Do you require less thrust to fly east than west in still-air conditions on a rotating earth? The centrifugal force of an eastbound aircraft must counter and thus reduce the effect of gravity while spinning 'with' the earth as your rotational velocity with respect to an unaccelerated frame of reference is greater. Less 'gravity-like force'=>less 'weight'=>less lift=>less drag=>less thrust. It must be a minimal effect but it disproves those who suggest flying circles IMC without power changes shows that the airmass is the only valid frame of reference.
I'm assuming they launch space shuttles eastward though I've never flown over florida at the right time to see for myself.