Celestial Bodies Dynamics

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)

No

Syllabus

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.