M.Sc. (ASTRONOMY & SPACE Physics) PART I (I Iisemesters)

SCHEME

M.Sc. (ASTRONOMY & SPACE Physics) PART– I (i iisemesterS)

2016– 2017 & 2017– 2018sessionS

Code / Title of Paper / Hours
(Per Week) / Max. Marks / Examination Time (hrs)
Semester–I / Total / Ext. / Int.
Core Papers
ASP 1.1.1 / Mathematical Physics / 4 / 80 / 60 / 20 / 03
ASP 1.1.2 / Classical Mechanics / 4 / 80 / 60 / 20 / 03
ASP 1.1.3 / Positional Astronomy / 4 / 80 / 60 / 20 / 03
Elective Papers*
ASP 1.1.4 / (i)Analog Electronics
(ii)Remote Sensing
(iii)Microwave and its Propagation / 4 / 80 / 60 / 20 / 03
ASP 1.1.5 / Lab Practice:
Laser-Optics / 9 / 120 / 90 / 30 / 03
ASP 1.1.6 / Computer Laboratory / 3 / 60 / 45 / 15 / 03
Semester –II
Core Papers
ASP 1.2.1 / Quantum Mechanics / 4 / 80 / 60 / 20 / 03
ASP 1.2.2 / Digital Electronics / 4 / 80 / 60 / 20 / 03
ASP 1.2.3 / Celestial and Fluid Mechanics / 4 / 80 / 60 / 20 / 03
Elective Papers*
ASP 1.2.4 / (i)Applied Optics
(ii)Mathematical Physics and Classical Mechanics
(iii) Computer Fundamentals and Programming with C++
(iv) Atomic and Molecular Spectroscopy / 4 / 80 / 60 / 20 / 03
ASP 1.2.5 / Lab Practice: Electronics / 9 / 120 / 90 / 30 / 03
ASP 1.2.6 / Computer Laboratory / 3 / 60 / 45 / 15 / 03

NOTE: Only one Elective paper will be offered depending on the availability of staff.*

Semester– I

ASP 1.1.1 / MATHEMATICAL PHYSICS

Maximum Marks: External 60Time Allowed: 3 Hours

Internal 20Total Teaching hours: 50

Total 80Pass Marks: 35%

Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examinations, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective section of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carries 10 marks. Section C will carry 20 marks.

Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks.

Use of scientific calculator is allowed.

SECTION A

Gamma and Beta functions: Definition and their relations

Bessel functions: Series solutions of Bessel's differential equation recurrence relations, Evaluation of Jn(x)for half-integral, generating function, Orthogonality (statement only).

Legendre Polynomials: Series solution of Legendre differential equation, Rodrigue and recurrence formulae, Generating function; Associated Legendre equation and polynomials;

Hermite polynomials: Series solution of Hermite differential equation, Hermite polynomials, Generating functions, Recurrence relations, Orthogonality (statement only), Simple integral involving Hermite polynomials.

Laplace transforms, Definition, Laplace transform of elementary functions, Basic theorems of Laplace transforms, Inverse Laplace transforms, its properties and related theorems, Convolution theorem, Use of Laplace transforms in the solution of differential and integral equations, Evaluation of integrals using Laplace transforms.

Fourier series and transform: Dirichlet conditions, Expansion of periodic functions in Fourier series, Sine and cosine series, The finite Fourier sine and cosine transforms, Complex form of Fourier series, Fourier integral theorem and Fourier transform, Parseval's identity for Fourier series and transforms.

SECTION B

Partial differential equations, One dimensional wave equation, The vibrating string fixed at both ends, D'Alembert and Fourier series solutions, Vibrations of a freely hanging chain, Two dimensional wave equation in rectangular membrane, Wave equation in the two dimensional polar coordinates and vibrations of a circular membrane, 3-D wave equation and its solution, Equation of heat conduction,Two dimensional heat conduction, Temperature distribution in a rectangular and circular plate, 3-D heat conduction equation.

Evaluation of polynomials: Horner's method; Root finding: Fixed point iteration, Bisection method, Regula falsi method, Newton method, Error analysis; System of linear equations: Gauss elimination, Gauss Seidel method, Interpolation and Extrapolation: Lagrange's interpolation, least square fitting;

Differentiation and Integration: Difference operators, Simpson and trapezoidal rules; Ordinary differential equation: Euler method, Taylor method.

Text Books:

Applied Mathematics: L.A. Pipes and Harwill, Mc Graw Hill Publication
Mathematical Physics: G.R.Arfken, H.I.Weber, Academic Press, USA (Ind.Ed.)
Laplace Transforms: M.R. Speigel (Schaum Series), Mc Graw Hill Publication
Numerical Methods: J.H. Mathews, Prentice Hall of India, New Delhi

Reference Books:

Advanced Engg. Mathematics: E. Kreyszig, Wiley Eastern Publication

ASP 1.1.2CLASSICAL MECHANICS

Maximum Marks: External 60Time Allowed: 3 Hours

Internal 20Total Teaching hours: 50

Total 80Pass Marks: 35%

Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective section of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carries 10 marks. Section C will carry 20 marks.

Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks.

Use of scientific calculators is allowed.

Section A

LagrangianFormulation:Conservationlawsoflinearmomentum, angularmomentumandenergyforasingleparticleandsystemofparticles, Constraintsand generalizedco-ordinates, Principle of virtual work, D' Alembert's principle and Lagrange's equations of motion, for conservative systems. Applications of Lagrangian formulation.

VariationalPrinciple:Hamilton's principle, Calculusofvariationsanditsapplicationto the shortestdistance,minimumsurfaceareaofrevolutionand the brachistochroneproblem.Lagrange'sequationsfromHamilton'sprinciple.Generalizedmomentum,Cyclicco-ordinates,SymmetrypropertiesandConservationtheorems.

TwobodyCentralForceProblem:Equivalentonebodyproblem,Equationsofmotionandfirstintegrals,Classificationoforbits,Differentialequationfortheorbit,Keplerproblem,Differentialandtotalscatteringcross-section,Scattering in aninversesquare force field and Rutherford scattering cross section formula, Scattering in lab and centerofmassframe.

SectionB

HamiltonianFormulation:Legendretransformation,Hamilton'sequationsofmotionandtheirphysicalapplications,Hamilton'sequationsfrom variational principle,Principleofleastaction.

CanonicalTransformations: Point and canonical transformations, Generatingfunctions,Poisson'sbracketsand its canonicalinvariance, Equations of motion in Poisson Bracket formulation, Poissonbracketrelationsbetweencomponentsoflinearandangularmomenta. Harmonic oscillator problem, check for transformation to be canonical and determination of generating functions.

SmallOscillations:Eigenvalueequation, Frequenciesoffreevibrationandnormalmodes,Normalmodefrequenciesandeigenvectorsofdiatomicandlineartri-atomicmolecule.

RigidBodyMotion:Orientationofarigidbody,Orthogonaltransformationsandpropertiesofthe orthogonal transformationmatrix,Eulerangles,Euler'stheorem, Infinitesimalrotation, Rate of change of vector in rotating frame, Components of angular velocity along space and body set of axes. Motion of heavy symmetrical top (Analytical treatment).

Text Books:

Classical Mechanics: H. Goldstein (Narosa Pub.)
Classical Mechanics: J.C. Upadhyaya (Himalaya Pub. House)

ASP 1.1.3POSITIONAL ASTRONOMY

Maximum Marks: External 60Time Allowed: 3 Hours

Internal 20Total Teaching hours: 50

Total 80Pass Marks: 35%

Use of scientific calculators is allowed.

SECTION A

Spherical Trigonometry: The spherical triangle, Terrestrial coordinates, The cosine formula, The sine formula, The analogue formula, The four part formula, Right angled and quadrantal triangles, Polar formulae, Trigonometrical ratios for small angles.

The Celestial Sphere: Altitude and azimuth, Equatorial coordinate system, Ecliptic coordiante system, Galactic coordinate system, Rising and setting of heavenly bodies, Rate of change of zenith distance and azimuth, Twilight.

Time: Sidereal time, Mean solar time and their relation, the sidereal year, The tropical year, The calendar, The Julian date, The equation of time.

Aberration: Law, Annual aberration in ecliptic coordinates, Aberrational ellipse, Aberration in equatorial coordinates, Elliptical motion of the earth and aberration, Measurement of constant of aberration, Diurnal aberration.

Parallax: Astronomical and geocentric latitude, Geocentric parallax, The parallax of the moon, Semi-diameter, Parallax in right ascension and declination, Parallax in zenith distance and azimuth, The solar parallax, Stellar parallax, Effect of parallax on star's longitude and latitude; Effect on stellar right ascension and declination, Measurement of stellar parallax, The parsec and light year.

SECTION B

Precession and Nutation: The phenomena, Effect of precession on right ascension and declination of a star, Nutation in obliquity and its effect on equatorial coordinates of a star, Planetary precession, The mean equator and the mean coordinates of a star, Secular variation and true coordinates of a star. The apparent place of a star.

Proper Motions of the Stars: Relationship between proper motion, tangential velocity and parallax, Radial velocity, Measurement of proper motion, Components of proper motion at different epochs referred to the same equatorial system and referred to the mean equators of two different epochs. Solar motion and parallactic motion, Secular parallax, Solar motion and radial velocity.

Planetary Phenomena: Geocentric motion of a planet, Heliocentric distance of a planet when stationary, Stationary point including orbital inclination, The phases of the planets and the moon.

Eclipses: Eclipses of the moon, Angular radius of shadow cone, The ecliptic limits, calculation of lunar eclipse, Eclipses of the sun, Ecliptic limits, Besselian elements for solar eclipse, Eclipse calculation for any station, Frequency of eclipses, Repetition of eclipses.

Text Books:

Text Book on Spherical Astronomy: Smart, W.M., CambridgeUniversity Press, 1977
Astronomy: Principles and Practice: Roy,A.E. and Clarke, D.C. (3rd Ed.), Institute of Physics Publishing, Bristol and Philadelphia, 1994

ASP 1.1.4 Elective Paper: Option (i)ANALOG ELECTRONICS

Maximum Marks: External 60Time Allowed: 3 Hours

Internal 20Total Teaching hours: 50

Total 80Pass Marks: 35%

Use of scientific calculator is allowed.

SECTION A

Two port network analysis: Active circuit model's equivalent circuit for BJT, Transconductance model: Common emitter. Common base. Common collector amplifiers. Equivalent circuit for FET. Common source amplifier. Source follower circuit(RR1)

Feedback in amplifiers: Stabilization of gain and reduction of non-linear distortion by negative feedback. Effect of feedback on input and output resistance. Voltage and current feedback (RR1)

Bias for transistor amplifier: Fixed bias circuit, Voltage feedback bias. Emitter feedback bias, Voltage divider bias method, Bias for FET(RR1)

Multistage amplifier:Direct coupled CE two stage amplifier. RC coupling and its analysis in mid- high-and low-frequency range. Effect of cascading on bandwidth. Darlington and cascade circuits(RR1)

Oscillators:Feedback and circuit requirements for oscillator, Basic oscillator analysis, Hartley, Colpitts, RC-oscillators and crystal oscillator (RR1)

SECTION-B

Band-pass amplifiers: Parallel resonant circuit and its bandwidth. Tuned primary and tuned secondary amplifiers(RR1)

Power amplifiers: Operating conditions, Power relations, Nonlinear distortion, Class A power amplifier, Push-pull principle, Class B Push pull amplifier(RR1)

Fundamentals of modulation: Frequency spectrum in amplitude modulation, Methods of amplitude modulation, Frequency modulation, Linear demodulation of AM signals, SSB system, AM and FM transmission, Receiving systems(RR1)

Operational amplifiers: Ideal operational amplifier. Inverting and non-inverting amplifiers. Differential amplifiers. CMMR. Internal circuit of operational amplifier. Examples of practical operational amplifier. Operational amplifier characteristics. DC and AC characteristics, slew rate (RR2)

Text Books:

Electronics Fundamentals and Applications: John D. Ryder (5th Ed.), PHI, New Delhi
Linear Integrated circuits: D.Roy Choudary and Shail B.Jain, New age international Publishers

ASP 1.1.4 Elective Paper: Option (ii) REMOTE SENSING

Maximum Marks: External 60Time Allowed: 3 Hours

Internal 20Total Teaching hours: 50

Total 80Pass Marks: 35%

Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examination, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective sections of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carry 10 marks. Section C will carry 20 marks.

Use of scientific calculators is allowed.

SECTION A

History and scope of remote sensing: Milestones in the history of remote sensing, overview of the remote sensing process, A specific example, Key concepts of remote sensing, career preparation and professional development.

Introduction: Definition of remote sensing, Electromagnetic radiation, Electromagnetic Spectrum, interaction with atmosphere, Radiation-Target, Passive vs. Active Sensing, Characteristic of Images.

Sensors: On the Ground, In the Air& in Space, Satellite characteristics, Pixel Size and Scale, Spectral Resolution, Radiometric Resolution, Temporal Resolution, Cameras and Aerial photography, Multispectral Scanning, thermal Imaging, Geometric Distortion, Weather Satellites, Land Observation Satellites, Marine Observation Satellites, Other Sensors, Data Reception.

SECTION B

Microwaves: Introduction, Radar Basics, Viewing Geometry & Spatial Resolution, Image Distortion, Target Interaction, Image Properties, Advanced Applications, Polarimetry, Airborne vs. Spaceborne, Airborne & Spaceborne Systems.

Image Analysis: Visual Interpretation, Digital processing, Preprocessing, Enhancement, Transformations, Classification, Integration.

Applications: Agriculture—Crop Type Mapping and Crop Monitoring; Forestry---Clear cut Mapping, Species identification and Burn Mapping; Geology---Structural Mapping & Geological Units; Hydrology-----Food Delineation & Soil Moisture; Sea Ice----Type & Concentration, Ice Motion; Land Cover----Rural/Urban Change, Biomass Mapping; Mapping-----Planimetry, DEMs, Topo Mapping; Oceans & Coastal-----Ocean features, Ocean Colour, Oil Spill Detection.

Text Books:

Introduction to Remote Sensing : James B. Cambell
Fundamentals of Remote Sensing: Natural Resources, Canada Centre of Remote Sensing.

ASP 1.1.4 Elective Paper: Option (iii)MICROWAVE AND ITS PROPAGATION

Maximum Marks: External 60Time Allowed: 3 Hours

Internal 20Total Teaching hours: 50

Total 80Pass Marks: 35%

Use of scientific calculators is allowed.

SECTION A

Microwave linear beam tubes: Conventional vacuum tubes, Klystrons, resonant cavities, velocity modulation process, branching process, output power and beam loading; multi cavity klystron amplifiers, reflex klystrons, helix travelling wave tubes, slow wave structures.

Microwave crossed field tubes: Magnetron oscillators: cylindrical, linear and coaxial, forward wave crossed field amplifier, backward wave crossed field amplifier, backward wave crossed field oscillator, their principle of operation and characteristics.

Microwave transistor and tunnel diodes: Microwave bipolar transistors, physical structures, configurations, principles of operation, amplification phenomena, power-frequency limitations, heterojunction bipolar transistors, physical structures, operational mechanism and electronic applications, microwave tunnel diodes, principles of operation, microwave characteristics.

Microwave field effect transistors: Junction field effect transistors, metal semiconductor field effect transistors, high electron mobility transistors, metal oxide semiconductor field effect transistors, physical structures, principle of operation and their characteristics. MOS transistor and memory devices: NMOS, CMOS and memories. Charged coupled devices: Operational mechanism, surface channel CCD's dynamic characteristics.

SECTION B

Transferred electron devices: Gunn effect diodes, Ridley-Walkins-Hilsum theory, modes of operation, LSA diodes, InP diodes, CdTe diodes, microwave generation and amplification.

Avalanche transit time devices: Read diode, IMPATT diodes, TRAPATT diodes, BARITT diodes, their physical structure, principle of operation and characteristics.

Microwave measurements: Measurement of impedance, attenuation, insertion loss, coupling and directivity, frequency, power and wavelength at microwave frequencies.

Microwave transmission lines: Transmission line equations and solutions, reflection coefficient and transmission coefficient, standing wave and standing wave ratio, line impedance and admittance, Smith chart, impedance matching. Microwave cavities, microwave hybrid circuits, directional couplers, circulators and isolators.