1,270. Ibbur

Hilchos Kiddush HaChodesh 5:13

The calculations currently used by every person in his own community to determine what day is Rosh Chodesh and what day is Rosh Hashana do not affect the calendar and are not relied upon because we do not establish leap years or set the months outside of Israel. We rely on the calculations of those in Israel to set calendar. The reason we make our own calculations is in order to have the information. We know that the residents of Israel rely on the same calendar so our calculations are intended to determine what day they in Israel will have established as Rosh Chodesh or a holiday. It is the calendar set by the residents of Israel that will establish a day as Rosh Chodesh or a holiday, not the calculations of those of us elsewhere.

Hilchos Kiddush HaChodesh 6:1

When the months were sanctified based on witnesses seeing the moon, the court would meticulously calculate the conjunction of the sun and the moon, the way that astronomers do, in order to know if the moon would be seen. The first calculations were mere approximations, not requiring great accuracy, calculated based on the average rates of motion for the sun and the moon. The time calculated in this manner is called the molad. The basics of the calculations used when there is no court to sanctify the month are called ibbur. These are the calculations that are used today.