Gravity cells on the moon affect its trajectory. The resolution of the
energy switches that they become in the three body problem causes our
weather and more..

Well, that is my opinion and I don't expect anyone to follow what I
say. They haven't yet. Still, I get such a kick out of being right
eventually/most of the time that I thought it time to venture out into
deeper waters.

The moon weighs some 1/81st the mass of the earth. They act as a
couple and should be considered one planet. They can't for instance be
separated from each other without doing incredible damage to their
relative positions to the other planets and to their astronomical
distance.

But they are distinct and do have different speeds. Consider that in
exchange for its capture, the moon travels so much further than us
each year. Whilst the earth is orbiting at some 2Pi x 93 million miles
per year, the moon is in effect orbiting the sun 12 to 13 x 2Pi x
250,000 miles or so further than the earth in that time period.