They are not linked at all. Believe me, if they were, that would be so stupendously, fantastically, amazingly USEFUL in organising your life, that women like me would be celebrating in the streets on a daily basis, hugging lunar calendars with joy.
I mean just think about it... if the two things were linked, in January I could look up what the relevant phase of the moon will be in December and say things like "Ooh, I have to make an 9 hour train journey in December and really don't want to do it on a day I'll feel wretched, so let's not book it for the 13th, 14th or 15th..."
In my life I've had times where my cycle was as short as 21 days, and times where it was a long as 8 weeks.
Also, not all women menstruate at the same time, so why is the amount of light which is bouncing off the Moon towards Earth affecting different women in different ways? (Anyone who mentions menstruation being linked to tides needs to be taken to the seaside and slapped with wet fish until they realise the tide is NOT on a monthly cycle. Even the spring tides occur twice a lunar month!).
Basically the Moon has these effects on Earth and the creatures upon it:
- Gravitational Pull - this creates the tides
- Moonlight - the phases of the moon as seen from Earth. This means a bit of light to see by at night.
Gravitational pull on the surface of the Earth is only affected by the Moon's (and Sun's) mass. The amount of light hitting the Moon and being reflected towards an observer on Earth does not increase or decrease the Moon's mass!
The tides operate on these cycles:
- In and out roughly twice daily. Approx every 12 hours 50 minutes.
- Spring tide (highest high tide and lowest low tide) twice a lunar month - every 14 days. This is caused by Moon + Sun's pull adding together.
- Neap tide (lowest high tide and highest low tide) twice a lunar month - again every 14 days. This is caused by Moon minus Sun's pull.
The phases of the moon are only linked to the state of the tide because the Sun's gravitational pull is involved. There is a good astronomy article on tides and the moon here. For example, spring tides occur a couple of days after the new moon and a couple of days after the full moon.
Sooooo... if you are suggesting that gravity causes menstruation, it should happen on a cycle matching the tides. Twice daily or twice a (lunar) month. And you'll need to explain why women's menstrual cycles don't alter in zero gravity.
If you are suggesting that moonlight causes menstruation, you'll have to explain:
- Why not all women have periods on the same phase of the moon?
- Why women have periods when the weather is too cloudy to see the moon?
- Why other, brighter sources of light - everything from the Sun to camp fires to light bulbs - don't have the same effect?
Animals which time things 'by the phase of the moon' are usually actually doing it by a combination of factors: the state of the tide, water temperature, number of daylight hours at that time of year, a benefit to the event happening at night, and so on.