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Celestial Mechanics

PROGRAM of

'Celestial Mechanics'

Forth Year


  • Subject of Celestial Mechanics. Relation between Celestial Mechanics and Other Parts of Astronomy. Mean Problems of Celestial Mechanics. Brief History of Its Development.

Non-Perturbed Motion

  • Statement of Problem of Two Bodies. Differential Absolute Coordinates Equations of the Problem. Differential Relative Coordinates Equations. Integrals of Squares. Integral of Energy. Laplace Integrals. General Integral of Non-Perturbed Motion. Determination of Arbitrary Constants by Initial Conditions. General Equation of Non-Perturbed Orbit. Orbital Coordinates, Their Bounds with Spatial Ones. Velocity of Material Point on the Orbit, Its Components. Other Integration Methods of Non-Perturbed Motion Differential Equations; Bine Equation for Case of Non-Perturbed Motion.

Investigation of Non-Perturbed Motion

  • Types of Non-Perturbed Orbits. Dependence of Orbit Types on Value and Direction of Initial Velocity. Keplerian Elements. Evolution of Orbit by Change of Value and Direction of Initial Velocity, by Change of Radius Vector. Ellipsical Motion, Kepler Equation. Basic Formulas of Ellipsical Motion. Hyperbolical Motion. Limit and Confluent Cases of Non-Perturbed Motion: Circular Motion, Parabolic Motion, Straight-Line Motion. Keplerian Elements for Any Type of Non-Perturbed Orbit by Initial Conditions.

Non-Perturbed Elliptical Motion Serieses

  • Lagrange Series. Laplace Limit. Use of Lagrange Series for Kepler Equation. Coordinates Expansion in Terms of Eccentricity Powers. Expansion of Velocity and Its Components. Fourier Series Expansion of Elliptical Motion Coordinates.

Determination of Non-Perturbed Orbit by Three Observations

  • Main Ideas of Lagrange-Gauss Method. Equation for Heliocentric Distances Determination. Determination of Elements by Second and Third Heliocentric Locations.

Elements of Perturbed Motion Theory

  • Statement of the Main Problem of Celestial Mecanics. Motion Differential Equations in Absolute Coordinates. Force Function and Its Features. Integrals of System Center of Mass Motion, Invariable Laplace Plane.Integrals of Squares, Integrals of Energy. Lagrange-Jackobi Equation. Equation of System of Bodies Motion in Barycentric Coordinates, in Relative Coordinates. Equation in Jackobi Coordinates. Perturbing Function. Newton Equation for Osculating Elements. The Case of Central Perturbing Force. The Case of Elliptical Motion. The Case of Perturbing Force of Medium Resistance. Derivation of Lagrange Equations, Methods of Their Integration. Expansion of Cartesian Coordinates in Terms of Perturbation, Variational Method. Structure of Elements Perturbation: Order of Perturbation: Secular, Periodical, Compound Ones.

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