if I fly opposite the direction of the Earth’s rotation at the same speed of the rotation, will I stay in the same time of day as the days pass?

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How does time even work?

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The Concorde had a record RTW westbound flying time of ~33 hrs (Lisbon-Santo Domingo-Acapulco-Honolulu-Guam-Bangkok- Bahrain-Lisbon), so you’d need to be going supersonic the whole time with inflight refueling to be able to make 24 hrs.

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