"The problem of the moon's rotation is basically the same as a penny paradox described in Chapter 2 of my 'Mathematical Carnival'. If you roll one penny around a fixed penny, keeping the rims together to prevent sliding, the rolling penny rotates twice during one round trip.

Or does it? Joseph Wisnovsky, an editor of Scientific American, has called my attention to a furious controversy over this question that raged in the letters department of this magazine for almost three years. In 1866 a reader asked: "How many revolutions on its own axis will a wheel make in rolling once around a fixed wheel of the same size?"
"One," the editors replied. A torrent of correspondence followed from readers who disagreed.
In volume 18 (1868), pages 105-06, Scientific American printed a selection from "half a bushel" of letters supporting the double-rotation view. For the next three months the magazine published correspondence from both "oneists" and "dualists". including engravings of elaborate mechanical devices they had made and had sent to establish their case.
(...)
The volume of mail reached such proportions that in April 1868 the editors announced they were dropping the topic but would continue it in a new monthly magazine, The Wheel, devoted to the "great question." "
‏¹

‏¹ Martin Gardner, Mathematical Circus, Mathematical Association of America, 1992, p.205-206

furthermaor (11:08 PM) :

lior (11:09 PM) :

furthermaor (11:09 PM) :

"Obviously it is no more than a debate over how one chooses to define the phrase "rotates on its own axis." To an observer on the fixed penny the moving coin rotates once. To an observer looking down from above it rotates twice. The moon does not rotate relative to the earth; it does rotate relative to the stars." ‏¹