From: doerfler@cbnewsf.cb.att.com (ronald.w.doerfler)
Subject: Re: Annual calendar of celestial events
Organization: AT&T
Date: Thu, 17 Dec 1992 20:28:37 GMT

In article <1992Dec16.192958.4557@sfu.ca> palmer@sfu.ca (Leigh Palmer) writes:
>In article <1992Dec16.164953.26956@cbfsb.cb.att.com>
>doerfler@cbnewsf.cb.att.com (ronald.w.doerfler) writes:
>>In article <7460062@hpfcso.FC.HP.COM> ajs@hpfcso.FC.HP.COM (Alan Silverstein)
>writes:
>>>A typical question is, "why are the sunrise/set and twilight min/max
>>>dates not on the solstices?"  It is because of the "equation of time",
>>>that is, the Sun runs "early" or "late" due to the ellipticity of the
>>>Earth's orbit.  Of course, the solstices and equinoxes themselves drift
>>>about 1/4 day later per year (versus the calendar) until we throw in a
>>>leap day every fourth year to reset the calendar to them.
>>
>>
>>In this vein, I might mention that the Dec., 1992 issue of the American
>>Mathematical Monthly has a good article on the length of the day and 
>>the solstices.  An even better article, in my opinion, is referenced
>>in this article, and is from the same journal in 1990.  Actually, the
>>older article does a much better job of deriving the effect of the 
>>angle of the ecliptic to the equator, and the newer article of deriving
>>the effect of the ellipticity of the earth's orbit.  It turns out that
>>the ecliptic angle is the dominant effect.  If you want the actual
>>equations that define the Equation of Time, these are the places to
>>find them.
>
>Did the article mention the fact, due to the same cause as the retardation
>of sunrise and sunset at the winter solstice, that spring and summer in
>the northern hemisphere last more than a week longer than fall and winter?
>Turns out that the sun hurries through our cooler seasons, and the Earth's
>rotation can't keep up with it. Kepler's second law explains it nicely.
>
>That's my favorite counterintuitive result. It's a nice thought, since it
>is snowing right now.
>
>Leigh

No, neither article mentioned this, as I recall.  This puzzles me, though.
How would one define the seasons without using the equinoxes and 
solstices to bound them?  They are very close to 3 months apart.  
Actually, I see your point: why define winter to start at the winter
solstice, when the sun is just beginning to rise higher in the sky--
this should be the middle of winter.  On the other hand, isn't it
the lag of the oceans, etc. due to heat capacity the reason the dead
of winter is in January?  I guess I need help in understanding this.
Are you taking winter to occur between the times when the sun is
halfway to 23.5 degrees south?

I see how the earth is traveling faster in the winter in the Northern
Hemisphere because it is closer to the sun.  In that case, though,
why are the equinoxes so equally spaced (at least within a day) at
three months apart?  

Wait, I just counted how many days are between March 22 and June 22,
and so forth, and since there are different numbers of days in the 
months, I found that there are indeed more calendar days in the 
spring and summer than in the fall and winter.  Hmmm, I bet there
is a correlation there historically.

Somewhat confused,

Ron Doerfler