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Yes. Gravity, causing the tides and slowing down the Earth's rotation. The angular momentum of the Earth-Moon system must remain the same. As the Earth's rotation slows its angular momentum drops. The moon's angular momentum rises by the same amount, which increases its speed, casuing it to move further away from the Earth.
At least some mass then, at least?
Yes,it is a perfectly good explanation,but only qualitative analysis, not to mention the quantitative calculation about the moon away from the Earth (3 cm per year).
A Core-Centered Theory of Gravity(CCTG) is the only viable explanation to fit all the facts. The gravitational constant, big G, works for all baryonic matter, but is much higher for dark matter(DM). The calculations of the weight of the planets, the Moon and the Sun are therefore underestimates. Hence a solution to the Missing Mass problem.
WHY IS THE MOON NOT SPINNING THEN?? 
If you repeat something often enough, you'll believe it.
But is this enough to push something with the mass of the Moon further away into a higher orbit? I suspect not.
My frame frame-dragging force formula is F=SJw/r^2 (S=2G/c^2, w=relative angular velocity). I get perfectly got the 3.8cm per year that moon is away from earth according to the formula. Please go to ...sorry, you cannot view external links. To see them, please
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Astronomical observation phenomena: So far Orlbers’s paradox phenomena don’t be observed.