I don't want to go too far off topic but I have a new question to pose about this, semi related to the earth sun moon gravitational attraction question in the OP.
If the Sun-Earth gravitational attraction is so much greater than the Earth-Moon, then why doesn't the Sun affect the tides more than the Moon for example? I'm guessing the answer will be distance is closer but isn't that taken into account with the gmm/r^2 equation?