Non-Newtonian motion of the moon I watched an interesting excerpt from a BBC show on the work of the McDonald Observatory in its laser measurements of the distance to the moon which are apparently accurate to within a few centimeters. The observatory used to make a measurement every day and by this means a plot of the Moon's orbit around the earth was obtained over a period of approximately 40 years from about 1970 to about 2010.

At the end of the excerpt Dr. Peter Shelus says that the measurements show that the shape of the moon's orbit is not quite as expected by "Newton's" theories, which I interpreted to mean that the orbit is non-Keplerian, but possibly he meant something else. It is hard to know because the excerpt just cuts off mid-sentence, so it is unclear what he was saying exactly.

In what way is the orbit of the moon irregular according to the MacDonald measurement series?

Also, as an aside, I notice that the observatory's funding was cut in 2009 so that these measurements are no longer being made, but two other observatories are making new series. Are these other observatories making daily measurements the way the MacDonald Observatory used to do?
The motion of the moon, as measured by the Lunar Laser Ranging data is not as predicted by Newton. As the scientist being interviewed says, Newton's model was correct to the accuracy of the data available to him, and was good enough to land the Eagle on the moon in '69. However the Lunar Laser Ranging data can position the moon to an accuracy of 3cm. 

Relativistic effects cause the moon to deviate from the orbit predicted by Newtonian mechanics by about 1m, mostly due to special relativistic effects such as Lorentz contraction. General Relativity accounts for a variation of 10cm. This is much less than the perturbation due to Jupiter (about 1km). However, general relativity does fully account for the motion of the moon, to the accuracy of the experiment.


  All tests are in agreement with Einstein's General Relativity which is used for the numerical integration of ephemerides. No variation of the gravitational constant is discernible. Source


Lunar ranging is ongoing at the Apache Point Observatory Lunar Laser-ranging Operation.