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<DIV><FONT face="Times New Roman">Hi Ed,</FONT></DIV>
<DIV><FONT face="Times New Roman">In case I can't get to the next meeting, the
attached PowerPoint slides capture what I recently set myself thinking about
during periods at night when I had trouble falling to sleep. It's all
trigonometry. The attached Excel spreadsheet compares my day-night formula with
the official data for 2013. I simplified by assuming a circular orbit, so my
values vary from the official ones, but by less than 10 minutes. Orbital
eccentricity probably also explains the anomalous sunrises. The Earth reaches
the narrowest point in its elliptical orbit (perihelion) in early January (and 6
mo. later). If the precise moment of the winter/summer solstice occurs at other
than noon for our longitude, it's possible for the longest/shortest night to
occur on an adjacent date from the exact solstice date. Similarly, the
increasing/decreasing sunrise times may get out of sync for a day or so due
to the changing distance to the sun (which changes fastest near perihelion and
aphelion).</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">I regret missing many of the meetings, but
commuting from Barrie forces me to give local events and weather higher
priority.</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">Cheers,</FONT></DIV>
<DIV><FONT face="Times New Roman">Paul</FONT></DIV></DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=edalmo@bell.net href="mailto:edalmo@bell.net">ED</A> </DIV>
<DIV><B>To:</B> <A title=natphil@listserv.physics.utoronto.ca
href="mailto:natphil@listserv.physics.utoronto.ca">natphil@listserv.physics.utoronto.ca</A>
</DIV>
<DIV><B>Sent:</B> Thursday, January 16, 2014 4:05 PM</DIV>
<DIV><B>Subject:</B> [natphil] Natural Philosophers - a Conundrum</DIV></DIV>
<DIV><BR></DIV>
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<DIV>Greetings,</DIV>
<DIV><BR></DIV>
<DIV>This is not another rant about poor attendance, although those who missed
this week's lecture missed a great one, this is a genuine plea for assistance in
understanding a natural phenomenon.</DIV>
<DIV><BR></DIV>
<DIV>The winter solstice occurred Dec. 21 as usual and we had 8 hrs. 55 mins. of
sunlight, from 7:49 A.M to 4:44 P.M. The days are supposed to start
getting longer with the sun rising earlier and setting later. Pretty basic so
far, however...</DIV>
<DIV><BR></DIV>
<DIV>On Dec. 31 we had 9 hrs. 1 min. of sunlight, from 7:51 (!) A.M. to 4:52
P.M. Then...</DIV>
<DIV><BR></DIV>
<DIV>Today, Jan.16, we have 9 hrs. 21 mins. of sunlight, from 7:49 A.M. to 5:08
P.M.</DIV>
<DIV><BR></DIV>
<DIV>Although we have gained 26 mins. of sunlight since the solstice, 26 days
ago, the sun still hasn't risen sooner!</DIV>
<DIV><BR></DIV>
<DIV>Explanations will be gratefully received at our next meeting on Feb.
4th.</DIV>
<DIV><BR></DIV>
<DIV>Ed Morrison</DIV>
<DIV><BR></DIV>
<DIV><BR></DIV></DIV></DIV>
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