Chaotic Dynamics of Resonant Satellite Orbits

Project Description:

The long-term orbital evolution of artificial satellites in Low Earth Orbit (LEO) is strongly affected by resonances produced by the coupling between the Earth’s oblateness and solar radiation pressure (SRP). These resonances can significantly alter the orbital elements of satellites and debris, potentially leading to large variations in eccentricity and inclination. Such effects are particularly important for understanding natural deorbiting mechanisms and for addressing the growing problem of space debris [1,2]. Since the pioneering work on collisional cascades in Earth orbit [3], understanding the dynamical processes governing the long-term stability of satellite orbits has become a key topic in space sustainability. The aim of this project is to investigate the nonlinear and chaotic dynamics associated with resonant satellite motion in simplified Hamiltonian models describing the combined effects of solar radiation pressure and the Earth’s oblateness. Starting from existing resonant Hamiltonian formulations, the student will re-derive integrable approximations for selected resonances and explore their dynamical structure. Numerical investigations will then be carried out to study the transition from regular to chaotic motion as system parameters vary. A central part of the project will be the numerical analysis of phase space using modern chaos detection techniques. In particular, the Smaller Alignment Index (SALI) will be employed to distinguish between regular and chaotic trajectories in the resonant models [4,5]. The student will compute phase space portraits and bifurcation diagrams illustrating the evolution of equilibrium points, separatrices, and resonance overlap as functions of orbital parameters, especially the satellite area-to-mass ratio (A/m). These structures will then be related to representative orbital trajectories that may lead to rapid increases in eccentricity and eventual atmospheric reentry. The anticipated outcomes of the project include the visualization of resonant phase space structures, the identification of chaotic regions that facilitate orbital transport, and a better understanding of how chaotic dynamics can contribute to natural deorbiting processes. The project combines analytical calculations with numerical simulations and will provide the student with valuable experience in nonlinear dynamics, computational modelling, and astrodynamical applications. References [1] E.M. Alessi, G. Schettino, A. Rossi, G.B. Valsecchi, MNRAS, 473. 2407–2414, 2018. [2] I. Gkolias, E.M. Alessi, C. Colombo, Celest. Mech. Dyn. Astron., 132, 55, 2020. [3] D.J. Kessler, B.G. Cour-Palais, J. Geophys. Res., 83, 2637–2646, 1978. [4] Ch. Skokos, J. Phys. A, 34, 10029–10043, 2001. [5] Ch. Skokos, T. Manos, Lect. Notes Phys., 915,129–181, 2016.

Research Area:

Astronomy

Project Level:

Honours

This Project Is Offered At The Following Node(s):

(UCT)

Special Requirements:

• Good computational skills in a programming language (e.g., Python, C, or MATLAB). • Basic knowledge of Hamiltonian dynamics and chaos theory.