, relax- ation time, dynamical crossing time), Examples of galactic potentials, Orbits of stars in axisymmetric and non-axisymmetric potentials, Lindblad resonances – 4 lectures
4. The restricted 3- body problems: Equations of motion in a rotating frame, Tisserand rela- tion, Jacobi integral, Lagrangian equilibrium points, Zero velocity curves, Perturbed orbits, Tadpole and Horseshoe orbits, Effect of drag, Applications to small moons – 6 lectures
5. Rotational and tidal effects: Tidal bulge, Potential theory, Tidal and rotational deformation, Shapes of solar system bodies, Roche zone, Tidal torques, Application to small moons – 6 lectures

Course Description:

(A) Objectives: The course aims to provide hands-on experience on instrumentation techniques related to astronomy, planetary and space sciences and engineering.

(B) Contents (preferably in the form of 5 to 10 broad titles): Students will be required to complete at least 2 experiments from each stream as described here -

1. Detector characterization in X-ray/UV/optical/nearIR; exper- iments related to working of CCD, CMOS, PMT, X-ray detectors etc.
2. Observing fundamental principles - Coherence, Van-Cittert- Zernike theorem, Hanbury Brown intensity interferometer; Double slit experiment, Heisenberg uncertainty; Michelson/Fabry-Perot interferometer; Faraday effect; Young’s modulus for different ma- terials.
3. Spectroscopy and polarimetry techniques - Characteriza- tion of filters, polarizing elements and dispersing elements; Brew- ster angle, wave-plates- Spectrometer and polarimetry; spectral reflectance from surfaces, rocks and minerals in different illumi- nation conditions; Spectra of various gases and flames - emis- sion/absorption experiment; fibre optics; optical telescopes.
4. Radio detection techniques - Amplifiers, mixers, filters, noise & detection, phasing, antennas, RFI mitigation, impedance match- ing, transmission lines.

Course Description:

A. Objective: Studying the universe is mostly done via understanding the electromagnetic radiation that each source emits. The nature of the spectrum indicates the underlying physical processes. This course intends to teach the processes that generate electromagnetic radiation and relevance in natural sources.

B. Content:

1. Ionization processes (3 L): Basic quantum mechanics concepts (energy levels, wave-particle du- ality), Collisional ionization, photo-ionization, recombination, ionization equilibrium, HII regions (Stromgren sphere), Saha ionization
2. Emission and absorption of thermal plasma (5 L): Bound-Bound transitions, Spontaneous/ stimulated transitions, Einstein’s coefficient, emission/absorption lines, emissivity and absorption coeffi- cient, doppler/Lorentz broadening, Free-Free emission, Thompson scattering, example of a spectrum and its features
3. Heating and Cooling (2L): Physical conditions in different astrophysical systems (interstellar, intergalactic mediums), Photo-heating, cooling curve, thermal equilibrium, thermal instability, multiphase gas (interstellar medium)
4. Radiative Transfer (6 L): Radiative transfer equation, thermal radiation (Kirchhoff’s law, black- body radiation, Rayleigh-Jeans law), brightness temperature, Scattering and diffusion, radiation as a fluid (Eddington approximation), gray atmosphere, green house effect
5. Non-Thermal Radiation (4 L): Synchrotron Radiation, beaming effect, polarization, Compton/ inverse-Compton Scattering

Course Description:

(A) Objectives: The course aims to introduce stu- dents to numerical techniques used in Space Science & Astronomy.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Vector Analysis (3 lectures) Vector differential calculus, gradient, divergence and curl, surface and volume integrals
2. Matrix Algebra (6 lectures) Introduction to matrices, diagonalization, solution of linear equa- tions using matrices.
3. Coordinate Systems (5 lectures) Curvilinear coordinates, coordinate transformation, applications to astronomy
4. Ordinary differential equations (6 lectures) First and second order ODEs and their solutions. Separation of variables method to solve PDEs and various types of boundary conditions - initial value problem vs boundary value problem etc.

Course Description:

(A) Objectives: The course aims to introduce stu- dents to numerical techniques used in Space, Planetary and Astronom- ical Sciences and Engineering.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Numerical Integration (2 lectures, 2 labs) Newton-Cotes formulae including trapezoidal rule and Simpson’s rule, Gaussian quadrature, convergence and scaling of error, Monte Carlo Integration
2. Numerical Root finding (1 lecture, 1 lab) Bisection method, Newton Raphson method for single and multi- dimensional systems.
3. Integration of Ordinary Differential Equations (ODE) (3 lectures, 3 labs) Initial Value Problem Forward and backward Euler method, Runge- Kutta Method, Stiff system of equations, implicit vs. explicit schemes, shooting method for the Boundary Value Problem.
4. Numerical Interpolation of functions (1 lecture, 1 lab) Linear and higher order interpolation with polynomials, Spline Interpo- lation

Course Description:

(A) Objectives: The course aims to introduce students to basic ideas and concepts in modern Astronomy & Astrophysics.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Historical Introduction (2 lectures) History of Astronomy (ancient Indian and Greek astronomy), Con- stellations & Nakshtras, magnitude scale, Parallax.
2. Astrometry (6 lectures) Celestial Sphere, Coordinates, Rise, set, and tracks of celestial objects, Precession, Basic calculations, Introduction to Calendars, Seasons on Earth, Eclipses & Transits, Hands-on sessions using Stellarium, cosmic distance ladder.
3. Universal Physical Principles and basics of radiation (6 lectures) Newton’s law of Gravitation, Conservation of energy and momen- tum, Electromagnetic Spectrum, Thermal radiation, Continuum and spectral line emission, examples of radiation from astrophys- ical sources
4. Observing tools (6 lectures) Types of telescopes, signal & noise, sources of noise, signal to noise ratio, Gaussian & Poisson statis- tics, detection probabilities.
5. Our Solar system and other exoplanets (6 lectures) Kepler’s laws and objects in the solar system, Planetary Atmo- spheres, Planetary Rings, exoplanets - detection methods.
6. Structure and life-cycle of stars (6 Lectures) Source of energy, Hydrostatic Equilibrium, Mass loss, Evolution (colour-magnitude, HR diagram), Star birth, Planetary nebulae, Novae, Supernovae, Gamma-Ray Bursts, Binary Stars, White dwarfs, Brown dwarfs, Neutron stars, Black holes.
7. Milky-Way, extra-galactic astrophysics and cosmology (8 Lectures) Structure of Milky-Way, Types of galaxies, nearby galaxies, Kine- matics, Dark matter, redshift measurements, galaxy clusters, Phys- ical conditions in Interstellar Medium & Intergalactic Medium, Tracers of interstellar medium, hands-on session using galaxy kine- matics data, basic introduction to cosmology, dark matter and dark energy.

Course Description:

(A) Objectives: The course aims to teach students about basics of galactic and extra galactic astronomy.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Universal Physical Principles in Astrophysical Context (7 Lectures) Newtons law of Gravitation, Theory of relativity, Quantum Me- chanics, Maxwell Equation, Radiative transfer interaction of light with matter - Absorption, scattering, emission and absorption, Thomson and Compton process, high-energy processes, Synchrotron emission.
2. Properties of Galaxies (12 Lectures) Observational properties, star-forming regions, Dust, Mass-to-light ratio, supernova remnants, Differential rotation, Stellar dynamics, Virial theorem, Stability, galaxy interactions, radiation from Inter- stellar Medium (Balmer lines, HI 21 cm-line, Infrared and Radio emission), Magnetic field.
3. Galaxy clusters (6 Lectures) Galaxy clusters - Observations, Observational Properties, Physical processes, Feedbacks, Intergalactic medium - X-ray emission, Thermal & non-thermal radiation, particle interaction with radiation.
4. Observational Cosmology and extra-galactic astronomy (12 Lectures) Evolution history of the universe and Hubble’s law, dark matter and dark energy, distance & angular size measurements, Cosmic distance ladder, Statistical Parameter estimation.
5. Space Missions (3 lectures): Brief summary of current and future missions - what they will measure and how they will do it.

Course Description:

(A) Objectives: The course aims to introduce students to instruments and detectors used in Space Science and Astronomy. It will introduce the basic principles and techniques, such as, detector design, calibra- tion, background, space qualification and data acquisition used in this field. It will describe the challenges faced in the Space relative to ground based instruments. It will describe some instruments, such as, the India’s first space observatory; Astrosat, LAXPC instrument on- board Astrosat, Moon and Mars missions in detail.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Introduction ( 3 Lectures ) Historical perspective, background, basics of space observations, differences w.r.t. ground based instruments, challenges.
2. Space observations(what we observe) ( 6 Lectures ) Electromagnetic spectrum, continuous and discrete spectroscopy, Cosmic rays, solar wind, solar flares, magnetic field, Spectroscopic techniques to deduce composition and physical properties.
3. Particle/Photon detectors & type (focussing & non-focussing) (8 Lectures ) Interaction of charged particles and photons with matter, electromagnetic wave detectors, charged particle detectors, such as, nuclear emulsions, GM counters, proportional counters, scintillators, semiconductor detectors etc.
4. Basic techniques and past instruments ( 8 Lectures ) Modelling background, basic techniques in detector calibration, data acquisition and space qualification, challenges faced in space observations, effect of Earth atmosphere and past space instruments.
5. Planetary space missions ( 6 Lecture ) Moon and Mars missions, Planetary mapping, meteorites and moon samples.
6. India’s first Space observatory: AstroSat ( 5 Lecture ) All five instruments which include all sky monitor, SXT telescope, LAXPC, CZIT instrument and UVIT telescopes (near optical and near UV)
7. LAXPC instrument ( 6 Lecture ) detailed description of LAXPC instrument, challenges in realizing the payload, performance in space, data.

Course Description:

(A) Objectives: The course aims to introduce students to advanced mathematical techniques used in Space Science & Astronomy. It will be offered as a compulsory review course for M. Tech. students in this discipline.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Vector Analysis ( 4 Lectures ) vector differential calculus, gradient, divergence and curl, surface and volume integrals
2. Linear vector spaces ( 10 Lectures ) Introduction to matrices, vector spaces, diagonalization of matrices, linear algebraic equations, existence and uniqueness of solutions, tensor analysis
3. Coordinate Systems ( 5 Lectures ) curvilinear coordinates, coordinate transformation, applications to Astronomy
4. Ordinary differential equations ( 5 Lectures ) first and second order differential equations, linear differential equations, existence and uniqueness of solutions, series solution, stellar structure equations.
5. Special functions ( 4 Lectures ) Bessel functions, spherical Bessel functions, Legendre functions, spherical harmonics, application to Cosmic Microwave Background.
6. Integral transforms ( 4 Lectures ) Laplace transform, Fourier transform.
7. Numerical Methods ( 10 Lectures ) numerical integration, numerical solution of ordinary differential equations, solution of non-linear algebraic, equations, interpolation, fast fourier transform, extremization of functions.

Course description:

1. Introduction – (1 lecture)
2. Dynamics, Physics & Astrophysics: Two- and three- body problems; Thermodynamics; Stel- lar properties; Nucleosynthesis – (5 lectures).
3. Solar heating and energy transport: Energy balance and transport - conduction, convection, radiation – (3 lectures).
4. Planetary atmospheres: Thermal structure; Composition; Molecular and eddy flows; Atmo- spheric escape – (5 lectures).
5. Planetary surfaces and interiors: Mineralogy & petrology; Interiors; Surface morphology, Impact cratering, examples. – (10 lectures).
6. Magnetic fields: Sun; Solar wind; Planetary magnetospheres – (4 lectures).
7. Formation processes: Solar System - overview and constraints; Protoplanetary disk’s evolution; Growth of solid bodies and gas giants; Migration; Planetary rotation; Asteroids, comets and moons; Exoplanets; Theory and observation – (10 lectures).
8. Major Space missions and their scientific contributions – (4 lectures).
9. Examples: Moon; Terrestrial planets; Gas giants – (3 lectures) (if time permitting).

Course Description:

(A) Objectives: The course aims to introduce students to numerical techniques used in Space Science & Astronomy. It will be offered as a compulsory review course for M. Tech. students in this discipline.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Numerical Integration (3 lectures) Newton-Cotes formulae including trapezoidal rule and Simpson’s rule, Gaussian quadrature, convergence and scaling of error.
2. Numerical Root finding (3 lectures) Bisection method, Newton Raphson method for single and multi- dimensional systems.
3. Integration of Ordinary Differential Equations (ODE) (6 lectures) Forward and backward Euler method, Runge-Kutta Method, Stiff system of equations, implicit vs. explicit schemes.
4. Numerical Optimization ( 3 lectures) Finding maxima and minima of functions
5. Fast Fourier Transforms (6 lectures) Basics of FFT (allocation and storage of data), Parseval’s theorem, solving Poisson’s equation with periodic boundary conditions using FFT.
6. Statistical tools (9 lectures) Parameter estimation using maximum likelihood estimators, covariance matrix and error ellipses.
7. Numerical handling of big data (12 lectures) Basics of parallel comupter architechture, distributed and shared- memory programming, developing parallel programs with specific examples.

Course Description:

(A) Objectives: The course aims to introduce students to fundamentals of Astronomy and Astrophysics. It will cover topics such as, multi- frequency astronomical observations, Astrometry, Photometry, Stellar structure and evolution, interstellar medium, Galaxies and the Milky Way, Introduction to Cosmology It will be offered as a compulsory course in the Radio Astronomy M.Tech. stream and as an elective for students of all branches.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Overview ( 5 Lectures ) Night sky, constellations, Retrograde motion of planets, Sidereal time, Kepler’s laws, Virial Theorem
2. Observations ( 5 Lectures ) Electromagnetic Spectrum, Observations at visible frequencies, Resolution, Seeing, Telescope mounts, Interferometry, observations at other wavelengths, cosmic rays
3. Astrometry ( 6 Lectures ) coordinate systems used in Astronomy, coordinate transformation, proper motion, Doppler effect, Aberration, precession of equinoxes
4. Photometry ( 5 Lectures ) Intensity and Flux density, Blackbody radiation, magnitude scale, color index, stellar temperatures, Radiation from astronomical sources, Bremsstrahlung, Synchrotron Radiation, Compton Scattering, Radiative Transitions/line-emission, Radiative transfer
5. Stars and Stellar evolution ( 12 Lectures ) Stellar spectra, Saha equation, Hertzsprung-Russell (HR) diagram, Star clusters and Associations, Stellar structure, pressure and temperature gradient, energy production, Rosseland mean opacity, equation of state, radiative pressure, stellar nuclear reactions, nuclear reaction rate, standard solar model, star formation and stellar evolution, evolution beyond the main sequence, white dwarfs, neutron stars and black holes, supernova explosion
6. Binary stars ( 4 Lectures ) Kinematics of binary star system, Classification of binary stars, Mass Determination
7. Milky Way ( 4 Lectures ) Distribution of matter in the Milky Way, Differential Rotation, Mapping the Galactic Disk, Formation of spiral arms
8. Galaxies ( 3 Lectures ) Classification of galaxies, Evidence for dark matter, Galaxy Clusters, Large scale structure of Universe

Course Description:

(A) Objectives: This is an introductory course in Radio Astronomy. The students are assumed to be familiar with basic Astronomy and Astrophysics. The course will introduce the different types of anten- nas and receivers used in Radio Astronomy, basic principles of antenna elements and arrays, Imaging, Aperture Synthesis, Deconvolution and CLEAN algorithm, Practical details of analysing single-dish observa- tions and radio interferometric data. It will be offered as a compulsory course for M. Tech. students choosing Radio Astronomy as their spe- cialization.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Cosmic Radio Sources ( 5 Lectures ) radio emission in the Solar System and, the Milky Way, extra-galactic radio sources, Physical mechanism generating radio waves
2. Signal Processing ( 8 Lectures ) Fourier pairs in Radio Astronomy, Statistical properties of signal, Probability Density, Expectation Values, Auto-correlation and power spectrum, Filters, digitization and sampling,
3. Antennas and Receivers ( 12 Lectures ) Practical aspects of Antenna, Field-of-view, resolution, single dish observations, spectroscopy, antenna power patterns, antenna arrays, electronic Coherent Receivers, Maximum-power transfer, transmission lines, impedance matching, reflections, Standing-waves, Radio Frequency Interference, time and frequency standards, Noise uncertainties, front and back-ends currently in use
4. Interferometer Response ( 6 Lectures ) cross correlation, coherence, convolution, delay and phase compensation, relationship between intensity and visibility, effect of bandwidth .
5. Calibration ( 6 Lectures ) Basic formalism and methods, use of calibration sources, calibration of amplitude and phase, antenna pointing and gain
6. Imaging ( 6 Lectures ) Aperture synthesis, deconvolution and cleaning the data, CLEAN algorithm, practical implementation on VLBI, VLA and GMRT.

Course Description:

(A) Objectives: The course is aimed introduce students to the ex- perimental techniques and equipment used in Radio Astronomy. The students will perform experiments, such as, characterization of coaxial cable, filter, amplifier etc. They will perform a double slit interference experiment in radio waves, observe galactic HI line using a horn an- tenna, study cross-correlation of signal using two antennas, and use interferometry to determine the angular size of the Sun. The course is designed for students who intend to pursue Radio Astronomy as their specialization.

(B) List of Experiments:

1. Coax cable characterization: Transmission line impedance, loss, standing wave, impedance mismatch, reflection, phase difference as a function of frequency
2. Filter characterization using Oscilloscope: Using broad-band noise as input, measurement of temporal coherence in the filter out- put – uses fourier relationship – coherence scale in time & band- width/centre frequency
3. 2-slit experiment in radio: Young’s double-slit experiment in radio
4. Filter characterization using spectrum analyser -simple filter using L&C
5. Design, fabrication and characterization of a microstrip filter
6. Amplifier characterization
7. Mixer characterization
8. Designing an attenuator-cum-Impedance Transformer – T or Pi networks of resistors
9. Observe the 21 HI cm line using a horn antenna and a simple receiver chain with SDR – find the local transit time of the chosen HI line source – find the width, velocity of the line, and compute the tangential velocity by observing the line in directions other than the galactic centre
10. Beam Pattern measurements: Horn beam patterns, in both E and H planes, are to be measured, by rotating the horn and measuring changes in power of the signal received from a local radiator
11. Beam Pattern measurement using the sun: Beam pattern mea- surements using the sun as source – knowing properties of ampli- fier, noise, etc. – estimate brightness temperature of the sun
12. Antenna Design: Use an open-source software platform to design an antenna – specifically, a broad-band antenna for a specified frequency range, and determine its beam pattern and frequency response
13. Correlation: Create a partially correlated noise by splitting a noise source into two and study its cross-correlation
14. Power Divider / Combiner: Understanding power divider / power combiner – 2 noise sources fed into the combiner, noise output measured
15. Interferometry to determine angular size of the sun: Making an interferometer – use 2 horns – continuation of no. 13 – instead of noise sources, observe the sun and possibly the HI line – measure Sun visibilities at two or more distinct baselines, and using these measurements, estimate size of the radio Sun

Course Description:

(A) Objectives: This course will introduce students to the exciting world of High energy processes, which may involve very strong grav- ity, very high temperature (million degree) and/or high magnetic field in our Galaxy and beyond. Astrophysical sources which show such high energy phenomena are binary stars in which one of the partner is a black hole or a neutron star. These sources emit significant ra- diation in X-rays, gamma-rays as well as radio waves. This course will introduce the student to the structure of such sources and their emission characteristics. The student will also learn X-ray and gamma ray detection techniques, challenges faced while developing space X- ray detectors and the current state of space X-ray detectors worldwide. Students will have access to data to study galactic black hole X-ray binaries or neutron star X-ray binaries including pulsars and will learn techniques for analysing data from such sources.

(B) Contents (preferably in the form of 5 to 10 broad titles:

1. Stars and stellar evolution (4 lectures) Brief review of stellar structure and evolution, Compact stars
2. Basic Concepts (6 lectures) Basic equations of gas dynamics, sound waves, plasma oscillations, Debye length, viscosity, shock waves in plasmas
3. Binary Stars (8 lectures) Introduction to binary star systems, mass transfer and formation of accretion disk, Roche lobe overflow, accretion through stellar wind
4. Accretion Disks (9 lectures) Structure of accretion disks, viscous torques, steady thin disks, structure of α-disks, emitted spectrum, different X-ray states in compact star binaries, outbursts in X-ray binaries
5. Detection of X-rays and gamma rays (5 lectures) Techniques for detection of X-rays and gamma rays; types of detectors; statistical and error analysis of data.
6. space X-ray detectors (5 lectures) Challenges faced in making space detectors; the Astrosat space observatory
7. Observations (5 lectures) Observations of black hole X-ray binaries, Neutron star X-ray binaries and X-ray pulsar; accretion disk and radio jet connection (C) pre-requisites: SPA6xx: Introduction to Astronomy and Astro- physics or an equivalent course (D) Short summary for including in the Courses of Study Booklet: Review of stellar evolution and Compact stars, brief overview of Gas dynamics, plasma Physics and shock waves, binary stars, mass transfer through Roche lobe overflow and stellar wind, formation and structure of accretion disks, steady α-disks, emitted spectrum, different X-ray states in compact star binaries, outbursts in X-ray binaries, detection of X-rays and gamma rays, space X-ray detectors, observations and study of X-ray binaries

Course Description:

(A) Objectives: The course aims to introduce students to basic prin- ciples of stellar structure and evolution. It will start with a detailed description of different kinds of stars, classification of stars based on the observed spectrum, and the Hertzsprung-Russell (HR) diagram. It will describe the basic equations of stellar structure and evolution. The dif- ferent nuclear fusion reactions which contribute at different stages will be discussed in detail. The course will also provide detailed description of stellar evolution from birth to the formation of compact star or a black hole. The Physics of compact stars, i.e. white dwarfs, neutron stars and black holes will be discussed along with explosive transient phenomenon, such as the supernovas.

(B) Contents (preferably in the form of 5 to 10 broad titles):

1. Overview (4 lectures) Introduction to Stars, length and mass scales, interstellar medium, Photometry, Blackbody radiation magnitude scale, color index
2. Stellar Spectra & classification (8 lectures) Stellar spectra, Saha equation,Hertzsprung-Russell (HR) diagram, Star clusters and Associations, Stellar
3. Stellar Structure (8 lectures) Stellar structure equations, pressure temperature gradient equations energy production, Rosseland mean opacity, equation of state, radiative pressure,
4. Stellar nuclear reactions (6 lectures) stellar nuclear reactions, nuclear reaction rate, standard solar model,
5. Stellar evolution (6 lectures) formation of stars, pre-main sequence stars, Hayashi track, main sequence and evolution beyond the, main sequence, last stages of stellar evolution
6. Compact Stars (6 lectures) white dwarfs, neutron stars and black holes, supernova explosion
7. Binary stars (4 lectures) Kinematics of binary star system, Classification of binary stars, Mass Determination