Airy’s Failure was an experiment performed in 1871 in which Sir George Biddell Airy failed to confirm the aether theory by measuring stellar aberration. The phenomenon of stellar aberration, in itself, was the first direct evidence of Earth’s motion around the sun.
Flat-Earthers claim that the “failure” in “Airy’s Failure” is the failure of proving the motion of Earth. In reality, the experiment aimed to confirm the aether theory. The “failure” was in proving the aether theory. The experiment relied on the already accepted knowledge that Earth is in orbit around the sun.