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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>Roger, <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>This is nice bit of scientific writing for the masses. We among the masses appreciate it. Nick <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Nicholas Thompson<o:p></o:p></p><p class=MsoNormal>Emeritus Professor of Ethology and Psychology<o:p></o:p></p><p class=MsoNormal>Clark University<o:p></o:p></p><p class=MsoNormal><a href="mailto:ThompNickSon2@gmail.com"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal><a href="https://wordpress.clarku.edu/nthompson/"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Friam <friam-bounces@redfish.com> <b>On Behalf Of </b>Roger Critchlow<br><b>Sent:</b> Friday, January 1, 2021 12:41 PM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br><b>Subject:</b> Re: [FRIAM] Sunset and Sunrise<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>Steve got most of it.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><p class=MsoNormal>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.<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>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.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>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.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>And finally note that sunrise and sunset occur when the sun is actually below the horizon:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><p class=MsoNormal>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), [...]<o:p></o:p></p></blockquote><div><p class=MsoNormal>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.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>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.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>My earlier failed explanation derailed because I was trying to make the eccentricity correction go in the opposite direction than it does.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>-- rec --<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Thu, Dec 31, 2020 at 11:43 PM Steve Smith <<a href="mailto:sasmyth@swcp.com">sasmyth@swcp.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><p><o:p> </o:p></p><div><p class=MsoNormal>and this <a href="https://www.timeanddate.com/astronomy/solar-analemma.html" target="_blank">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. <o:p></o:p></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal><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">https://www.herts.ac.uk/about-us/media-centre/news/2020/longest-known-exposure-photograph-ever-captured-using-a-beer-can</a> <o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Science progresses by grad students forgetting what they're doing and leaving their experiments running after they leave school?<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>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">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. <o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>-- rec --<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Wed, Dec 30, 2020 at 12:38 AM <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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. (};-)]<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>N<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Nicholas Thompson<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Emeritus Professor of Ethology and Psychology<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Clark University<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="mailto:ThompNickSon2@gmail.com" target="_blank"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="https://wordpress.clarku.edu/nthompson/" target="_blank"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>From:</b> Friam <<a href="mailto:friam-bounces@redfish.com" target="_blank">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">friam@redfish.com</a>><br><b>Subject:</b> Re: [FRIAM] Sunset and Sunrise<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Try this one, Nick. It sounds like what you're saying:<o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><a href="http://wxguys.ssec.wisc.edu/2019/12/16/solarday/" target="_blank">http://wxguys.ssec.wisc.edu/2019/12/16/solarday/</a><o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM<o:p></o:p></p></div></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Tue, Dec 29, 2020, 8:18 PM <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Frank, <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Andl notice another thing. The sentence is, on its face, nonsense. The tilting of the orbit has nothing to do with its elliptical shape. <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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">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. <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Have you noticed that the rising full moon is moving rapidly up the horizon. By march it will be rising in the NE. <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Nicholas Thompson<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Emeritus Professor of Ethology and Psychology<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Clark University<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="mailto:ThompNickSon2@gmail.com" target="_blank"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="https://wordpress.clarku.edu/nthompson/" target="_blank"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>From:</b> Friam <<a href="mailto:friam-bounces@redfish.com" target="_blank">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">friam@redfish.com</a>><br><b>Subject:</b> [FRIAM] Sunset and Sunrise<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-family:"Arial",sans-serif;color:#202124'>This topic came up at a recent meeting. The word "main" makes me wonder what the other reasons are.</span><o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-family:"Arial",sans-serif;color:#202124'> </span><o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#202124'>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><o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>-- <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Frank Wimberly<br>140 Calle Ojo Feliz<br>Santa Fe, NM 87505<br>505 670-9918<o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Research: <a href="https://www.researchgate.net/profile/Frank_Wimberly2" target="_blank">https://www.researchgate.net/profile/Frank_Wimberly2</a><o:p></o:p></p></div></div></div></div></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></p></blockquote></div></div></div><p class=MsoNormal>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></p></blockquote></div><p class=MsoNormal><o:p> </o:p></p><pre>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<o:p></o:p></pre><pre>FRIAM Applied Complexity Group listserv<o:p></o:p></pre><pre>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriamun/subscribe" target="_blank">bit.ly/virtualfriam<o:p></o:p></a></pre><pre><span class=MsoHyperlink><a href="http://bit.ly/virtualfriamun/subscribe" target="_blank">un/subscribe</a></span> <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><o:p></o:p></pre><pre>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><o:p></o:p></pre><pre>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></pre></blockquote></div><p class=MsoNormal>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></p></blockquote></div></div></body></html>