Michelson-Morley’s 1887 experiment falsified the Aether hypothesis. Flat earthers reject this conclusion and claim the experiment “proved the earth is stationary”. They often misquote Bernard Jaffe’s writings from 1960 to support this false claim.

Sir George Stokes proposed that the Aether is at rest in relation to the surface of the earth:

From the 1887 paper by Michelson and Morley

If you were to ignore all other evidence of rotation like opposite rotating celestial poles, stellar parallax, the precession of the equinoxes, Coriolis, Eötvös, etc. one could propose that the earth is stationary. However, in 1925, Michelson, Gale, and Pearson published another experiment that measured the difference in time taken for light to travel in opposite directions around a large rectangle.

Flat earthers interpret this as the aether swirling around the surface of the earth.

If the earth and aether are stationary according to Michelson-Morley, then the aether cannot simultaneously be swirling around according to Michelson-Gale. You can’t have both.