From: "Fred Sawyer" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, August 12, 2001 5:05 PM Subject: Re: Equinox discrepancy
> Bill, > > The formulas you cite give approximate answers. They depend on the > simplifying assumption that the solar latitude is zero. Actually, although > small, the latitude is not zero. If equinox occurs when longitude is 180, > then with a small latitude, the sun's position will have right ascension > slightly different from 180 and declination will be nonzero. > > Fred Sawyer > > ----- Original Message ----- > From: <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Sunday, August 12, 2001 10:48 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 > > >
