Nothing! Astronauts fly faster (or slower, or whatever) than the Earth's rotation. I don't get what you're driving at? Have you started a Super Bowl party early?
Google "International Dateline" .....
Nothing. The rotation of the Earth and the duration of a day is just an arbitrary designation of reference by observers. If the plane left on Saturday at noon and flew approximately 4X the speed of the Earths rotation in the rotational direction it would arrive back at it's starting point at about 6 in the evening, same as if it stayed there...
No big deal. At the poles a man can walk faster than the earths rotation.
The Air Force actually did this with an SR-71. The abandoned the experiment because the plane almost colided with its own tail.