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

Question

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...

Answer 1

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.

Answer 2

There are a few definitions and effects that come in to play:

1. The definition of the equinox is not when the Sun's declination is $0^\circ$, but is defined as when the Sun's geocentric ecliptic logitude is $0^\circ$ and $180^\circ$. And this generally does not coincide with the Sun's declination being $0^\circ$. So, the Sun having a non-zero declination will cause the center of the Sun to set at different times at different latitudes.

2. The definition of sunrise and sunset is based on the top edge of the Sun. Combined with the fact that the Sun's path through the sky is only $90^\circ$ at the equator. At any latitude other than $90^\circ$, the Sun's path will intersect the horizon at a shallower angle, so the time between the center of the Sun and the top edge of the Sun sinking below the horizon will be longer. The extreme examples of this would be the poles where the Sun just skims the horizon for several days.

3. As you mentioned in your question, the equinox is an instant in time. The time sunrise/sunset comes for most places will not be that instant. Since the Sun moves about $1^\circ$ per day, this will also play a role in the Sun's declination not being $0^\circ$.

I'll also add that these same affects also cause the official sunrise and sunsets to not be exactly East and West on the equinoxes.