Its frequently thought that new moons send a woman into labor. That isn't always true but hospitals do see more women that day but it doesn't mean eeeveryy one will go into labor :)
There is something to be days about it as labor and delivery rooms are always full on full moons. But I was due July 25 with my daughter and thought for sure I would have her on the full moon of Aug 2 but she wasn't born for another 5 days on Aug 7.
Has nothing to do with gravity lol
It's true that most women give birth somewhere around 2 weeks before or after their due date. Usually because of calculation errors, like if mom doesn't know the exact first day of her last period, or if she does but the ultrasound suggests otherwise, baby is growing faster than expected, etc.
It didnt work for me with my last and my MIL swore it would happen.
I'm not sure about the gravitational pull, but yes. Many women go into labor on a full moon. The number of women in l&d increases during full moons, but that's not to say you definitely WILL go into labor then. Otherwise everyone would be born at the same time of the month, and that's not the case.