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1- Research Topic: Chaos near resonances in Earth satellite orbits: Implications for the Debris Problem

Resonances are regions in the phase space of a dynamical system in which the frequencies of some angular variables become nearly commensurate integer ratios. Such regions have a profound effect on the motions of the system, giving rise to a rich spectrum of highly complicated dynamical behaviors. Recently, it has been realized that lunisolar secular resonances (i.e., those cased by the Moon and the Sun on long timescales) are of particular importance in the medium-Earth orbit regime. Studying the long-term effects of lunisolar secular resonances is at the core of this research, not only because we need to understand their stability properties, but also because we would like to know whether they could be used (and how) for eventually deorbiting satellites, by forcing them to slowly drift towards high eccentricities and different inclinations.    

2- Main Results:

In Rosengren et al. (2015; MNRAS), we find that secular resonances, involving linear combinations of the frequencies of nodal and apsidal precession and the rate of regression of the lunar nodes, occur in profusion so that the inclination-eccentricity phase space of the navigation satellite constellations is threaded by a devious stochastic web. We show that chaos, the source of orbital instability observed in the nominal post-mission disposal orbits of these satellites, ensues where the lunisolar resonances overlap. In Daquin et al. (2015; arXiv), we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions and give insight into the structure, extent, and evolution of the chaotic regions. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales. The precarious state of the GNSS constellations, perched on the threshold of instability, makes it understandable why all efforts to define stable graveyard orbits, especially in the case of Galileo, were bound to fail; the region is far too complex to allow of an adoption of the simple geosynchronous disposal strategy. 

3- References: (selected publications and talks)

- Daquin, J., Rosengren, A.J., Deleflie, F., Alessi, E.M., Valsecchi, G.B., Rossi, A.: The dynamical structure of the MEO region: long-term stability, chaos, and transport. 2015.

- Rosengren, A.J., Alessi, E.M., Rossi, A., Valsecchi, G.B.: Chaos in navigation satellite orbits caused by the perturbed motion of the Moon. Monthly Notices of the Royal Astronomical Society. 449, 3522–3526, 2015.

- Daquin, J., Rosengren, A.J., Deleflie, F., Rossi, A.: Diffusive chaos in navigation satellites. Presented at the Chaos, Complexity and Transport Conference, Marseilles, France, 1-5 June 2015

- Rosengren, A.J., Daquin, J., Alessi, E.M., Valsecchi, G.B., Rossi, A., Deleflie, F.: The onset of dynamical instability and chaos in navigation satellite orbits. Presented at the American Astronomical Society Division on Dynamical Astronomy Meeting, Pasadena, California, 3-7 May 2015


1. The resonant structure of the medium-Earth orbits of the four navigation constellations (see Rosengren et al. 2015, MNRAS, for more details).

2. Dynamical evolution of three orbits superimposed on the FLI map at the GLONASS semimajor axis, showing long-term stability, chaotic motions, and transport in the inclination and eccentricity phase space (see Daquin et al. 2015, arXiv, for more details).

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