1,294. These Calculations are Not Exact

Hilchos Kiddush HaChodesh 10:7

Both sets of calculations [i.e., based on the two opinions about the precise length of a solar year] are only approximate. They are based on the average rate at which the sun travels but they do not necessarily represent the sun’s actual position at any given time. When compared to the sun’s actual position, the vernal equinox will occur about two days before the time reached by these two processes – both the one that assumes a solar year to be exactly 365 and one-quarter days and the one that assumes a solar year to be something less than that.

Hilchos Kiddush HaChodesh 11:1

As has already been discussed, the Sanhedrin made exacting calculations to determine whether the moon would appear. We are therefore confident that those who possess the proper intentions, who love words of wisdom and who strive to unravel secrets would like to know the process used to determine if the moon would appear on a given night.