# Times of Latest Sunrise and Earliest Sunset

Quote of the Day

The road to wisdom? Well, it's plain and simple to express. Err and err and err again, but less and less and less.

— Piet Hein

## Introduction

I have lived most of my life in Minnesota, so you would think that I would be used to cold weather by now. The key to having a pleasant winter is dressing properly. The one thing that I still struggle with is the short duration of our daylight in winter. Because of our limited daylight, I need to know the time of sunrise and sunset to plan my outdoor activities. So every morning I listen to the radio when they list our local  sunrise and sunset times.

I recently noticed that the date of our earliest sunset was coming six days before the winter solstice. I then checked the date of our latest sunrise and that date was twelve days after the winter solstice. I know that the winter solstice has the shortest daylight duration of all the days of the year, but it has neither the latest sunrise nor the earliest sunset. This seemed odd to me. Let's investigate these observations.

## Background

### Scope

I will be focusing my discussion on Minneapolis, which is the largest city near my home. I obtained my sunrise, sunset, and daylight duration times for Minneapolis from this web site.

I will not derive the formulas used to compute sunrise and sunset times as these formulas are well document elsewhere (e.g. formula for both). For this post, I chose to obtain my data from a web page (I am getting lazy in my old age).

### Definitions

The terms sunrise and sunset are defined in terms of the Sun's position relative to the horizon. The fact that things start getting dark as the Sun rises and sets  is associated with atmospheric light scattering. We use terms like dusk and twilight. to describe the light level present.  Figure 1 illustrates the Sun's position relative to the horizon  for the terms sunrise, sunset, dusk, dawn, and twilight (Source).

Figure 1: Illustration of the Terms Sunrise, Sunset, Dusk, Dawn, Horizon, and Twilight.

My analysis will be focusing on sunrise and sunset time.

## Analysis

### Approach

I just grabbed the sunrise, sunset, and daylight duration numbers for Minneapolis from this web page and plotted them in Excel.

### Daylight Duration

Figure 2 confirms that the winter solstice (Dec 21 in 2013) has the shortest daylight duration.

Figure 2: Daylight Duration Around the Winter Solstice.

### Sunrise and Sunset Times

Figure 3 shows the sunrise and sunset times around the time of the winter solstice. Notice how the earliest sunset occurs six days before the winter solstice, and the latest sunrise occurs twelve days after the winter solstice.

Figure 3: Times of Latest Sunrise and Earliest Sunset in Minneapolis.

While the time of earliest sunset occurs six days before the winter solstice, our days continue to get shorter because the sunrise time is getting later faster than the sunset time is getting earlier. After the winter solstice, the duration of daylight begins to increase sunset time is getting later faster than the sunrise time is getting earlier.

## Conclusion

Here is what I accomplished with this exercise:

• I confirmed that the day of shortest daylight duration is the winter solstice.

The interesting thing about this fact is that the winter solstice has neither the latest sunrise nor the earliest sunset.

• I see that the date of earliest sunset is six days before the winter solstice.

Sunset times are later for the six days after Dec 15th. You would think that later sunsets means more total daylight, but sunrise is coming so late as to more than compensate for the later sunset.

• I see that the date of latest sunrise occurs twelve days after the winter solstice.

At this point, we now start seeing the duration of daylight begin to increase more rapidly.

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### 3 Responses to Times of Latest Sunrise and Earliest Sunset

1. Another very interesting post, which takes me back to my years at the Naval Academy, when we were supposed to be able to calculate the Equation of Time based on a given position and with the help (so to say) of our log tables, ephemeris tables, a 13" slide rule, our understanding of spherical trigonometry and the severe look of our Professor of Astronomy. This is a fascinating chapter in the study of time's nature and measure. It is fascinating to consider that the time we read off our watches is a measure of the mean position of the sun and not of its real position. So if we define noon as the passage of the sun on any meridian, local noon and watch noon would only coincide on solstices and equinoxes. That's due to the combined effects of the ellipticity of Earth orbit and the obliquity of Earth axis. These two combined effects cause (also) the asymmetrical distribution of sunrise and sunset times along the year (which you noticed in Minnesota and that I can confirm to take place in London as well); in the northern hemisphere this is more visible around the winter solstice (which also anticipates by a few days the perihelion, around the 3rd January).
Finally, as a small anecdote, it is customary in Catholic countries to celebrate Saint Lucia, as the patron saint of the blinds. She is celebrated on the 13th December which, in accordance with the Julian calendar, was the shortest day of the year; but Julius Caesar didn't take my Astronomy lessons nor he read your post (he was probably busy conquering Europe), hence he got confused by the fact that around that day you don't have the shortest day but the earliest sunset.
Happy New Year!

2. Moose says:

I have what ought to be a dumb question: how did you import the dates from that site into excel? I get them as December-1-2013 which I can't for the life of me turn into an excel date.

I want to look at whether position in the time zone matters... Minneapolis seems pretty close to the center, but is the answer different near the edges?

Thanks for a fun post. It's something I've been noticing as I decide when it will be light enough to ride my bike home from work again.

• mathscinotes says:

I have what ought to be a dumb question: how did you import the dates from that site into excel?
I used the "From Web" command on the Data tab. You can also just select the calendar cells on the screen and past them into Excel. Same thing.

I get them as December-1-2013 which I can’t for the life of me turn into an excel date.
Just use the Text to Columns command on the Data Tab. Tell it that you will be converting a Date of form MDY.

I want to look at whether position in the time zone matters… Minneapolis seems pretty close to the center, but is the answer different near the edges?
In the post, I refer to a Wikipedia page that discusses the sunrise and sunset equation. If you look closely at the equation, sunrise and sunset times depend on local solar noon, which varies with longitude. So the answer is different along the edges.

Thanks for a fun post. It’s something I’ve been noticing as I decide when it will be light enough to ride my bike home from work again.