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Course, academic year 2023/2024
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Celestial Mechanics II - NAST011
Title: Nebeská mechanika II
Guaranteed by: Astronomical Institute of Charles University (32-AUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:4/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: prof. RNDr. David Vokrouhlický, DrSc.
doc. Mgr. Miroslav Brož, Ph.D.
Classification: Physics > Astronomy and Astrophysics
Comes under: Doporučené přednášky 1/2
Co-requisite : NAST005
Annotation -
Last update: T_AUUK (23.03.2015)
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.
Course completion requirements -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (07.06.2019)

Oral examination preceded by a short written exercise.

Literature -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (04.01.2019)

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

Teaching methods - Czech
Last update: T_AUUK (31.03.2008)


Requirements to the exam - Czech
Last update: prof. RNDr. David Vokrouhlický, DrSc. (06.10.2017)

Zkouška sestává z písemné a ústní části. Písemná část obvykle představuje vyřešení příkladu. Nesplnění písemné části však nevylučuje úspěšné složení zkoušky.

Syllabus -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (04.01.2019)
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.

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