Measurement precision of celestial events The local weatherman declared that fall starts at exactly 10:21am (local time). Ignoring the fact that seasonal boundaries have multiple definitions (meteorological, astronomical, etc.), what he perhaps means to have said is that the fall equinox occurs at that moment.

Presumably, that is the moment at which Earth's axis of rotation is exactly perpendicular to the Sun-Earth line.

My question is: to what degree of precision can this be measured? The weatherman's statement was to the minute. But is it actually measured to a finer precision? If so, plus or minus how many seconds? 

What about the the solstices? Can they be measured to the same degree of accuracy? Are there factors which uniquely affect the accuracy of either measurement?
This doesn't answer your question, but has two screenshots, so that's something :)

If you run http://ssd.jpl.nasa.gov/?horizons with these settings:



part of the output looks like this:



This shows the Sun crosses the equinox point between the 8th and 9th second of 14:21 (which is 10:21 your local time). HORIZONS will even let you compute at half second intervals but not beyond that.

If you use the http://naif.jpl.nasa.gov/naif/tutorials.html library, you can compute the time down to the nanosecond or better, but this doesn't really help because we don't know the Sun's position, the Earth's position, or even the direction the North Pole is pointing to that level of precision.

So, not an answer, but some hopefully helpful comments.