In the times of the Holy Temple, the Sanhedrin actually determined the date of Yom Tov, based on the citing of the moon. This is a special power that God gave the Jewish people to control time, and is irrespective of any scientific knowledge.

Be that as it may, information as to the proper date of Yom Tov often did not reach the Diaspora communities until many days later, and they would celebrate two days of Yom Tov out of doubt.

In the 5th century BCE, when Jewish unity was threatened by the exile from Israel, the patriarch Hillel II set a perpetual calendar and instituted an official "Second Day Yom Tov."

They did this even though they themselves had full awareness of the precise dates of all the holidays. The Talmud (Rosh Hashana 25a) already had pinpointed the length of the lunar month as 29.53059 days. It wasn't until the atomic age that NASA scientists -- using satellites, hairline telescopes, laser beams and super-computers -- were able to calculate the lunar month as 29.530588.

So why was a second day Yom Tov added? In order to make a distinction, to add to the Jewish awareness that one is living in the Diaspora and does not claim permanent residence in the Holy Land.

So the fact that we have atomic clocks today does nothing to alter the status of the second day Yom Tov in the Diaspora.