In honor of the first day of autumn, I've been playing with spherical trig for recreation, and I made a spreadsheet to calculate an ephemeris (sunrise, sunset, etc.) for my location. I noticed that when I tried to figure the exact moment of the equinoxes by using fractional days, I couldn't get the numbers to come out right. If things worked perfectly, then the sun's declination should be exactly zero when its RA is exactly 0 hours (spring) or 12 hours (fall), but they don't quite match up. One event is a few minutes before or after the other. So I have some questions for astronomers: 1) Is the mismatch "real," i.e. they actually do differ by a bit because of perturbations in the earth's motion or something, or would they match exactly if my algorithms were more accurate, or my software used higher precision? 2) If it is real, which is the official definition of the division between seasons, the one based on declination, or the one based on RA, or something else? 3) Is there a website or book that gives or describes the exact formulas used by professionals? (I do have Meeus' "Astronomical Algorithms," but I'm using a simplified formula from http://aa.usno.navy.mil/faq/docs/SunApprox.php [Broken] for my solar coordinates). Thanks for any help.