And the night (unlike the day WRT the Sun) cannot be defined by using the Moon.
I guess you mean, not easily.
Sam, the Gemara in Pesachim actually suggests that it is possible tobe exact. According to one view, Rebbi Meir holds that people don’t make any mistake at all and Rebbi Yehuda allows for a half hour. But even according to the most allowing view, it is merely saying that it is possible to make the mistake, but not that it is expected.