Testing the FLI in the region of the Pallas asteroid family

Gachet

et al. 2016

We consider Earth satellite orbits in the range of semi-major axes where the perturbing effects of Earth's oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the longterm orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of first importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations, and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.

Section: Secular Dynamics Of Medium-and High-earth Orbitsmentioning

confidence: 99%

From Order to Chaos in Earth Satellite Orbits

Gkolias

Gachet

et al. 2016

“…Figures 5 and 6 present several dynamical quantities of interests, in a series of maps, ‡ ‡ for semimajor axes and parameters near two sample disposal orbits of Section 2: the FLIs (Froeschlé et al 2000;Todorović & Novaković 2015), characterizing the degree of hyperbolicity; the Lyapunov time, an estimate of the prediction horizon (Lighthill 1986); and collision time. The FLIs of all regular orbits appear with the same dark blue colour, while light blue corresponds to invariant tori, yellow and red to chaotic regions, and white to collision orbits.…”

Section: Numerical Stability Analysismentioning

confidence: 99%

“…5 and 6, have been obtained by varying only the initial inclination and eccentricity, with the initial phases (t 0 , Ω, ω) being fixed for all computed FLI. Given the inherent difficulty to capture the dynamics of the whole six-dimensional phase space in a plane of dimension two, we must settle for only a partial insight into the dynamical structure (Todorović & Novaković 2015;Richter et al 2014). We now fix the action-like quantities to their approximate nominal values, along with the epoch date, and investigate the geometrical organisation and coexistence of chaotic and regular motion in the Ω-ω phase space (Fig.…”

Section: Numerical Stability Analysismentioning

confidence: 99%

See 1 more Smart Citation

Galileo disposal strategy: stability, chaos and predictability

Rosengren

Mon. Not. R. Astron. Soc.

Tsiganis

et al. 2016

Recent studies have shown that the medium-Earth orbit (MEO) region of the Global Navigation Satellite Systems is permeated by a devious network of lunisolar secular resonances, which can interact to produce chaotic and diffusive motions. The precarious state of the four navigation constellations, perched on the threshold of instability, makes it understandable why all past 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. We retrace one such recent attempt, funded by ESA's General Studies Programme in the frame of the GreenOPS initiative, that uses a systematic parametric approach and the straightforward maximumeccentricity method to identify long-term stable regions, suitable for graveyards, as well as large-scale excursions in eccentricity, which can be used for post-mission deorbiting of constellation satellites. We then apply our new results on the stunningly rich dynamical structure of the MEO region toward the analysis of these disposal strategies for Galileo, and discuss the practical implications of resonances and chaos in this regime. We outline how the identification of the hyperbolic and elliptic fixed points of the resonances near Galileo can lead to explicit criteria for defining optimal disposal strategies.

“…This scalpel has been used extensively over the past decade across different dynamical problems, ranging from Symplectic Maps studies to Dynamical Astronomy, including Astrodynamical practical problems [38][39][40][41]. The work of C. Froeschlé, M. Guzzo and E. Lega over the last decade provides a good overview of its possibilities and range of applications.…”

Section: Highly Resolved Phase-space Viewsmentioning

confidence: 99%

Drift and Its Mediation in Terrestrial Orbits

Front. Appl. Math. Stat.

Gkolias

Rosengren

2018

The slow deformation of terrestrial orbits in the medium range, subject to lunisolar resonances, is well approximated by a family of Hamiltonian flow with 2.5 degree-of-freedom. The action variables of the system may experience chaotic variations and large drift that we may quantify. Using variational chaos indicators, we compute high-resolution portraits of the action space. Such refined meshes allow to reveal the existence of tori and structures filling chaotic regions. Our elaborate computations allow us to isolate precise initial conditions near specific zones of interest and study their asymptotic behaviour in time. Borrowing classical techniques of phase-space visualization, we highlight how the drift is mediated by the complement of the numerically detected KAM tori.