We must come at the cross-road of Pre-relativity.When Michelson-Morley Experiment was devised , whole world of Physics expected NULL result on Earth because Earth is getting displaced in one direction.The NULL result came as a Surprise. First, Ether was rejected.Then Lorentz Contraction was developed to equalize distances in two directions. The STR just made this contraction experimentally unverifiable through chain of speculations.
The Michelson-Morley Experiment on Moon , if gives NULL result, then STR is correct.
If it gives not-NULL result then there is Absolute Space and Earth remains undisplaced in this Absolute Space despite its orbital motion (as shown in my model of Clock).