On Wed, 3 Jul 1996, Roderick Wall wrote: > Hi to everyone on the Sundial mailing list. > > I have a question regarding the Equation of time correction that I hope > someone may be able to answer for me. > > The correction of time is predominantly determined by the result of two > separate effects. > > (a) the eccentricity of the orbit of the earth around the sun. > > (b) the tilt of the earth axis relative to the path around the sun. > > To find the complete Equation of time the above two effects are added > together. >
That is correct. > My question is with regard to the tilt of the earth axis effect. > > The SUNDIAL AUSTRALIA ISBN 0 646 22200 7 book indicates that (for the > tilt of the earth axis effect) there is no difference between local noon > and solar noon at dates corresponding to the Equinoxes and Solstices (4 > times per year), but produces a difference of up to +/- 9.86 minutes > between each Equinox and Solstice (4 times per year). > > Can someone please explain and describe the above effect. > > Thanks in advance: Roderick Wall > > E-mail: [EMAIL PROTECTED] > > Note: my old e-mail address was: [EMAIL PROTECTED] > > Melbourne Australia. Imagine that the eccentricity of Earth's orbit was exactly zero but the obliquity of the ecliptic was still about 23.45 degrees. In that case the Sun would appear to move along the ecliptic at a uniform rate, completing the circuit in one year. But we tell time with the fictitious Mean Sun, which moves at the same constant rate, but along the *equator*. Let the arc from the First Point of Aries to the Sun along the ecliptic be labelled S, and the RA of the Sun be labelled R (This is the arc along the equator from the First Point of Aries to the point where the arc from the pole through the Sun crosses the equator.) The RA (Mean Sun) would be the same as S, but different from R. the difference S - R would be the Equation of Time. Some work with spherical trig formulae gives tan (R) = cos (epsilon) x tan (S) where epsilon is the obliquity of the ecliptic. This expression can be solved for the quantity S - R using trigonometric substitutions and a series approximation; you can find the working in references like W. M. Smart's Textbook on Spherical Astronomy. The first term of the expression (which is a series approximation) is S - R = E = tan^2 (epsilon/2) x sin (2 S) plus much smaller terms in sin (4 S), sin (6 S), etc. The value of tan^2 (epsilon/2) is about .04307 radians or 9.87 min. And sin (2 S) has the value zero at S = 0, 90, 180, and 270 deg, i.e., at the equinoxes and solstices. So to the degree that the approximation holds in the series (error less than 2 percent) this is the explanation of the passage you quoted. Hope that helps and you haven't got a headache now. . . :-) Mike Dworetsky, Department of Physics | Haiku: Nine men ogle gnats & Astronomy, University College London | all lit Gower Street, London WC1E 6BT UK | till last angel gone. email: [EMAIL PROTECTED] | Men in Ukiah.
