CBL - Campus del Baix Llobregat

Projecte llegit

Títol: Dinámica orbital y comportamiento resonante de la población de asteroides Thule

Estudiants que han llegit aquest projecte:

Director/a: RODRÍGUEZ DEL RÍO, ÓSCAR

Departament: MAT

Títol: Dinámica orbital y comportamiento resonante de la población de asteroides Thule

Data inici oferta: 03-02-2026     Data finalització oferta: 03-10-2026


Estudis d'assignació del projecte:
    GR ENG SIS TELECOMUN
    GR ENG SIST AEROESP
    GR ENG TELEMÀTICA
Tipus: Individual
 
Lloc de realització: EETAC
 
Paraules clau:
Frequency analysis, Orbital dynamics, Numerical Simulation
 
Descripció del contingut i pla d'activitats:
This project invites the student to explore the Thule asteroids-one of the most intriguing dynamical families in the Solar System-through the lens of modern dynamical systems theory. The Thules occupy a 4:3 mean-motion resonance with Jupiter, completing four orbits around the Sun for every three of Jupiter's. Far from being a simple orbital coincidence, this resonance creates a rich dynamical environment shaped by stability islands, resonant libration, and long-term protective mechanisms that prevent close encounters with the giant planet.

The student will investigate how the 4:3 resonance structures the motion of the Thules, why their orbits cluster into characteristic configurations in a rotating reference frame, and how invariant manifolds and resonant tori organize their long-term evolution. Using numerical simulations and phase-space analysis, the project will examine the stability of these orbits, the role of Jupiter's perturbations, and the subtle interplay between resonance, eccentricity, and inclination.

The work may also explore how non-gravitational effects-such as the Yarkovsky drift-interact with the resonant web, potentially transporting objects into or out of the Thule region. By comparing different dynamical models (from simplified restricted three-body formulations to more complete N-body integrations), the student will evaluate which structures are robust and which depend sensitively on model assumptions.

This is an ideal project for a student interested in celestial mechanics, resonant dynamics, and the geometric structures that shape the architecture of the Solar System. The Thule group offers a natural laboratory where theory, simulation, and dynamical intuition come together beautifully.
 
Overview (resum en anglès):
This Bachelor's Thesis investigates the orbital dynamics of the Thule asteroid population using the Circular Restricted Three-Body Problem (CRTBP), considering the Sun-Jupiter system as the reference model. A complete methodology was developed, including the acquisition of real orbital elements from the JPL Small-Body Database, their transformation into the rotating reference frame, and the numerical integration of the equations of motion in MATLAB. The resulting trajectories were analysed through the Jacobi constant, three-dimensional representations and frequency analysis using the Fast Fourier Transform (FFT). Finally, the results were compared with restricted N-body simulations. The study shows that the analysed asteroids exhibit stable long-term resonant behaviour associated with the 4:3 mean-motion resonance with Jupiter, confirming that the CRTBP provides an appropriate framework for describing the main dynamical structures governing the Thule asteroid population.

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