Two Days of Yom Tov
I live in England and want to know: Why do we celebrate one day of Yom Kippur, but two days of the other holidays? What's the difference?
The Aish Rabbi Replies
In the times of the Holy Temple, the high court (Sanhedrin) would declare each new month (Rosh Chodesh) only after witnesses would come and say that they saw the new moon. This is a special power that God gave the Jewish people to control time, and is irrespective of any scientific knowledge. When the Sanhedrin declared the day to be Rosh Chodesh, they would send messengers to notify everyone which day is the first day of the month, so that they could correctly calculate the Yom Tov, or other occasions.
Those who lived far from Jerusalem, where the messengers could not reach before the 15th of Nissan (Pesach) or the 15th of Tishrei (Sukkot), would keep two days Yom Tov, out of doubt regarding which day the witnesses saw the new moon.
Nowadays, we do not have the Sanhedrin declaring Rosh Chodesh, and everything follows a preset calendar established by the patriarch Hillel II in the 5th century CE. Yet we still keep two days Yom Tov (Sukkot, Pesach and Shavuot) in the Diaspora, in commemoration of those days when we had two days Yom Tov in the Diaspora. (Maimonides - Kiddush HaChodesh 5:5)
On another level, some want to suggest that a second day Yom Tov was added in order to make a distinction for those living in the Diaspora: that for a Jew, not residing in the Holy Land is in a sense an aberration.
The reason that Yom Kippur is only one day even in the Diaspora is that it would be too difficult for people to fast for two days straight.
On Rosh Hashana (which is always the first day of Tishrei - i.e. Rosh Chodesh), we sometimes had two days of Rosh Hashana in Jerusalem as well. If the witnesses did not arrive the first day, they would keep Yom Tov that day, just in case they'd show up in middle of the day; and the next day. Therefore, by rabbinical decree, even in Jerusalem, we observe nowadays two days Yom Tov. (Maimonides - Kiddush HaChodesh 3:9, 5:7-8)