Does autumn start astronomically on the same day every year?

The fall semester does not start astronomically on the same day every year, but the window of possible dates is very small. In most years, the fall semester can be expected to begin on September 22 or 23. From time to time it could happen on September 21 or 24. But the last time we saw an autumn equinox on September 21 was more than a thousand years ago, and we don't expect it to be on September 24 until the year 2303.