Semester: VII (2+2), VIII (2+2)

**INTRODUCTION.** Theoretical Astronomy as a Part of Science that Deals
with Motions of Celestial Bodies. Gravitational Theory of Motions of Planetoids and
Comets. Units for Mass, Length and Time. Differential Equations of
Motions of Celestial Bodies and their Numerical Integration.

**STABLE MOTION.** Differential Equation of Kepler's Motion and its Integral. Different
Kinds of Orbits and Movements along them. Position and Velocity of a Body.
Orbiting Elements as Constants of Integration. Basic Systems of Elements.
Initial Conditions for Motions and and Determination of Elements by Using them.
Lagrange's Indirect Elements. Relation Between Sector Area and Triangle in an Elliptical Orbit.

**CALCULUS OF EPHEMERIDES.** Ephemerides of Planetoids and Comets; their
Explicite and Approximate Determination; Calculus of the Position.
The Date of Oposition and Time of Perihelion Passage. Direct Way of Computing
and Numerical Integration of Differential Equation of Kepler's Motion.
Observed and Calculated Possitions of a Body.

**CALCULUS OF ORBITS.** Stable Orbits of Planetoids and Comets. Basic
Principles of their Determination on the Basis of Observations Made from
Earth. Calculus of Ephemerides as the Way of Determination of Initial
Conditions of Motion in a Stable Orbit.

a) Calculus of the Circular Orbit (Gauss-Encke's Method),

b) Calculus of the Elliptical Orbit (Gauss-Encke's Method,
Laplace-Leuschner's Method,
and Veisel's Method),

c) Calculus of the Parabolic Orbit (Olbers' Method).

**CORRECTIONS OF KEPLER'S ORBITS.** Approximation of a Real Motion by Using
Stable Orbits. Accuracy of Orbits Computation and Results Corrections.
Correction of Orbital Elements. Correction of Initial Conditions of Motions.

**CALCULUS OF SPECIAL PERTURBATIONS.** Real Motion of Planetoids and Comets
(Gravitational Theory). Perturbations and their Influence. Two Basic Ways
to Calculate Special Perturbations. Use of the Numerical Integration of
First and Second Order Differential Equations. First Order Calculus,
Some Corrections and Successive Extrapolations. Direct Way to Calculate Perturbing
Coordinates and the Influence of Perturbations on the Rectangular Coordinates.
Perturbing Acceleration and its Computation. Calculus of Special
Perturbations in Orbital Elements. Variations of Basic Methods; Choice of
Parameters for Variations (Choice of Osculating Elements).
Review onto the Task of Gravitational Theory of Motions of
Planetoids and Comets.