John Shepherd wrote:
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.
We're talking about the same question now, but I beg to differ on the
answer. The tilt of the Earth's axis cannot explain any difference in the
length of the seasons. The only reason you need to bring the tilt of the
Earth into the discussion at all is to define the equinoxes as the times
when the Earth is on the line through the sun which is perpendicular to both
the axis of the Earth's orbit and the axis of the Earth's rotation.
The Equation of Time itself has nothing to do with the question, but if it
did, the component with the 6 month period couldn't explain the difference
because it is zero at the equinoxes and solstices.
The eccentricity of the orbit, on the other hand, is on the order of 1%, and
1% of a year is a few days, so without doing a detailed calculation, the
average difference ((spring+summer)-(fall+winter)) could be on the order of
the 21 hours cited by Willy. The magnitude of (spring-summer), since the
perihelion is near the winter solstice, must be much smaller. Up to five
minutes ago, I was going to insist that the eccentricity of the orbit
explains the effect. It is certainly true that that contributes a
difference, but can it be that we still don't have the right answer, the one
that explains the lion's share of the 21 hours? (Or else I still haven't
understood John's answer. It happens.)
--Art Carlson
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