So, I saw this meme about some minister commenting that the Earth doesn't rotate, for if it did then planes only need to be in the air and the destination city would come to it. I know this is absurd but it got me pondering about how to achieve this practically.
I know that the ISS in a LEO covers the entire earth in 90 minutes. But how high do you need to go in a straight line so as not to be affected by the Earth's rotation and cities would literally come to you?
Answer
The Earth "compells" an aircraft to rotate with it through the fluid drag of its atmosphere. So a practical answer to your question is then "above the atmosphere", which is at about a $100{\rm km}$ height. This is the von Kármán line, which is often taken as the definition of the edge of space. The definition is made because at this height, a standard aircraft would need to fly at the orbital velocity to gain a lift equal to its weight. Therefore, the atmosphere above this height has a negligible effect on a spacecraft's dynamics and it will continue to orbit the Earth with negligible thrust indefinitely, if it flies at the orbital speed of about $7.2{\rm km\,s^{-1}}$ or more (in which case it will either undertake elliptical orbits with 100km or so perigee, or its orbit can be converted, through a sequence of small thrust manoeuvres, to a higher altitude circular one).
So one can definitely get to an altitude where one is not dragged along by the Earth's atmosphere, but one cannot hover there without continual thrust. Most likely one is orbiting, and, in low Earth orbit, the orbit speed is greater than the speed of rotation of the Earth's surface.
I don't know exactly what von Kármán had in mind as the standard aircraft, but chances are that the definition would work out pretty much the same for a very wide variety of aircraft.
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