INTRODUCTION. Problems in Celestial Mechanics and the Theory of Earth's Artificial Satellites Motion. Kepler's Laws. Newton's Law of Gravity.

TWO BODIES PROBLEM AND THE STABLE ORBITING OF PLANETS AROUND THE SUN. Determine the Problem. Both Vectorial Integrals of Differential Equation of Stable Heliocentric Planetary Motion. Geometric Meaning of these Vectorial Integrals. Sixth Scalar Integral of Vectorial Differential Equation. Basic Integrals of Differential Equation of Stable Planetary Motion around the Sun in their Final Form. Calculus of Vectorial Elements from Initial Conditions. The Satellites Problem Reduced to the Two Bodies Problem. The Connection between Vectorial and Elliptical Elements of Planetary Motion.

THE PROBLEM OF N BODIES. Determine the Problem. Basic Integrals of the Problem of N Bodies. Translational Motion of the Solar System. Laplace's Invariable Plane.

FUNDAMENTAL THEORY OF PLANETARY PERTURBATIONS. Differential Equations of Heliocentric Planetary Motion. Basic Vectorial Equations of Perturbations. Lagrange's Brackets and their Properties.

INTRODUCING VECTORIAL ELEMENTS INTO THE CALCULUS OF PERTURBATIONS. Computation of Lagrange's Brackets of Vectorial Elements. Differential Equations of Vectorial Elements.

SURVEY OF CLASSICAL PERTURBATIONS THEORY. Differential Equations of Elliptical Elements. Integration of Differential Equations of Planetary Perturbations. Classification of Perturbations.

SECULAR PERTURBATIONS. Importance of Secular Perturbations. Differential Equations of Secular Perturbations. Secular Perturbations of Planets. Some Basic Conclusions from those Integrals.

LAPLACE'S EQUATION. SPHERICAL FUNCTIONS. Laplace's Operator in Orthogonal Coordinates. Gravitational Potential. Laplace's Equation. Spherical Functions. Legendre's Polynomials. Representation of Functions at Spherical Surface by their Series on Spherical Functions. Additional Theorem of Spherical Functions.

REPRESENTATION OF GRAVITATIONAL POTENTIAL. Representation of Rigid Body Potential by Series on Spherical Functions. Gravitational Potential of Spheroid. Potential of the Earth's Attraction. Earth's Ellipsoid. Normal Gravitational Potential of the Earth.

PERTURBATIVE ACCELERATION BECAUSE OF EARTH'S ELLIPTICITY. Coordinates of Perturbative Acceleration in Representation of the Earth's Normal Potential.

DIFFERENTIAL EQUATIONS OF PERTURBATIVE MOTION. Differential Equation of Perturbative Motion of the Earth's Artificial Satellite. Differential Equations of Elliptical Orbital Elements of the Earth's Artificial Satellite with Coordinates of Perturbative Acceleration. Equations of Longitude of the Ascending Node, Parameter and Inclination. Equations of Eccentricity, True Anomaly and Argument of Pericentre. Equations of Lambda1 and Lambda2. Equation of Latitude Argument. Solving the System of Equations by Using the Method of Successive Approximations.

SECULAR PERTURBATIONS OF SATELITES. Secular Perturbations of the Earth's Artificial Satellite Elliptical Orbit. Secular Perturbations Caused by Noncentral Earth's Attraction. Perturbations of Orbiting Period of an Elliptical Orbit. Draconic Period. Siderial Period at Ascending Node.