As for the moon, the Romans cut it out of their calendar more than 2000 years ago, and our "months" are not "moonths" at all. In fact it is one of only two major calendars that do not pay respect to both sun and moon: the other is the Islamic one of 12 lunar months, adding up to about 354⅓ days, so that dates drift round the seasons in a cycle of about 33 years. What a pity the early Christians were so eager to distance themselves from the Jews that they ditched the Jewish/Babylonian calendar, which was one of the first fruits of ancient astronomy. That's why Easter is so difficult to calculate.
It is such fun to keep track of the moon. Back in the 1970s there were lots of wrist-watches that showed its phases. Unfortunately, many of them did not keep time with the moon, which takes about 29½ days to go from new to new. Perhaps that is why people stopped buying them, so that now you need to trawl the internet to find a moon phase watch. I found a lovely one called the Tidemaster. As its name suggests, it can also be used to keep track of the tides. And I've often wondered whether the subtle daily variations of gravity do not affect our bodies...
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