LORELAI: Um, guys, hi, there’s a lady up there with a rock the size of Neptune around her neck talking about the debutantes of ancient Greece. It’s a lot easier to fall asleep if you’re sitting down, trust me.
The planet Neptune, the eighth planet from the Sun, was officially discovered in 1846, although it had been previously sighted and thought to be a star. It has a mass of 1.0243×1026 kg, making it 17 times more massive than the Earth. It is named after the Roman god of the sea, who interestingly, carries a trident, which Rory referenced earlier.
Symbolically, Neptune is associated with dreams and fantasy, suggesting that the debutante ball is creating an illusion, and there is little that is solid or genuine behind it. Notice that Emily despairs that the elegant ballroom is not all that it appears, the debutantes are “false” in that they have artificially changed their appearance, and that there is something insubstantial about the proceedings – which we barely manage to see. Not to mention that the ball itself takes a rather surreal turn, as if it is all just a dream. (Is it pure coincidence that Lorelai immediately talks about falling asleep?).
Lorelai’s statement about “the debutantes of ancient Greece” can be taken as nothing more than a joke – as if the MC’s reminiscences about her own debut must be positively ancient. However, the ancient Greeks did hold puberty rites for girls, of which you could say debutante balls are the spiritual successor. It seems very unlikely the MC would really mention ancient puberty rites, but the ball is just bizarre enough for this to be taken at face value.