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Projecte llegit

Títol: Estudi de la ressonància 3:2 dels asteroides Hilda en el sistema Sol-Júpiter

Estudiants que han llegit aquest projecte:

Director/a: RODRÍGUEZ DEL RÍO, ÓSCAR

Departament: MAT

Títol: Estudi de la ressonància 3:2 dels asteroides Hilda en el sistema Sol-Júpiter

Data inici oferta: 19-01-2026     Data finalització oferta: 19-09-2026


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 Hilda asteroids-one of the most intriguing dynamical families in the Solar System-through the lens of modern dynamical systems theory. The Hildas occupy a 3:2 mean-motion resonance with Jupiter, completing three orbits around the Sun for every two 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 3:2 resonance structures the motion of the Hildas, why their orbits cluster into characteristic triangular 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 Hilda 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 Hilda 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 Hilda asteroid population, which is characterised by a 3:2 mean-motion resonance with Jupiter. The analysis is performed using the planar circular restricted three-body problem, considering the Sun-Jupiter system and treating the asteroids as bodies of negligible mass. Real orbital data obtained from the Jet Propulsion Laboratory Small-Body Database are used to transform the initial conditions into the Sun-Jupiter rotating reference frame and numerically integrate the equations of motion.

The study examines the orbital distribution of the Hilda population and compares several members of the Hilda and Schubart collisional families. The results show a strong concentration of the semimajor axis around 3.97 AU, whereas eccentricity and inclination exhibit a wider dispersion. The resulting trajectories display differences in their geometry and libration amplitude, although all the analysed asteroids remain confined within the resonant region throughout the integration interval.

Frequency analysis based on the fast Fourier transform reveals a dominant peak close to the normalised frequency of 1.5, quantitatively confirming the 3:2 resonance with Jupiter. The results demonstrate that the model qualitatively reproduces the main dynamical features of the Hilda population. Nevertheless, a more accurate description of certain objects and their long-term orbital evolution would require three-dimensional, elliptic or N-body models.

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