<div dir="auto">Thank you, Roger!<br><br><div data-smartmail="gmail_signature">---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Jan 1, 2021, 11:41 AM Roger Critchlow <<a href="mailto:rec@elf.org">rec@elf.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>Steve got most of it.</div><div><br></div>The short explanation is that days get shorter or longer because of the tilt of the earth's axis moves the sun's path north and south. The sun's path follows lines of latitude in the sky, ie arcs parallel to the equator, so the arcs are shorter when the sun is on the other side of the equator and longer when the sun is on the same side of the equator. And if you're far enough from the equator the arc can become a circle or be entirely below the horizon depending on the season.<div><br></div><div>But note that the sun's latitude changes continuously, so it actually traces a helix in latitude screwing its way south to the winter solstice, and then screwing its way north to the summer solstice. Talking of the path as parallel to latitude lines amounts to using a fixed latitude for the day. The helical motion makes sunsets a little more wintry than sunrises from midsummer to midwinter, and vice versa from midwinter to midsummer.</div><div><br></div><div>And note that the earth's motion in orbit is fastest around its perihelion, January 4, so the speed of the sun through the helix is fastest in January and slowest in July. This makes the time from sunrise to sunset a little shorter around the perhihelion.</div><div><br></div><div>And finally note that sunrise and sunset occur when the sun is actually below the horizon:</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">For the special case of sunrise or sunset, the zenith is set to 90.833 degrees][ (the approximate correction for
atmospheric refraction at sunrise and sunset, and the size of the solar disk), [...]</blockquote><div>This makes the time from sunrise to sunset a little longer when the sun's path makes a shallower angle with the horizon, ie around the winter solstice in north temperate regions.</div><div><br></div><div>So, yes, it depends on the tilt of the earth's axis to the ecliptic, on the eccentricity of the earth's orbit relative to a circle, and very much on where the observer is located on the earth.</div><div><br></div><div>My earlier failed explanation derailed because I was trying to make the eccentricity correction go in the opposite direction than it does.</div><div><br></div><div>-- rec --</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Dec 31, 2020 at 11:43 PM Steve Smith <<a href="mailto:sasmyth@swcp.com" target="_blank" rel="noreferrer">sasmyth@swcp.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<p><br>
</p>
<div>and this
<a href="https://www.timeanddate.com/astronomy/solar-analemma.html" target="_blank" rel="noreferrer">https://www.timeanddate.com/astronomy/solar-analemma.html</a> provides
some visual intuition, but the text doesn't quite lead *me* to a
succinct explanation. I could ramble on speculatively but the
main thing I take away from this is that the *axis* of the
analemma reflects the tilt of the earth axis relative to our orbit
of the sun... and the eccentricity of our orbit yields the sqew of
the analemma away from an ellipse. I suspect these geometric
arguments are buried in Roger's albebraic description of same. <br>
</div>
<blockquote type="cite">
<div dir="ltr"><a href="https://www.herts.ac.uk/about-us/media-centre/news/2020/longest-known-exposure-photograph-ever-captured-using-a-beer-can" target="_blank" rel="noreferrer">https://www.herts.ac.uk/about-us/media-centre/news/2020/longest-known-exposure-photograph-ever-captured-using-a-beer-can</a>
<div><br>
</div>
<div>Science progresses by grad students forgetting what they're
doing and leaving their experiments running after they leave
school?</div>
<div><br>
</div>
<div>I was going to explain your rise/set/length paradox, but my
explanation got confused in my head. But you can do it
yourself. <a href="https://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF" target="_blank" rel="noreferrer">https://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF</a>
contains the formulae for computing the time of sunrise and
sunset given the date, longitude, and latitude. It's less
than two pages of text and they're in Boulder so they even
mention Mountain Standard Time at one point. Hundreds of
thousands of years of human worrying about when the sun will
rise and when it will set, all boiled down to 11 equations. </div>
<div><br>
</div>
<div>-- rec --</div>
<div><br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Dec 30, 2020 at 12:38
AM <<a href="mailto:thompnickson2@gmail.com" target="_blank" rel="noreferrer">thompnickson2@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div lang="EN-US">
<div>
<p class="MsoNormal">Yes. I see. Nifty. But it repeats
the assertion that the tilting of the earth also has to
do with it. Could it be that the fact that the earth is
not quite a sphere be playing a role, in which case the
tilting on the axis would make a difference? Where are
all our knowitall nerds when we need them. (};-)]</p>
<p class="MsoNormal">N</p>
<p class="MsoNormal">Nicholas Thompson</p>
<p class="MsoNormal">Emeritus Professor of Ethology and
Psychology</p>
<p class="MsoNormal">Clark University</p>
<p class="MsoNormal"><a href="mailto:ThompNickSon2@gmail.com" target="_blank" rel="noreferrer"><span style="color:rgb(5,99,193)">ThompNickSon2@gmail.com</span></a></p>
<p class="MsoNormal"><a href="https://wordpress.clarku.edu/nthompson/" target="_blank" rel="noreferrer"><span style="color:rgb(5,99,193)">https://wordpress.clarku.edu/nthompson/</span></a></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<div style="border-right:none;border-bottom:none;border-left:none;border-top:1pt solid rgb(225,225,225);padding:3pt 0in 0in">
<p class="MsoNormal"><b>From:</b> Friam <<a href="mailto:friam-bounces@redfish.com" target="_blank" rel="noreferrer">friam-bounces@redfish.com</a>>
<b>On Behalf Of </b>Frank Wimberly<br>
<b>Sent:</b> Tuesday, December 29, 2020 9:27 PM<br>
<b>To:</b> The Friday Morning Applied Complexity
Coffee Group <<a href="mailto:friam@redfish.com" target="_blank" rel="noreferrer">friam@redfish.com</a>><br>
<b>Subject:</b> Re: [FRIAM] Sunset and Sunrise</p>
</div>
<p class="MsoNormal"> </p>
<div>
<p class="MsoNormal">Try this one, Nick. It sounds like
what you're saying:</p>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal" style="margin-bottom:12pt"><a href="http://wxguys.ssec.wisc.edu/2019/12/16/solarday/" target="_blank" rel="noreferrer">http://wxguys.ssec.wisc.edu/2019/12/16/solarday/</a></p>
<div>
<p class="MsoNormal">---<br>
Frank C. Wimberly<br>
140 Calle Ojo Feliz, <br>
Santa Fe, NM 87505<br>
<br>
505 670-9918<br>
Santa Fe, NM</p>
</div>
</div>
</div>
<p class="MsoNormal"> </p>
<div>
<div>
<p class="MsoNormal">On Tue, Dec 29, 2020, 8:18 PM
<<a href="mailto:thompnickson2@gmail.com" target="_blank" rel="noreferrer">thompnickson2@gmail.com</a>>
wrote:</p>
</div>
<blockquote style="border-top:none;border-right:none;border-bottom:none;border-left:1pt solid rgb(204,204,204);padding:0in 0in 0in 6pt;margin-left:4.8pt;margin-right:0in">
<div>
<div>
<p class="MsoNormal">Frank, </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Andl notice another thing.
The sentence is, on its face, nonsense. The
tilting of the orbit has nothing to do with its
elliptical shape. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">I have tried to figure out
the answer to this question for years and the
only explanation that I have come up with is
that during the period from early December to
early January, the days stay roughly the same
length but noon moves. It has to do with the <a href="https://www.space.com/3304-earth-closest-sun-dead-winter.html#:~:text=The%20noontime%20position%20of%20the%20Sun%20in%20the,line%20running%20through%20the%20analemma%20is%20the%20meridian." target="_blank" rel="noreferrer">analemma</a>.
Notice that the day-to-day path of the highest
sun is moving parallel to the horizon and
perpendicular to the meridian during that
period. If you think of that moment as “noon”,
noon is moving. But why the analemma? Your
guess is as good as mine. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Have you noticed that the
rising full moon is moving rapidly up the
horizon. By march it will be rising in the NE.
</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Nicholas Thompson</p>
<p class="MsoNormal">Emeritus Professor of
Ethology and Psychology</p>
<p class="MsoNormal">Clark University</p>
<p class="MsoNormal"><a href="mailto:ThompNickSon2@gmail.com" target="_blank" rel="noreferrer"><span style="color:rgb(5,99,193)">ThompNickSon2@gmail.com</span></a></p>
<p class="MsoNormal"><a href="https://wordpress.clarku.edu/nthompson/" target="_blank" rel="noreferrer"><span style="color:rgb(5,99,193)">https://wordpress.clarku.edu/nthompson/</span></a></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<div style="border-right:none;border-bottom:none;border-left:none;border-top:1pt solid rgb(225,225,225);padding:3pt 0in 0in">
<p class="MsoNormal"><b>From:</b> Friam <<a href="mailto:friam-bounces@redfish.com" target="_blank" rel="noreferrer">friam-bounces@redfish.com</a>>
<b>On Behalf Of </b>Frank Wimberly<br>
<b>Sent:</b> Tuesday, December 29, 2020 8:48
PM<br>
<b>To:</b> The Friday Morning Applied
Complexity Coffee Group <<a href="mailto:friam@redfish.com" target="_blank" rel="noreferrer">friam@redfish.com</a>><br>
<b>Subject:</b> [FRIAM] Sunset and Sunrise</p>
</div>
<p class="MsoNormal"> </p>
<div>
<div>
<p class="MsoNormal"><span style="font-family:Arial,sans-serif;color:rgb(32,33,36)">This
topic came up at a recent meeting. The
word "main" makes me wonder what the other
reasons are.</span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-family:Arial,sans-serif;color:rgb(32,33,36)"> </span></p>
</div>
<p class="MsoNormal"><span style="font-size:12pt;font-family:Arial,sans-serif;color:rgb(32,33,36)">The
main reasons for the <b>earliest</b> sunset
to occur in early December and the <b>latest
sunrise</b> to occur in January are the
fact that Earth's axis is tilted (23.5°) and
Earth's orbit around the sun is <b>not</b> a
perfect circle shape.</span> <br clear="all">
</p>
<div>
<p class="MsoNormal"> </p>
</div>
<p class="MsoNormal">-- </p>
<div>
<div>
<p class="MsoNormal">Frank Wimberly<br>
140 Calle Ojo Feliz<br>
Santa Fe, NM 87505<br>
505 670-9918</p>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal">Research: <a href="https://www.researchgate.net/profile/Frank_Wimberly2" target="_blank" rel="noreferrer">https://www.researchgate.net/profile/Frank_Wimberly2</a></p>
</div>
</div>
</div>
</div>
</div>
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