One question I've always had with this: How does the rotation of the earth affect an airplane's flight time, if any? And how does this change with altitude?
A more nuisance would be that earth rotating generate all sorts of things in the atmosphere, including winds and Coriolis effect on the winds, and you can account for that considering the winds. Btw a flight from Chile to France and back, will have a leg significantly shorter (up to 2 hs in a 13hs flight) and which leg it is, depends on the time of the year.
I get that what really matters is the relative motion, but it still seems to me that there might be a gravitational/inertial effects at play, even if tiny.
Consider this thought experiment: Planes cannot really fly into space, but assume they can. At a certain altitude, it cannot be said the the plane is moving perfectly in step with the gravity of the earth. At infinite altitude, that certainly cannot be the case.
So that tells me there is some deviation due to the inertia of the plane, even at low altitudes. Like I said, the effect might be tiny, but would be interesting to learn more about it nonetheless.
However, rotation of the earth imparts a coriolis force on the air, which results in jetstream winds. Aircraft routes are optimized to use/avoid jetstreams for shorter travel times.
So, when flying towards the east, catching these currents can significantly reduce flying time. When flying towards the west, we want to avoid them by flying below or elsewhere.
But it still seems to me that there might be a gravitational/inertial effects at play as well. At a (hypothetical) infinite altitude, it can no longer be said the the plane is moving perfectly in lock-step with the gravity/rotational acceleration of the earth. This implies the inertia of the plane relative to the rotation of the earth still has an effect at lower altitudes.
The effect might be tiny, but would be interesting to learn more about it nonetheless.
Something like this does exist under general relativity :
https://en.m.wikipedia.org/wiki/Frame-dragging
However,
> This does not happen in Newtonian mechanics for which the gravitational field of a body depends only on its mass, not on its rotation.