Diffusion in the asteroid belt

Varvoglis, H.

doi:10.1017/s1743921304008610

Proc. IAU

2004

DOI: 10.1017/s1743921304008610

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Diffusion in the asteroid belt

H. Varvoglis

Abstract: Abstract. In the beginning we review briefly the evolution of the ideas on the motion of the bodies in our solar system, from Newton's clockwork Universe to the presently accepted ubiquity of chaotic transport in the asteroid belt. Then we discuss the result of chaotic motion, which is transport in phase space, and we introduce the concept of diffusion of an asteroid in action space. We proceed by reviewing recent work on numerical as well as analytical study of asteroids following chaotic trajectories and we … Show more

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Cited by 2 publications

References 23 publications

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Chirikov diffusion in the asteroidal three-body resonance (5, −2, −2)

Cachucho

Cincotta

Ferraz-Mello

2010

Celest Mech Dyn Astr

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The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation developed by Chirikov is applied to the Nesvorný-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and across the separatrices of the (5, −2, −2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to 10 8 years.

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Chirikov diffusion in the asteroidal three-body resonance (5, −2, −2)

Cachucho

Cincotta

Ferraz-Mello

2010

Celest Mech Dyn Astr

View full text Add to dashboard Cite

show abstract

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

Daquin

Rosengren

Alessi

et al. 2016

Celest Mech Dyn Astr

114

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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 weblike 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 resonanceoverlap 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.

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Diffusion in the asteroid belt

Cited by 2 publications

References 23 publications

Chirikov diffusion in the asteroidal three-body resonance (5, −2, −2)

Chirikov diffusion in the asteroidal three-body resonance (5, −2, −2)

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

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