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Are satellites moved to keep them aligned? Are they at risk of becoming unusable from the small, but measurable changes to Earth's rotation?

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The very small changes in the Earth's rotation rate pale in comparison to the much larger perturbations that geosynchronous satellites experience from the Earth's non-uniform gravitational field, gravitational perturbations from the Moon and the Sun, and non-gravitational perturbations (radiation pressure) from the Sun.

In addition to the above, the ability of a geosynchronous satellite to hold its position is imperfect. Because of those perturbations and the not quite perfect control, geosynchronous satellites are assigned a longitude band in which they must operate, as opposed to exactly hovering over a specific point. The tiny changes in the Earth's rotation rate is yet another perturbation that geosynchronous satellites must accommodate to stay within their assigned bands, but this is a tiny perturbation, essentially in the noise.

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