Good... Lord. Measurements of orbital path deviations are refined enough to capture deviations that tiny. Just for reference, if the average diameter of the moon is 3475 kilometers, or 3 475 000 000 millimeters, we are calculating deviations 0.0000001% in size. HOLY MOLY. I just figured that orbital paths had more annual (or monthly in the case of the moon) deviation than that. I guess that means 4+ billion years of astronomical and gravitational activity in our solar system have resulted in very uniform orbits.Tidal forces also affect the shape of the lunar orbit (specifically its eccentricity) over time as well. But even after tidal forces are taken into account, there is an extra bit that remains unaccounted for. It seems the difference between the Moon’s apogee and perigee is changing by an extra 3.5 millimeters per year, and we’re not entirely sure why that is.
You're forgetting a thing. We've calculated/observed this phenomenon from several hundred thousand kilometres away. To put it in perspective: the Moon, in average, is about 30 arcminutes in the sky (one arcminute is 1/60th of a degree - so 30 arcminutes is half a degree). As you stated, the diameter of the moon is about 3475 km. That gives us, at that distance (3475/30) ~116km per arcminute. Which in turns is almost 2km per arcsecond. 2km is 2,000,000 mm. Which means that 1mm is 1/2000000th of an arcsecond. With 3.5mm, that's about 0.000000175 (if my math is right) arcsecond. We've got equipment to observe and calculate something close to one billionth of a degree to a degree of certainty that makes it significant instead of a rounding error.