# Unequal post-solstice sunrise/sunset rate of change- why?

I noticed this in real-world experience on the way to and from work and confirmed it with the tables on timeanddate.com - since the winter solstice, our days (sunlit hours) in the northern hemisphere are lengthening, but the sunset is getting later faster than the sunrise is getting earlier. Why?
I tried to understand it using Cornell’s astronomy site as well as analemma.com, but it still escapes me.
The progressive lengthening of days due to the tilted earth passing its orbital point of maximal (northern) tilt away from the sun makes perfect intuitive sense to me, but if that is the only effect in play, it seems like sunrise and sunset should move apart at an equal rate.

As time passes the day gets longer.
Time is still moving forward during the day.

the earth does not go in a circle around the sun, but rather an ellipse. If it were a circle, the “noon” position would mean the sun is directly overhad at noon. Instead, the tangent to the orbit (“noon” position) is pointing somewhere slightly away from the sun. It’s only pointing at the sun at 4 times in the orbit. Also, the seasons are determined by axial tilt, not the distance to the sun - the difference in length and width of the orbit is 94M miles vs 92M IIRC - and in fact the earth is closest to the sun during north hemisphere winter I think.

So basically, yes the days are getting longer - but the position of the sun at the “middle” of that day is not staying directly at 12:00 noon.

If you look at some fancy globes, they have a “figure 8” pattern (usually in the Pacific) which indicates the actual position of the sun at noon as the earth does its orbit.

Its even worse than you think.

You have the longest day and the shortest day. You also have the earliest sunrise, latest sunrise, earliest sunset and latest sunset. And probably some other stuff.

IIRC none of these coincide exactly with another.

I THINK the earth’s elliptical orbit in conjunction with the axial tilt is the main culprit, along with what seems obvious is not always what the math says.

Unless you are in just the right place in your timezone the sun won’t be at it’s highest point at 12:00PM. This will lead to unequal gains in the length of each half of the day.

before the solstice, around December 8-9, the sunset is at its earliest, and from then on gets later and later. The sunrise continues getting later until around January 3-4, at which point it starts getting earlier.

I think it’s at least partly related to the fact that the pole (in this case the north pole) isn’t simply tilting toward and away from the sun. Instead, as we pass through the instant of solstice (the moment at which the north pole is pointed farthest from the sun), the north pole goes from leading (pointing “forward” along the earth’s orbital path) to lagging (pointing toward where the earth came from). The effect is a gradual shift in “noon” (the time at which the sun is highest in the sky) toward later in the day around the time of the winter solstice. The net result is that the earliest sunset occurs in early December, and the latest sunrise occurs early January - both despite the fact that the shortest duration of daylight is around December 21 (the day of the solstice).

Search the web for sunrise/sunset calculators, and you’ll find apps and spreadsheets out there for calculating these things for any location on the globe. Years ago I found a set of equations to punch into Excel to make your own, at which point I could generate plots to see these things happening.

The tip of the Earth’s axis is not exactly aligned with the major axis of the Earth’s orbit.

Ignoring axial tilt for a moment, The time from noon to noon isn’t actually the time it takes for the Earth to rotate 360 degrees. It’s the time that it takes for the Earth to rotate 360 degrees minus the small angle that the Earth has moved around the sun during that time. The problem is that the “small amount” varies over time because the Earth’s orbit is not circular.

Perihelion (Earth’s closest point in its orbit around the sun) was around midnight UT between Jan 2nd and Jan 3rd this year - so only a couple of days ago.

The relevance is that when the Earth (or any body) is closesr to it’s orbital partner it moves faster along its orbital path so that “small amount” is larger than average right now.

Since perihelion and the solstice don’t coincide, the behavior is more complex than simply having one longest night with the earliest sunset and latest sunrise.

If perihelion and solstice coincided (if the earth’s maximal tilt happened when it crossed the major axis of the ellipse) would the sunrise and sunset move apart from each other at equal rates?

No - reference unclelem’s post above, and that “360 degrees minus a little bit”. That “little bit” is at its greatest while the Earth is nearest the Sun, and this affects the day length (noon to noon). Sunrise and sunset are symmetrical about solar noon (to a good approximation) but solar noon is ahead of clock noon for some of the year, behind it for the rest, because the solar day is of varying length (and the clock day is an average).

No. As long as the Earth has an elliptical orbit, high noon will drift later near perihelion and earlier near aphelion.

In addition, the axial tilt itself causes high noon to drift later near both solstices and earlier near both equinoxes. To eliminate high noon drift entirely, the Earth would have to have an upright axis and a circular orbit.

Note that the two effects reinforce each other in winter–it’s solstice, and it’s near perihelion–maximum high noon drift. In summer, they somewhat offset, but the solstice effect wins–high noon drifts later, but not by as much. So sunrise and sunset are more assymetric around the winter solstice than summer.

[Pedant Mode] It’s called an Analemma

http://www.analemma.com/

http://solar-center.stanford.edu/art/analemma.html

[/Pedant Mode]

Key points mentioned above are correct, but there is a local effect, too. Regarding “high noon”, the sun’s apparent position is relative to your position on earth. If your latitude matches the sun’s declination, then the sun will pass directly overhead at noon. Otherwise, there will be some error between the sun’s position and the zenith (i.e., the point directly overhead).

This page explains it all, very clearly, complete with pictures. I tturns out the analemma is involved.

http://www.math.nus.edu.sg/aslaksen/teaching/analemma.pdf

Totally safe for work, if no one minds pictures of analemmas.

Ignorance fought.
Thank you.