Celestial Mechanics II - NAST011
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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.
Last update: T_AUUK (23.03.2015)
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Oral examination preceded by a short written exercise. Last update: Vokrouhlický David, prof. RNDr., DrSc. (07.06.2019)
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D. Brouwer, and G. Clemence, Methods of Celestial Mechanics, Academic Press, New York, 1961
W.M. Smart, Celestial Mechanics, Longmans, Green and Co., 1953
V. Szebehely, Theory of Orbits, Academic Press, New York, 1967
C.D. Murray, and S.F. Dermott, Solar System Dynamics, Cambridge University Press, 2008 Last update: Vokrouhlický David, prof. RNDr., DrSc. (04.01.2019)
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Přednáška. Last update: T_AUUK (31.03.2008)
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Zkouška sestává z písemné a ústní části. Písemná část obvykle představuje vyřešení příkladu. Nesplnění písemné části však nevylučuje úspěšné složení zkoušky. Last update: Vokrouhlický David, prof. RNDr., DrSc. (06.10.2017)
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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. Last update: Vokrouhlický David, prof. RNDr., DrSc. (04.01.2019)
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