Question for Astronomers about the Equinoxes

[brocks]

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 here (http://aa.usno.navy.mil/faq/docs/SunApprox.php) for my solar coordinates).

Thanks for any help.

[Philosophaie]

Find the actual time on:

http://en.wikipedia.org/wiki/Equinox

When changing hours and minutes in Julian Dates add (hour+minutes/60-timezone-dst)/24 to Julian Date at midnight for local time. Dst is 1 for dst and 0 for not dst.

Compare with the real data on JPL Horizons

http://ssd.jpl.nasa.gov/horizons.cgi?s_body=1

[brocks]

Thanks for the JPL link, but I'm more confused than ever.

Googling around, almost every website that gives a layman's explanation of the equinox says it occurs at the moment the sun is directly above the equator, i.e. its declination is exactly zero. But the Meeus book says that the official definition is based on its longitude, which translates to RA.

The JPL site gives 9:03 UT for the time when the RA is exactly 12 hours, and 8:57 UT for the time when the declination is exactly zero, so they don't match up, either, and both differ from the widely published times of either 9:04 or 9:05 UT for the equinox. Also, those times are for the "apparent" RA and dec. The times for the "astrometric" RA and dec, which involves differences I don't really understand but are listed on the JPL page that generates the data, are about four hours later. I don't see how subtle differences involving nutation or gravitational deflection of light can make a four-hour difference.

Help from pros greatly appreciated.

[Philosophaie]

Hope this helps:

http://books.google.com/books?id=rlZAAAAAIAAJ&pg=PA217&lpg=PA217&dq=nutation+and+apparent+RA&source=bl&ots=w-gWk5dSJ8&sig=0j14R9BJY7J2GX0czlVgyYBBeuI&hl=en&ei=cMt8Ts-RGqmLsQKHqcA0&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CB4Q6AEwAA#v=onepage&q=nutation%20and%20apparent%20RA&f=false

[brocks]

Hope this helps:


I think it will, although not without a lot of effort on my part. But if it was easy, everybody could do it, right? Thanks very much.