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Originally Posted by milo
I'm unsure exactly what you're trying to say here, 'hovering' implies that an external force is being used to keep it in place which would make arguments based on conservation of angular momentum pointless.
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Why? It's acting along a line through the center of our assumed perfect sphere (that is, directly opposed to gravity), so there won't be any torque, and thus no change in angular momentum. If we wouldn't disregard forces that operated like that, then we'd quickly run out of uses for conservation of angular momentum, because things like orbits would no longer have it conserved.
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Originally Posted by milo
Regardless you're mistaken in thinking you'd drift 'half way around the world', your ground track would only move until your rotational velocity had 'balanced out' for your particular altitude.
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"Balanced out"?