VII Semester 2+2, VIII Semester 2+2

**INTRODUCTION.**

Subject, Problems and Methods in Stellar Astronomy.
Observed Characteristics of Stars. Time Dependence of Characteristics.

**STELLAR STATISTICS.**

Distribution Functions and Some of their
Characteristics. Univariate and Multivariate Distributions.
Transformation of Variables. Problems in the Statistical Description
of the Galactic System. Apparent Magnitude and Absolute Magnitude
Distributions. The Total Number of Stars. Integral Equations of Stellar
Statistics. Basic Equations in an Absolutely Transparent Medium. The
Normal Form. General Solution of the Space Density Function. Analytical
and Numerical Methods in Finding the Solution. Interstellar
Absorption Low in Continuous and Discontinuous Medium. Effect of Interstellar Absorption
on the Space Density Function. Fluctuations of the Apparent Luminosity of
the Galactic Field - Basic Equation,
the Equation for Moments of the
Differential Luminosity Function.

**STELLAR KINEMATICS.**

Relationships between Observational and
Descriptive Kinematic Characteristics. Transformations of Coordinate
Frames. Local Centroid and Residual Velocities. Local Solar Motion in the
Galaxy - Determination of the Motion Elements from Radial Velocities,
Determination of the Solar Apex from Annual Proper Motions. Statistical
Parallaxes. Tau and Nu Components of Annual Proper Motions. Mean Annual Parallaxes
from Tau and Nu Components.
Residual Velocity Distribution - Spherical Distribution, Two Star Stream Hypothesis,
Ellipsoidal
Distribution. Quadratic Form Transformation. Determination of the Velocity
Ellipsoid from Observations. Local Field of Centroid Velocities - the
Helmholtz Theorem for Stellar Systems. Plane-Parallel Motion.
Determination of the Plane-Parallel Motion from
Observations - Radial Velocity Method and Annual Proper Motion Method. Galactic Rotation.
Asymmetry of Stellar Motions. General Formulae of Galactic Rotation. Local
Field of the Barotropic Rotation of the Centroid. The Interpretation of Oort's
Formulae. Dynamical Interpretation of the Rotation Parameters. Dynamical Constants
of the Galaxy. Analysis of Oort Coefficients.

**DYNAMICS OF STELLAR SYSTEMS.**

Modelling of Gravitational Systems.
Basic and Perturbative Forces. Cumulative
Effect of Perturbative Forces. Relaxation. Statistical Stellar Dynamics.
Phase Density Function. Basic Equation of Stellar Dynamics, Jeans'
Theorem. General Solution of the Basic Equation. Direct Problem
of Stationary Systems. Quasiergodic Systems. Asymmetric Potential.
Systems with Rotating Symmetry. Systems with Spherical Symmetry.
Elements of Ellipsoidal Dynamics for Stationary
Systems. Theoretical Velocity Ellipsoid. Potential
Function. Comparison with Observations. Quasiintegrals. Stellar Orbits in
the Galactic Disk. Epicyclical Approximation. Stability of Circular Orbits.
Stability of Stellar Condensations. The Virial Theorem and
Application to Stellar Systems.
Stellar Hydrodynamics. Moment Equations in Generalized Coordinates.
Interpretation of the Velocity
Asymmetry.

**STRUCTURE OF THE GALAXY.**

Populations and Sub-Systems.
The Central
Region - the Stellar Bulge with a Gaseous Disk. The Core. The Disk - Stars in
the Galactic Disk, Open Clusters, Associations, Grouping of Young Stars,
Interstellar Medium. Spiral Structure. Vertical Structure
of the Disk. The Halo - Stars in the Halo, Globular
Clusters. Quasistationary Models of the Galaxy. Polytropic Models. Rotation Curve and
Mass of the Galaxy. The Schmidt Model. Other Models. The Dark Matter.

**GRAVITATIONAL INSTABILITY.**

Analysis of Small Perturbations - Mode
Method and Method of Integral Transformations. Instability of
Interstellar Medium - Linearization of Basic Equations, the Jeans
Instability Criterion. Character of Long Wave Evolution. The Density Wave Theory of
the Galactic Spiral Structure - Description of Spiral Perturbation, the
Model of the Infinitely Thin Disk, Resonances, Velocity Field of Spiral Waves.
Asymptotic Solution of Poisson Equation for Small Perturbations. Stability
of Gaseous Disks. Stability of Stellar Disks. Group Velocity of Spiral
Waves. Theoretical Models and Observations.