State of the Art

Recent studies on space debris show the occurrence of a plethora of dynamical phenomena: the overlapping of resonances and the onset of chaos, the existence of a web-like structure of luni-solar resonances, the chaotic variation of the orbital elements, the occurrence of bifurcations of equilibria, the existence of libration regions which lead to excursions in the eccentricity, the chaotic transport in the phase space. These intricate dynamics exists, for examples, in the neighbourhood of GNSS constellations. Despite the fact that the MEO region will be populated by four complete constellations, namely GPS, GLONASS, Galileo and BeiDou, there are no internationally agreed mitigation guidelines, as for LEO and GEO. Thus, it is mandatory to understand the dynamics of these objects. Past approaches were based mainly on deriving single or double-averaged (over short period terms) forms of the equations of motion. Such derivations, dating back to the 60’s, have been refined over the years. These approaches are able to identify critical solutions depending on the particle’s major semi-axis, eccentricity and inclination, as well as the main secular frequencies of motion, as induced by the Earth’s oblateness, as well as luni-solar secular perturbations. However, an important drawback of these analytical approaches is their failure to characterise the chaotic nature of the orbital dynamics close to particular resonances. The study of the chaotic dynamics, as well as its consequences for the long term diffusion of populations of space debris, becomes particularly important for highly inclined orbits, where, luni-solar resonances lead, in particular, to domains of extended resonance overlap. A complete investigation for every Earth orbital region is still incomplete. Furthermore, the use of perturbation theory will allow the study of the separation of nearby orbits in the fully non-linear regime.


WP3 covers all activities related to dynamic modelling, resonances and long term evolution of space objects in different orbital regimes and how this can be exploited to dispose of space debris. It includes the coupling of natural dynamics with passive and/or active disposal strategies.

Research Output

Margheri, A. and Misquero, M. (2020), A dissipative Kepler problem with a family of singular drags. Mech. Dyn. Astr. 132, 17, 29 March 2020,

Ortega, R. and Misquero, M. (2020), Some Rigorous Results on the 1:1 resonance of the spin-orbit Problem, SIAM J. Appl. Dyn. Syst., In press, Accepted on 2 July 2020, Preprint available at

Misquero, M. (2020), The spin-spin model and the capture into the double synchronous resonance, Nonlinearity, In press, Accepted on 26 October 2020, Preprint available at

Celletti, A., Pucacco, G., & Vartolomei, T. (2020). Proper elements for space debris, Submitted at Celestial Mechanics and Dynamical Astronomy.

Efthymiopoulos, C., Legnaro E., Daquin, J., and Gkolias, I.: A deep-dive into the 2g+h resonance (preprint).

Legnaro, E., and Efthymiopoulos, C.: Analytical theory for Inclination dependent Lunisolar Resonances (preprint).

Paoli, R. (2020) The dynamics around extended bodies: tools and techniques. Presented at the Stardust-R Global Virtual Workshop I (GVW-I), Online. 7-10 Sep. 2020,

Peñarroya, P., Vyas, S., Paoli, R., & Kajak, K. M. (2020) Survey of Landing Methods on Small Bodies : Benefits of Robotics Manipulators to the Field.Poster presented at the International Symposium on Artificial Intelligence, Robotics and Automation in Space (i-SAIRAS), Online. 19-23 Oct. 2020, DOI: 5281/zenodo.4275978.

Paoli, R. (2020) The dynamics around the Earth and other extended bodies. Presented at The Conferences of the Doctoral Schools of the Romanian University Consortium, Online. 22-23 Oct. 2020,

Paoli, R. & Gales, C. (2021) Semi-analytic theory for Solar Radiation Pressure semi-secular resonances. (In preparation).

Paoli, R. & Gales, C. (2021) Spherical Harmonic coefficients for some constant density polyhedra and their gravitational influence. (In preparation).