The Michelson Morley method does not measure the speed of light.
It compares the speed of light in two different directions 90 degrees to each other.
Light is spit into two components and bounced off of fixed mirrors some way distant.
The mirrors send them back and they are recombined and observered.
Where the light waves reinforce each other you get a bright bar and where there interfere you get a dark one (an interference pattern)
Now the Earth is moving around the Sun so if you turn the experiment 180 degrees the light travelling in the same direction as the Earth will now be travelling in the opposite direction as the Earth so you would think it would take longer and the pattern of the fringes should move.
But they don't