# Why is the sunset at different times at the same longitude at equinox?

I happen to live in two places that are literally at the same longitude but several thousand kilometers apart from each other (~47°N and ~68°N). It's just a few days until equinox - and I assumed that the sun would set at the very same time in both places. Equinox is supposed to be at September 22, 13:31 UTC. Using suncalc.org I calculated sunset for the northern location at 19:00h while the sun is supposed to set at 18:55 at the southern location.

Can someone please explain why this is?

I can't think of any effects due to refraction of the light as the angle is the same. The only idea I have that it might be due to the definition of sunset. If it is not calculated using the center of the sun, it might be off as sunsets take much longer in polar regions. Still, I'd be surprised if it was 5 minutes.

Also, I do understand that equinox is at 13:31 UTC which does not necessarily align with the sunset (in fact sunset is 3.5h after equinox). But to make things even more strange, even the next day the sun sets later in the north than it does in the south - I'd expect it the other way round. It is actually another day later, September 24, that the sun will set at exactly the same time in both places - (more than) two days after equinox.

PS: Not an astronomer myself, I'm just curious - please bear with me...

• My guess: draw a picture of the sun & the earth w/ proper direction of axial tilt, and see how/when the final "edge" of the sun drops from view as a function of latitude. – Carl Witthoft Sep 14 '20 at 16:32

## 1 Answer

The only idea I have that it might be due to the definition of sunset.

The instance of sunrise occurs when the first bit of the Sun becomes visible at the horizon, while the instance of sunset occurs when the last bit of the Sun disappears below the horizon. This means the actual position of the center of the Sun is about 50 arc minutes below the horizon at sunrise / sunset.

At sunrise and sunset on the days of the equinoxes, the angle between the Sun's path and the horizon is roughly equal to 90° minus the absolute value of an observer's latitude. The Sun's path is much more oblique at your more northern location.

It takes the Sun about 200 seconds (3.333 minutes) to traverse those 50 arc minutes at the equator on the equinoxes. At some latitude $$\lambda$$, it takes about $$200 \sec(\lambda)$$ seconds for the Sun to go from 50 arc minutes below the horizon to the horizon on the days of the equinoxes. That's 4.89 minutes at 47° latitude and 8.90 minutes at 68° latitude, a difference of four minutes.

The remaining minute could easily be due to rounding. Web sites typically publish sunrise and sunset times rounded to the minute because the difference between actual and predicted times varies by over a minute due to due to variations in the atmospheric state.

• Thank you so much for the explanation! So my initial idea was not that wrong - but I'd never guessed that it would be such a big difference. The influence of atmospheric states also is very interesting, never considered that. – Aileron79 Sep 15 '20 at 8:50
• @Aileron79 - Consider the South Pole as an extreme example. Viewing sunrise as a process that starts when the Sun first appears on the horizon and ends when the Sun becomes completely above the horizon, it takes two days for the Sun to rise at the South Pole. The Sun sets about six months later during another two day long process. – David Hammen Sep 15 '20 at 19:12