Some ancient scrips, more specifically Ayurveda has mentioned that women's menstrual cycle is linked to the lunar cycle and it's not a coincidence that both of these cycles are about 28 days. It's not something established by modern science yet but very recently this is becoming a topic of interest and some scientists say that it might be possible. It kind of makes sense to me why it could be true, our bodies are regulated by hormones and hormones are regulated by our environment and our perception of the environment anyway.
According to Ayurveda, as far as I've learned, ideally a woman's periods should sync with the new moon and fertile period with full moon. And it also says that women's erogenous zones and sex drive also shifts according to the lunar cycle, so different parts of her body are sensitive on different days.