Syllabus
* Elements of perturbation theory.
Osculating orbital elements, Lagrange and Gauss form of the equations of perturbation theory, nonsingular elements, periodic and secular part of perturbations. Simple theory of artificial satellite motion in an atmosphere.
* General form of planetary gravitational field.
General solution of Laplace equation in spherical coordinates, expansion in spherical harmoncs. Stokes coefficients. Gravitational field of planets, satellites and the Sun. Secular perturbations due to the J2 and J3 potentials.
* Coordinate systems for the problem of N bodies.
Relative and Jacobi coordinates. Kozai problem, Kozai resonance, applications.
* Lagrange-Laplace secular theory of planetary motion.
Secular part of the perturbing function for 2 and N planets. Equations of motion, integrals. Solution of linear problem, fudamental frequencies of the planetary system. Motion of an asteroid in the planetary field, linear secular resonances, application.
* Precession of planet and Cassini laws.
Gravitational torque due to the Sun, averaged value over rotational and revolution cycles. Hamiltonian formulation (obliquity and precession angle), Colombo top model, integrability. Aplications for planets, satellites and asteroids.
Annotation
Theory of perturbations, Lagrange and Gauss form of equations, nonsingular elements, secular and periodic perturbations, satellite motion in an atmosphere, gravitational field in multipole expansion, satelite motion in J2 and J3 potentials, relative coordinates, Kozai problem, Lagrange-Laplace secular theory of planetary motion. Cassini laws,
Colombo top model.