Florent Deleflie

The dynamical structure of the MEO region: long-term stability, chaos, and transport

It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon’s nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. 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.

Galileo disposal strategy: stability, chaos and predictability

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 ESAs General Studies Programme in the frame of the GreenOPS initiative, that uses a systematic parametric approach and the straightforward maximum-eccentricity 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.

Dynamical properties of Geostationary Transfer Orbits over long time scales: consequences for mission analysis and lifetime estimation

Space debris mitigation is one objective of the Fre nch Space Operations Act, in line with IADC (Inter-Agency Space Debris Coordination Committee) recommendations, through the removal of non-operational objects from populated regions. Long term orbit propagation techniques are required to check the compliance of a chosen disposal orbit against the law. This paper deals with the particular dynamical properties of Geostationary Transfer Orbits. Because of the high eccentricity of these orbits, c omplex phenomena may occur such as coupling between Earth and Sun perturbations, making lifetime estimation highly sensitive to initial conditions or computation parameters. Th is sensitivity can be handled by the processing of statistical lifetimes results, as sho wn in this paper. Numerous propagation cases have been processed and are confronted with theoretical analysis. The paper discusses the possibility of properly estimating the lifetime of objects in Geostationary Transfer Orbit and presents the current work on the good practices that will be associated with the French Space Act.

GRGS Evaluation of ITRF2008, from SLR Data

As an ILRS Analysis Center (AC), we report further the official (final) ITRF2008 solution delivered by the ITRS product center. Following the operational analysis scheme of SLR data, that we perform over the period 1995–2010, we compute for the Lageos-1 and Lageos-2 satellites weekly arcs with ITRF2005 and ITRF2008. Then, we evaluate the sets of orbital parameters, of Earth Orientation Parameters (EOPs), and of Station Coordinates (SSCs). We also compare our results to those obtained by other ACs, in terms of SSCs, EOPs, translations and scale factors.