Celestial Bodies Dynamics
0
2023-2024
01019532
Physics
Portuguese
Face-to-face
6.0
Elective
1st Cycle Studies
Recommended Prerequisites
Classical Mechanics, Linear Algebra and Analytic Geometry, Infinitesimal Analysis.
Teaching Methods
15 weeks of classes (60 h), distributed as follows:
Lectures (T): 2 h / week;
Exercises (TP): 2 h / week
Final assessment:
• 100.00% TP (Final Exam).
Learning Outcomes
This course aims at letting the students understand the evolution of stellar and planetary systems: orbital interactions, spin movements, resonances, chaos, tidal forces, interaction with planetesimals discs and / or magnetic fields.
Familiarize students with modern concepts and tools for studying the dynamics of celestial bodies, developing mathematical and geometric reasoning, and solidifying many of the knowledge about the laws of physics previously acquired.
Work Placement(s)
NoSyllabus
Part I - The two-body problem
Demonstration of Kepler's laws
Kepler's equation
Elliptical expansions
Hill variables
Delaunay variables
Lagrange Planetary Equations
Part II - The N-body problem
Disturbing function
Expansion into Legendre polynomials
Expansion in Laplace coefficients
Perturbation theory
Secular perturbations
Mean-motion resonances
Hierarchical systems
Generalization to N-body systems
Symplectic integrators
Part III - Bodies with structure
Kinetic energy of the free body
Euler angles
Andoyer variables
Potential energy of the rigid body
Precession of the equinoxes
Spin-orbit resonances
Cassini states
Love numbers
Centrifugal potential
Tidal potential
Tidal dissipation.
Head Lecturer(s)
Alexandre Carlos Morgado Correia
Assessment Methods
Assessment
Exam: 100.0%
Bibliography
- Resumos das aulas colocados no InforDocente;
- Murray & Dermott, “Solar System Dynamics”, Cambridge University Press;
- Cole & Woolfson, “Planetary Science”, IoP (Institude of Physics Publishing);
- Morbidelli, “Modern Celestial Mechanics . Apects of Solar System Dynamics”, CRC Press.