The Moon is a Harsh Mistress?

This is a serious question and I don't want smart answers, all right? It is well known that earth's moon controls the tides on earth, the breeding of oysters, and that the full moon can make people go nuts - that's why many police forces world-wide put on more staff on the night of a full moon. This has been established without a shadow of doubt and now I get to my question. The human body is 98%(?) water and for so many generations man has been subject to the moon's influence, but what happens after an astronaut leaves earth with no moon - will there be problems? What happens once he gets to mars where there are two moons? I doubt this has ever been explored by NASA scientists and I'm really interested to find out what others think.