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Re: Sunset and Sunrise

Posted by Roger Critchlow-2 on Jan 01, 2021; 6:40pm
URL: http://friam.383.s1.nabble.com/Sunset-and-Sunrise-tp7599973p7600000.html

Steve got most of it.

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.

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.

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.

And finally note that sunrise and sunset occur when the sun is actually below the horizon:
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), [...]
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.

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.

My earlier failed explanation derailed because I was trying to make the eccentricity correction go in the opposite direction than it does.

-- rec --

On Thu, Dec 31, 2020 at 11:43 PM Steve Smith <[hidden email]> wrote:


and this https://www.timeanddate.com/astronomy/solar-analemma.html 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.  
https://www.herts.ac.uk/about-us/media-centre/news/2020/longest-known-exposure-photograph-ever-captured-using-a-beer-can

Science progresses by grad students forgetting what they're doing and leaving their experiments running after they leave school?

I was going to explain your rise/set/length paradox, but my explanation got confused in my head.  But you can do it yourself.  https://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF 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.  

-- rec --


On Wed, Dec 30, 2020 at 12:38 AM <[hidden email]> wrote:

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.  (};-)]

N

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

[hidden email]

https://wordpress.clarku.edu/nthompson/

 

 

From: Friam <[hidden email]> On Behalf Of Frank Wimberly
Sent: Tuesday, December 29, 2020 9:27 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Sunset and Sunrise

 

Try this one, Nick.  It sounds like what you're saying:

 

http://wxguys.ssec.wisc.edu/2019/12/16/solarday/

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

 

On Tue, Dec 29, 2020, 8:18 PM <[hidden email]> wrote:

Frank,

 

Andl notice another thing.  The sentence is, on its face, nonsense.  The tilting of the orbit has nothing to do with its elliptical shape. 

 

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 analemma.  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. 

 

Have you noticed that the rising full moon is moving rapidly up the horizon.  By march it will be rising in the NE. 

 

 

 

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

[hidden email]

https://wordpress.clarku.edu/nthompson/

 

 

From: Friam <[hidden email]> On Behalf Of Frank Wimberly
Sent: Tuesday, December 29, 2020 8:48 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: [FRIAM] Sunset and Sunrise

 

This topic came up at a recent meeting.  The word "main" makes me wonder what the other reasons are.

 

The main reasons for the earliest sunset to occur in early December and the latest sunrise to occur in January are the fact that Earth's axis is tilted (23.5°) and Earth's orbit around the sun is not a perfect circle shape.  

 

--

Frank Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
505 670-9918

 

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