The thing that Airy and Michelson-Morley were really trying to prove was the movement (or lack thereof) of the earth in the aether. The thing that they essentially proved was that there is no aether, not that the earth doesn't move in space:
At the time, of these experiments, one of the prevailing theories of the nature of light was that it required a medium through which it could travel and this was know as the aether. Both of these experiments were trying to determine the effects of the aether on the motion of light, by a theoretical process called aether drag. Airys experiment showed that there is no aether being dragged along by the Earth (and objects flying through space in general) and the Michelson-Morley experiment showed that the Earth isnt flying through the stationary aether. In either case, the experiments dont show that the Earth isnt moving, but instead that there is no aether and the null results for both cases can be explained with special relativity. In fact, there is even a measurable amount of aberration in the location of stars that varies between +/- 20 arcseconds across the course of a year, depending on where the Earth is in its orbit, giving us evidence that the Earth is, in fact, moving.
Of course, there is aether. But the nature of the aether is highly unknown without considering parallel universes.
