Alexandrium was a fortified castle in Samaria near the Jordan Valley on a mountain between Bet-Shean and Jericho, likely named for the Hashmonean King Alexander Jannæus (103-76 B.C.) .
It was destroyed and rebuilt under Herod the Great, only to be finally razed by Vespasian or Titus.
Rosh Chodesh is the name for the first day of every month in the Hebrew calendar, marked by the appearance of the new moon. The occurrence of Rosh Chodesh was originally based on the testimony of witnesses observing the new moon. When two reliable witnesses appeared before the Sanhedrin the day was declared as Rosh Chodesh. At first the beginning of each Hebrew month was signaled to the communities of Israel and beyond fires lit on mountaintops, but after the Samaritans and Boethusians began to light false fires, messengers were sent. The Mishna mention Sartaba As one of the places they did fires to signal the New month.
The Hasmonaen Castel
The Herodian Palace