The University of Arizona

Looking for Chaos in Earth's Orbital Regions

Looking for Chaos in Earth's Orbital Regions

Series: Program in Applied Mathematics Colloquium
Location: Math 402
Presenter: Aaron Rosengren, Aerospace & Mechanical Engineering, University of Arizona

The dynamical environment occupied by satellite constellations is subject to motions that have widely disparate timescales: the earthly day, the lunar month, the solar year, and various precession frequencies ranging from a few years to nearly 26 000 years for the equinoxes. This provision of frequencies in the Earth-Moon-Sun system gives rise to a diverse range of complex resonant phenomena associated with orbital motions. Only recently has the precarious state of the Earth's navigation satellites, perched on the threshold of chaos, been fully appreciated and understood. The circumterrestrial phase space where these satellites reside is permeated by a devious network of lunisolar secular resonances (i.e., those caused by the Moon and Sun on long timescales) that mercilessly distort their orbits, slowly pumping the eccentricities to Earth-reentry values. This fortuitous dynamical situation, however, can be judiciously exploited for space debris remediation in the new paradigm of self removal of satellites through resonances and chaos, from their otherwise long lifetime orbits. Indeed, even in the geosynchronous region, where it has traditionally been thought that space objects would remain indefinitely due to the absence of atmospheric drag, there exist many natural disposal trajectories brought on by resonant interactions. These considerations emphasize the importance of investigating the analytical character of the mechanisms that drive these complicated behaviors and of developing realistic dynamical models for numerical cartographic studies of the phase space. Moreover, such dynamical assessments are of considerable practical interest for the identification of long-term stability regimes, such that satellites (and their aging components) placed in these graveyards will not interfere with the constellations.

In this colloquium, we will present our investigations on the detection of regular structures and chaotic zones in the circumterrestrial space from low-altitude orbits up to the geosynchronous regime and beyond, for the purposes of passive debris mitigation and remediation. We will examine the phase-space topology induced by these resonant harmonics, and outline how the identification of the hyperbolic and elliptic fixed points of the resonances can lead to explicit criteria for defining optimal disposal strategies. We show, furthermore, that increasing the satellites area-to-mass ratio using a solar sail helps promote the deorbiting process, through coupled gravitational and radiation pressure perturbations. This talk will link theoretical aspects of resonances and chaos with practical applications, and will provide fundamental insight into the basic features of the long-term dynamics of Earth satellite orbits.

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