reading his first email correctly. I was guilty, as Profs. often are, of thinking the question was something we have heard many times and answering that and not what was asked. I also had made a quick incorrect calculation in my head and as the answer was the same as Willy's used that. To compound this I then went on vacation and did not access my email for over a week.
Now back to the original question: Why is the difference between the time between the Vernal equinox and the Summer Solstice different from the Summer Solstice and the Autumnal Equinox?
This effect is approximately due to the tilt of the Earth's axis ( http://www.uwrf.edu/sundial/Eqntime.html ) on the Equation of Time (EoT), which can be approximated by a sine wave of a period of 6 months and amplitude of 10 minutes. The actual length of a day, as defined by solar noon to solar noon, is the Equation of Time minus the EoT. This is what must be integrated over the period involved. What I meant by averaging is that an integral over a period is equal to the average over that period TIMES the period. In this case the average of the half period of a sine wave is 10 mins*2/Pi or 6.37 mins. This is multiplied by 90 (or more accurately 92) days gives about 10 minutes. The solar time is less than the standard time by this and we get the same number but of opposite sign for the period after the solstice. So the difference is twice that or approximately 20 minutes. The elliptical orbital effect is very small on this difference essentially cancelling.
Originally I thought the question was concerning the difference between the time from the Vernal Equinox to the Autumnal Equinox, through the Summer Solstice and the time period from the Autumnal Equinox to the Vernal Equinox, through the Winter Solstice. This difference is due to the orbital contribution with the tilt effect cancelling. The difference from this approximate calculation comes out to be about a 1.3 days. Which is a lot less than the actual 7.7 days. The shift of the Earth's perihelion from the Winter Solstice has a very small effect at present.
The reasons for this under estimate are only partially because the EoT is not a some of two sine waves. The integrations average to zero a lot of the higher terms. The real problem is that the position of the equinoxes change as the Earth's orbit becomes more elliptical. The equinoxes remain on a line through the Sun and move away from the fattest part of the ellipse. So two effects make winter shorter than summer (in the Northern Hemisphere): 1) The Earth moves fastest passing through the Perihelion ; 2) The equinoxes are closer to the perihelion than to the aphelion.
As some recent discussion has indicated, this is harder to calculate. My apologies again. -- Emeritus Professor John P.G.Shepherd Physics Department University of Wisconsin-River Falls 410 S. 3rd. St. River Falls,WI 54022 Phone (715)-425-6203 Fax (715)-425-0652 -
