Correct me if I am wrong, but if we count sunsets by the center of the Sun apparently crossing the horizon then the Sun is supposed to set every day at latitudes under the arctic circle. (Yes if you count in the disc then adjust by 0.27 degrees.)

I was playing around with PyEphem (a python library that claims an approximately 1 arcsecond accuracy), and found that according to it the sun stays up for a couple of days even under it ($66.2<90-23.4$). Can someone explain what is going on?

I created this simple plot to illustrate the issue. The left panel shows the whole period while the right panel shows that the problem is not that the data is under sampled. The plot goes from 2021-06-13 00:12:58.085383+00:00 to 2021-06-28 23:54:05.880661+00:00.

enter image description here

And one more example: Kuusamo is a city at 65°58′N 29°11′E and apparently it also has a few days when the sun doesn't set: LINK1 LINK2

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    $\begingroup$ You've defined the problem in a way that necessarily produces the very anomaly you're asking about. Almost everyone regards a sunset as meaning the Sun has entirely disappeared below the horizon, rather than only half of it having "set". Are you allowing for part of the solar disc remaining above the horizon at the time of the northern summer solstice even at latitudes below (but close to) the Arctic Circle? $\endgroup$ – Chappo Hasn't Forgotten Monica Mar 22 at 23:22
  • $\begingroup$ Yes, i did the half disc thing consistently. Notice that even 66.2 < 90-23.4-0.27 so I don't think you are right. I also added a an example to the bottom that is surely correctly computed and is even more to the south. $\endgroup$ – mr_tuna Mar 22 at 23:27
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    $\begingroup$ Normally, you should wait at least a week before accepting an answer. This will allow you to get more answers and look for feedback on existing answers. $\endgroup$ – slowerthanstopped Mar 23 at 15:51
  • $\begingroup$ Relevant: what-if.xkcd.com/42 $\endgroup$ – Tim Mar 24 at 9:18
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    $\begingroup$ @slowerthanstopped: Sometimes a question has a simple factual answer. There's no reason to delay accepting when someone posts it, in a case like this. You should still keep an eye on your question in case of comments on the answer pointing out that it's not that simple, but if you're pretty sure an answer fully answers the question, you should accept it. That doesn't close the question or stop anyone else from answering, and you can even change your accept vote if an even better answer comes in. (You don't want to long-term leave a less good answer pinned to the top, even if sufficient.) $\endgroup$ – Peter Cordes Mar 24 at 13:19

From the PyEphem Quick Reference Guide:

Rising and setting are sensitive to atmospheric refraction at the horizon, and therefore to the observer’s temp and pressure; set the pressure to zero to turn off refraction.

It seems likely that, if you're using the default settings, the result returned is including atmospheric refraction, giving the results you would expect to see at the location, where the sun is visible even though a direct line to the disc of the sun would put it below the horizon.

Image showing atmospheric refraction from TimeandDate.com

Image is from "What is Refraction of Light" by By Konstantin Bikos and Aparna Kher at timeanddate.com

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    $\begingroup$ This was it. I never expected to have this turned on out of the box. Thanks! $\endgroup$ – mr_tuna Mar 23 at 0:05

Correct me if I am wrong, but if we count sunsets by the center of the Sun apparently crossing the horizon then the Sun is supposed to set every day at latitudes under the arctic circle.

That is not how PyEphem defines sunrise and sunset. It defines sunrise as the time the top of the Sun would nominally first appear above an unobscured horizon (no mountains), and sunset as the time the top of the Sun would nominally first disappear below an unobscured horizon. The Sun has a non-zero angular radius, so that alone changes things.

Moreover, as notovny's answer explicitly addresses, the Earth's atmosphere typically makes the Sun appear to rise well before the top of the Sun would first appear to rise above the horizon if those atmospheric effects didn't exist, and appear to set well after the top of the Sun would disappear would disappear over the horizon if those atmospheric effects didn't exist.

PyEphem uses the U.S. Naval Observatory's values for the Sun's apparent angular radius (16 arc minutes) and for the typical atmosphere refraction (34 arc minutes), resulting in a total of 50 arc minutes. This makes the calculation of sunrise and sunset much easier for pyEphem: Sunrise occurs when the elevation angle of the "real" center of the Sun exceeds -50 arc minutes, and sunset occurs when the elevation angle of the "real" center of the Sun finally drops below -50 arc minutes.

As an aside, these definitions of sunrise and sunset are why daytime lasts longer than twelve hours at the equinoxes.


Wikipedia's article on the Arctic Circle provides the explanation. Firstly, it says:

because the sun appears as a disk and not a point, part of the midnight sun may be seen on the night of the northern summer solstice up to about 50 minutes (′) (90 km (56 mi)) south of the Arctic Circle.

As the Arctic Circle is currently at roughly 66°34′N, this means a portion of the Sun is still visible on that night at around 65°44′N - the very latitude of the city of Kemi.

Another factor to take into account is the elevation of the viewing point. Kemi is not very high - just 4m above sea level - but it's likely there are higher points of land within the city, and tall buildings too. Greater elevation brings more of the Sun's disc into view.

UPDATE: the question was edited since this answer was posted, and Kemi was replaced with Kuusamo, "a city at 65°58′N" – which is further north than Kemi, and therefore would be able to see the midnight Sun for even longer.

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    $\begingroup$ Also, Kuusamo is at about 250 m above sea level. $\endgroup$ – jamesqf Mar 23 at 17:06

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