she was recently told the date for Passover is *also calculated in that fashion
The first day (beginning with sundown) of Pesach is the 14th day of the Hebrew month of Nissin, and one of the four New Years of the Hebrew Calendar. The 14th day of NIssin is, by definition, the day of the full moon. During the time of Temple, witnesses had to having sighted the new moon (that would be the first sliver of moon, I believe); this was done in the outer courtyard of the Temple. It is recorded that Rabban Gamliel could predict the new moon without error, but the testimony is a requirement of law. In spite of this, it was accepted that the new moon could fall on only one of two days. The fourteenth day following the day of the attested sighting was the Pesach. The observation of two of each of the high holidays (the "Shalosh Regaleem," or three holidays in which the Jews were required to assemble in Jerusalem and Rosh Hashannah (but not Yom Kippur)) was instituted by the Rabbis in during the Babylonian exile: When valid testimony of the new moon had been given, a rider (riders?) were sent from Jerusalem to announce which day would be the 14th of Nissin. The message would be taken as far as the rider could travel in fourteen days. After that, the message would, obviously be late. Therefore, all those who beyond the radius of fourteen days' ride from Jerusalem were required to keep two holidays, since one would certainly be on the correct day.
Later, the riders were replaced by signal fires along chains of mountain tops leading out of Jerusalem. The Mishna reports that the fires were lit, first this and then the next until all the exile looked ablaze. The signal fires were abandoned when a renegade group of rabbis began lighting fires of their own without connection to the Temple testimony. According to the Mishna, these renegades called themselves "sadduceem."
The calculation of Easter, which wandered quite a bit, was the reason for establishing the Gregorian calendar. It was quite a feat of reckoning and a controversial idea that was not simple to implement. I hardly remember the story, but it is given in fair detail in "Calendar," which was published within the last three or four years.
