Home > Concepts > How come hours of daylight changes very slowly around the solstice, but very rapidly around the equinoxes?

How come hours of daylight changes very slowly around the solstice, but very rapidly around the equinoxes?

January 10, 2015

This question came in as a an off topic comment to my post yesterday 01/09/2015.  It deserves a good answer.  So here goes.

Day to day change in daylight hours occur when the Sun appears to move south or north.  For us in the northern hemisphere the daylight hours get shorter when the Sun appears to move south, and longer when the Sun appears to move north.  If we spread out the sky in a Mercator projection, like they do the earth or one of those satellite tracking maps, it would look like the image below.

Mercator map of the heavens

Mercator projection of the heavens from declinations +60 to -60 degrees declination, centered on the vernal equinox. The center horizontal white line is the celestial equator, and the yellow sinusoidal line is the ecliptic, the apparent path of the sun. Note the planets and Moon also stick close to that line. The date of the image is January 9, 2015. Venus and Mercury are on top of each other and unlabeled under the ‘a’ in Capricornus. Created using Cartes du Ceil (Sky Charts).  Click image to enlarge.

Note that the steepest part of the ecliptic occurs at the equinoxes, the vernal or March equinox in the center and the autumnal or September equinox at the left and right edges.  That’s where the sun’s motion north or south is the greatest, so the daily change in daylight hours is the greatest.  Near the solstices at 6 and 18 hours* the Sun isn’t changing its north-south motion very much, so the daylight hours aren’t changing much from day to day.  If you were watching the sky at local solar noon, you’d think that at the solstice the sun would stop its motion and stand still before heading back.  That’s what the word solstice means:  sun-standstill.  The variation is daylight hours also depends on your location.  At the equator, it doesn’t change at all.  Of course at the other extreme, at the poles, there’s 6 months of daylight and 6 months of night.

* The east-west direction in the heavens is like longitude on the Earth but it’s called right ascension and is measured in hours where 15 degrees equals one hours.  Astronomers use clocks to keep track of it.  Declination is the same as latitude on the Earth.  In astronomy longitude and latitude were already in use for ecliptic based coordinates.

So what causes the wavy path in the sky?  Lets check out the earth from the sun’s point of view, so to speak.

Earth's axial tilt.

Earth’s axial tilt. The horizontal line is the plane of the Earth’s orbit and what we see projected on the sky as the ecliptic. The tilt of the Earth’s axis to the plane of its orbit by 23 1/2 degrees, gives us the seasons and why the celestial equator and ecliptic cross at a 23 1/2 degree angle. Credit Dennis Nilsson.

Both the celestial equator and the ecliptic are great circles in the sky.  They intersect at an angle of 23 1/2 degrees at the equinox points.

Lets take a look at the difference in daylight hours at three times in the year, the equinox and the two solstices for Traverse City, MI whose latitude is just shy of 45° north.  The following three images were generated in stereographic projection, which exaggerates the distance of things near the horizon and diminishes the distance of things in the center, the zenith.  So actually the speed of the sun is unchanging across the sky.

Winter solstice

The sun’s daily path through the sky from horizon to horizon on the first day of winter, the winter solstice. Credit My LookingUp program.

Equinox

The sun’s daily path through the sky from horizon to horizon on an equinox the first day of spring or autumn. Credit My LookingUp program.

Note that at the equinox the sun rises due east and sets due west.

Summer Solstice

The sun’s daily path through the sky from horizon to horizon on the first day of summer, the summer solstice. Credit My LookingUp program.

One more diagram to illustrate the change in the sun’s north-south position in the sky.

Analemma

This figure 8 is called an analemma. One can find it on old globes in the Pacific Ocean. Created using my LookingUp program.

This is the Sun plotted for mean solar noon over one year at 7 day intervals.  One can see the rapid motion in the north-south position of the sun around the equinoxes versus the solstices.  The more rapid the north-south motion of the Sun the greater the change in day-to-day daylight hours.  The line with “East West” on it is the celestial equator.  Check out my December 2, 2014 post on why it’s a figure 8.

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  1. Richard Fidler
    January 10, 2015 at 8:26 am

    I pretty much understand why daylight changes rapidly at the equinoxes and slowly at the solstices based upon your map showing the ecliptic and how the steepest part is at the equinoxes. Also, the figure eight drawing makes sense. But why does the curve of the ecliptic seem to linger for a time at the solstices before plunging? Does it have to do with the speed of the Earth in its orbit? Or is it that at the solstices every day’s movement results in little progress as the line of the Earth’s axis points towards the sun and consequently much progress at the equinoxes? (I know that direction of that axis does not change as the Earth goes around the sun. I am trying to get a picture in my head to explain how it works given the sun and the Earth at the solstices and the equinoxes. Haven’t quite got there yet.

    One thing: at the equator, day length does change over the course of the year, doesn’t it? At the equinoxes it would be 12 hours long, but at the summer solstice up north it would would sink towards the south by 23 degrees and at the summer solstice in the south it would sink towards the north by the same amount. Or maybe I don’t have that figured out, either 🙂

    Thanks for your answers, Bob.

    • January 12, 2015 at 9:19 pm

      I’m going to try again with a post. This would be real easy if I had a celestial globe, but it doesn’t work on a static web page. I know you’re local by your email IP address, so come in some time to a astronomy society meeting at 8 p.m. or star party at 9 p.m. at the NMC Rogers Observatory on the first Friday of the month. There’s a celestial globe there from which I or professor Jerry Dobek can show you. However I will try again with a second post today (01/12/15).

      It’s out: https://bobmoler.wordpress.com/2015/01/12/more-questions-about-the-length-of-daylight-hours/

      Hope that helps.

      Bob

    • January 12, 2015 at 10:42 pm

      Hi Richard,

      I’m going to try again with a post. This would be real easy if I had a celestial globe, but it doesn’t work on a static web page. I know you’re local by your email IP address, so come in some time to a astronomy society meeting at 8 p.m. or star party at 9 p.m. at the NMC Rogers Observatory on the first Friday of the month. There’s a celestial globe there from which I or professor Jerry Dobek can show you. However I will try again with a second post today (01/12/15).

      It’s out: https://bobmoler.wordpress.com/2015/01/12/more-questions-about-the-length-of-daylight-hours/

      Hope that helps.

      Bob

      Bob Moler

      NASA/JPL Solar System Ambassador

      bob@bjmoler.org Phone: 231.946.8649 Cell:: 231.631.3874 Ephemeris web page: ephemeris.bjmoler.org Blog: bobmoler.wordpress.com

      Bob Moler’s Ephemeris weekdays on Interlochen Public Radio

      Also streaming live on the Internet at ipr.interlochen.org

      6:49 a.m. ET on News IPR (This is a new time):

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      On Sat, Jan 10, 2015 at 8:26 AM, Bob Moler's Ephemeris Blog wrote:

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  1. January 12, 2015 at 10:33 pm
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