When did Rosh Hashanah begin? According to a scientific observation, the sliver of moon was first sighted on Tuesday night. My understanding is that Rosh Hashanah begins at the appearance of such. Is it correct that Rosh Hashanah really began on Tuesday night? Is it a mistake to celebrate a day too early?
In the days of the Talmud, witnesses would report to the Sanhedrin that they saw the new moon, and then the court would declare that the month started. Even if the court knew that the moon should be visible, if no witnesses came, they would wait until the next day to make it Rosh HaShanah or Rosh Chodesh.
When the sage Hillel Nesiah saw that there would no longer be a court, he instituted a calendar system on a nineteen year cycle, and declared the starts of the month in perpetuity. Therefore, we no longer rely on direct observation of the moon to decide our calendar, and it would be a mistake to celebrate a day early.
And this matter is a law of Moses from Sinai: That at a time that there is a Sanhedrin, we set [the new month] by sighting; and when the Sanhedrin does not exist, we set [it] according to this calculation that we [use] to calculate today, and we are not concerned about the sighting. Rather, sometimes the day we set with this calculation will be the day of sighting; [and sometimes it will be] a day before it, or a day after it.