Chapter 27 in the book Astronomical Algorithms by Jean Meeus (Published by Willmann-Bell, Inc.) contains formulas for calculating the March/September equinoxes and the June/December solstices. The formulas are straightforward to evaluate on a computer but are a bit too complicated to reproduce here. In his "approximate method," Meeus has a table indicating that the largest error for the March (resp. September) equinox that results from using his formulas in the years between 1951 and 2050 is less than 51 (resp. 44) seconds. He also gives a more accurate method if smaller errors are required.
----- Original Message ----- From: <[EMAIL PROTECTED]> To: <[email protected]> Sent: Sunday, August 12, 2001 9:48 AM Subject: Re: Equinox discrepancy > Hello All, > I know Fred must be right about the declination being non-zero at the > equinoxes, but I can't figure out why. As I understand, solar celestial > right ascension must equal solar ecliptic longitude (Lambda) on the equinoxes > (0 degrees spring and 180 degrees fall). The formulas (see addendum below) > for declination and right ascension that I have (and which I suspect are also > used in the Dialist Companion) relate these values respectively to the sine > and tangent of Lambda, such that they should equal zero when Lambda equals > zero, and 180 when Lambda equals 180. Perhaps someone can help me find my > error. > -Bill > > Addendum: > Find Lambda the ecliptic longitude of the sun from this formula: > lambda = L[=mean longitude of the sun] + (1.919 - 0.005 x > T[=fraction of Julian Century]) x sin(M[=mean anomaly of the sun]) + 0.020 x > sin(2M) > Find the right ascension of the sun from this formula: > Right Ascension = arctan (tan(lambda) x cos(epsilon)) in same > quadrant as lambda > Find the declination of the sun from this formula: > declination = arcsin (sin(lambda) x sin(epsilon)) > --------------------------------------- > Subj: Re: Equinox discrepancy > Date: 8/10/2001 11:37:09 PM Eastern Daylight Time > From: [EMAIL PROTECTED] (Fred Sawyer) > Sender: [EMAIL PROTECTED] > Reply-to: <A HREF="mailto:[EMAIL PROTECTED]">[EMAIL PROTECTED]</A> > (Fred Sawyer) > To: [EMAIL PROTECTED] (Bill Gottesman), [email protected] (Sundial > List) > > Bill, > > As the help file with the Dialist's Companion points out, this measurement > is only approximate in this software package. In fact, however, equinoxes > and solstices are not defined astronomically in terms of the sun's > declination - they are defined in terms of its true longitude. This is > noted in the help file. Using a zero declination to denote equinox only > gives you an approximation. So you should really be viewing the equinox as > the time when the zodiac indicator changes from virgo to libra. According > to the Dialist's Companion, this happens at 19:06:53 which is pretty good > considering that the help note suggests that this measure should only be > considered good to within about ten minutes (solstices are more difficult > than equinoxes). > > Fred Sawyer
