How was the mass of the moon first calculated? How do we measure it now?
In the history of astronomy there was no correct concept of masses before Newton. The Greeks had found reasonably accurate volumes of the Earth and Moon, but masses were unkwnown. The planetary mass determination relies on Kepler's third law. Newton indirectly measured the mass of the Moon, trying to estimate the ratio between the solar and lunar masses looking at sea tides. I suggest this lecture to clarify any doubts (in particular the first two pages).