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It's a geostationary sat. It doesn't move.
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No, but the airplane it would be talking to does. Hard enough when your transceiver is wide open, if you narrow your FOV to a thin cone in order to block jamming signals, the GEO now has to physically track the airplane somehow.

Either the whole satellite rotates or the transciever is on a mount that can rotate

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Unless you plan on having 1 satellite per airplane, something tells me it's harder to constrain the FOV than you might suggest. There's also the small problem of the energy, complexity, & weight of having motorized parts on the satellite (or fine-grained attitude control for the satellite itself to track the craft).
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