1,343. When the Sanhedrin Relied on Calculations

Hilchos Kiddush HaChodesh 18:10

Whenever it seems from the Talmud that the court is relying on calculations, or that it there is a tradition extending back to Moshe in this matter has been entrusted to them so it is in their hands whether to make a month deficient or full - and similarly, the incident that once occurred in which Rabbi Yehuda HaNasi declared nine months to be deficient (Erchin 9b) - these and all similar things are the case when the moon is not witnessed in its proper time.

Hilchos Kiddush HaChodesh 18:11

Similarly, when the Sages say that a day is added to a month when necessary, this is only when a full month was declared based on calculations, so that a deficient month and a full month will alternate. The Sages have the power to declare consecutive full months or consecutive deficient months as necessary. It’s only when the moon is not in its proper time that the court declares full months out of necessity. If the moon is seen in its proper time, its appearance beginning after the conjunction with the sun, then it is always sanctified.