The accuracy of a new theory of Earth satellite motion is assessed across inclination and orbital altitude. This theory is based on periodic orbits in the zonal potential, with a Floquet solution for nearby motion, augmented by perturbation solutions for other perturbing forces. It is completely numerical and well adapted to the rich computational environments of today. Its root mean square error is generally in the tens of meters over a one day data arc, for eccentricities less than e = 0.1. The perturbation methods fail near geopotential resonances, but the theory has been adapted to handle the vicinity of a resonance without significant loss of accuracy. The geometric structure of the solution is also explored, and it is shown that most orbits in the full geopotential are static structures that rotate with the Earth's rotation. Geopotential KAM tori shrink down to a two dimensional surface as the analog of zero eccentricity orbits. A first attempt is made at visualizing the torus over the Earth's surface. Precision calculation of low eccentricity KAM tori may lead to much decreased stationkeeping costs for Walker constellations.
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