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My grammar book says that 'over' is used for horizontal movement at a higher level.

The helicopter is flying over the sky.

Is this correct?
I think It may mean the helicopter is flying at a higher level than sky, which could be stratosphere by stretch of the meaning of 'over'.

Is there better prepositions here?

Thanks
LiJ
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Alternatives could be "across" or "through".
In one sense, if you think of "the sky" as a two-dimensional blue sheet overlaying the world, a helicopter could be flying over it [on the world's side of the sheet].
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Got it! Thanks, Feebs.