What do you mean by "resolution"? The Michelson interferometer was an attempt to measure to speed of Earth through the aether by looking for fringe shifts as the Earth rotates and orbits the Sun. To get an order of magnitude for the minimum speed it could have detected, try first assuming that relative to the interferometer, ether flows parallel to one of the light paths at speed v. Then imagine Earth's rotation turning the device 90 degrees, so that ether now flows parallel to the other light path at v. Calculate the fringe shift that results, and plug in reasonable values for the minimum detectable fringe shift and arm length to get an idea for v.