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.
I'm sorry but I have to disagree. BETWEEN the Vernal Equinox and the
Summer solstice the correction due to the tilt is NOT zero. Every day
EXCEPT at the equinox and solstice the day is a bit shorter (as the
sun is early) due to this tilt contribution. Summing up these days
(Solar days which the Civil calendar uses and not Sidereal days which
astronomers use) leads to a shorter Spring than the summer where the
days are now a bit longer.
The tilt of the Earth has to be brought in as the difference between
the Solar and Sidereal day depends on the apparent motion of the sun.
The orbital motion of the Earth about the sun is approximately
360/365.25 degrees per solar day. It is approximate due to the
eccentricity of the Earth's orbit. Ignoring the latter for the
moment, the Earth has to rotate almost an extra degree for the Sun to
cross the meridian again. This takes nearly 4 minutes of time which
is the average difference in time between the Solar day and the
Sidereal day. The tilt of the earth's axis complicates this because
the projection of the rotation onto the orbital plane varies. This
leads to the tilt contibution to the Equation of time with the 6
month period.
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
If you go out to the US Naval Observatory web site at:
http://aa.usno.navy.mil/data/ you can check the date and time of the
the equinoxes and solstices and find the differences. I found their
Julian date converter most useful as you can convert everything into
a decimal number of days and just take the difference. Anyway for
2002,I found the difference that Willy was talking about to be 0.991
days or 23 hrs 47 mins but the difference
((spring+summer)-(fall+winter)) is 7.665 days.
--
Cheers,
John
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