# The Shortest Day

As I write this post, it’s completely dark outside and it’s only 5 o’clock in the afternoon. Today is 4 December, and most people I come across think that it will continue to get dark earlier and earlier in the afternoons until 21 December, the shortest day of the year (at least for those of us in the northern hemisphere). This, however, is not the case.  The evenings in fact start to draw out a week or so before December 21, although it does not start to get lighter in the  mornings until  early in the new year.

This post aims to explain this interesting phenomenon.

Sunrise and Sunset in December

The table below shows the sunrise and sunset times for London in December 2014.

In the table the daylight interval column shows the number of hours, minutes and seconds between sunrise and sunset. This clearly shows that December 21 has the shortest period of daylight. However, the time of sunrise continues to get later and later throughout the whole of December, whereas the time of sunset starts getting later after December 12.  This is good news for Mrs Geek, who walks home from work in the dark at this time of year.

The column in the table showing the solar noon gives the time of day that the Sun is at its highest in the sky or, to put it another way, the middle of the day at the mid-point between the times of sunrise and sunset.  The table shows that, during December, the solar noon moves later and later by about 30 seconds each day.

Why does the solar noon shift ?

solar day is not always exactly 24 hours.  In fact, it is 24 hours only four times a year, and never in December.  The definition of a solar day is the period of time between solar noon on one day and solar noon on the next day.  It is at its shortest, around 23 hours 59 mins 38 seconds, in mid September and at its longest, around 24 hours 30 seconds around Christmas Day.

As you can imagine, it would be complete chaos if our clocks and watches had to cope with days of different lengths, so we use 24 hours, the average over the whole year, for all timekeeping purposes (See Note 1).

So, as I mentioned before, the solar days in December are on average 24 hours and 30 seconds, while our clocks and watches are still assuming that each day is exactly 24 hours.  This causes the day to shift about 30 seconds later each day,  as shown in the diagram below.  This explains why the evenings start drawing out before the shortest day, but it continues to get darker in the mornings until the new year.

Sundials and the “equation of time”

Before the invention of accurate clocks sundials were widely used to keep time.

Sundial in Harrogate in the North of England

As the length of a solar day varies over the course of a year, the solar time, which is the time given by a sundial, will not be the same as the time measured by a clock which assumes that all days are exactly 24 hours long. Before the invention of accurate clocks in the 17th century because the variation is so small virtually everyone in the world, apart from a very small number of astronomers, would have been unaware of this.

However, in the eighteenth and nineteenth century as mechanical clocks started to take over timekeeping from sundials, the difference between the time measured by an accurate clock which is called mean time and solar time became an issue for everyday life. Astronomers call this difference ‘the equation of time’.  It was first  calculated and measured by the British astronomer John Flamsteed (1646-1713) in 1673.

Incidentally Flamsteed was appointed by the king as the first British Astronomer Royal in 1675, for which he was given the allowance of £100 per year.  He also set up the Royal Observatory at Greenwich, shown below.

The diagram below shows how the equation of time varies throughout the year.

As you can see from the diagram, if we were to use a sundial to measure time

• from 15 Apr to 13 June and 1 Sept to 25 December to the sundial would be fast
• from 25 December to 15 Apr and 13 June to 1 September the sundial would be slow.

The days when the differences are greatest are

• November 3/4 when at 11:44 am, a sundial in London would be showing a time of 12 noon
• February 11/12 when at 12:14 pm a sundial in London would be showing a time of 12 noon. See Note 2

Why does the length of a solar day vary ?

The reason why the length of the solar day varies is due to two different factors.

1. The fact that the Earth moves in an elliptical (oval-shaped) orbit around the Sun and its speed varies, being faster in earlier January, when it is closer to the Sun and slower in early July, when it is further away.
2. The fact that the axis of the Earth’s rotation is tilted.

The combination of these two factors gives the equation of time shown in the picture above. How these factors affect the length of the day and thus the equation of time is little too complicated to cover in a blog such as mine, which is aimed at the non-scientist. If you want to find out more the equation of time page on the Royal Greenwich Observatory website gives a lot of further information. To view it click here

What about the southern hemisphere ?

In the southern hemisphere the longest day is around December 21. What happens  is that the Sun starts rising later before December 21, but it doesn’t start getting dark earlier in the evening until well after December 21. This is illustrated in the table below, which shows the sunrise and sunset times for December for Wellington in New Zealand, which lies at a latitude of roughly 41 degrees South.

Note 1

The Earth’s rotation  is slowing down, causing the length of a day to get gradually longer. In the year 1900 a mean solar day was 24 hours long. Now, in the early 21st century, a mean solar day is actually 24 hours 0.002 seconds long. To prevent the day we measure using accurate clocks  from drifting away from the “natural day” we need to add an second called a leap second ever few years. For more information on this see my post: The Days are Getting Longer.

Note 2

For most places in the world the Sun isn’t at its highest in the sky at 12 noon. This is because, rather than each area having its own local time, the world is divided into time zones, which are normally a whole number of hours ahead of or behind Greenwich Mean Time (GMT). For example, Manchester, where Mrs Geek and I live, is roughly 2.5 degrees West of Greenwich, but is on the same time zone. Because it is further West, the Sun rises and sets later than it does in Greenwich.  From late Oct to late March, in Manchester the Sun  is at its highest in the sky at 12:10 pm (on average) compared to 12-noon at Greenwich.  At the end of March the UK puts its clocks forward by one hour, so from late March to late October the Sun will be (on average) at its highest in the sky at 1:10 pm in Manchester.

## 15 thoughts on “The Shortest Day”

1. The first time I had heard that the earliest sunsets are in early December, I did find it hard to believe, so I decided to test it. (I live at about 40 degrees latitude in eastern North America.) By paying attention, I saw that in the last week of December there, the sun sets noticeably later than the first week of the month, nearly 10 minutes. Astronomy is always throwing us a new surprise.

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2. Reblogged this on Scientific Sense and commented:
Most of us in Africa, especially in East Africa are used to 12hrs daylight….this article would be an interesting read for most of us

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3. Thank yo! Time has always seemed to me a mean taskmaster; now it is shown intrinsically mean, at least via clocks. Most appropriate!

A vague impression from somewhere suggests that the earth precesses; that might affect the equation of time? Or is that limited to the magnetic poles? And will time be affected by the apparent ongoing geomagnetic reversal?

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4. According to the equation of time, one of the four dates when solar time and clock time are equal is December 25th. But you say that a solar day is never 24 hours in December. Am I missing something?

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The best way understanding this effect is by considering the fact that during December the solar noon, which is time when the Sun is at its highest in the sky, gets progressively later throughout the month.

The reason for the shift is that, as stated in the post , because the actual length of all the [solar] days in December are a roughly 24 hours and thirty seconds long , but we always take a day to be exactly 24 hours long for civil timekeeping purposes, the day effectively shifts by 30 seconds later each day.

To see this, look at the table at the start of the post, which shows the time of the solar noon at three day intervals for London and you’ll see that at the start of December the solar noon is at 11:50 am and at the end of December it is at 12:03 pm (rounded off to the nearest minute). The fact that the solar noon is around 12:00 on Christmas doesn’t mean that a day is 24 hours long on Christmas day

This effect continues into January, but at steadily reducing rate. By the end of January a [solar] day is 24 hours and 5 seconds long and the solar noon ,in London, will be about 12:14 (GMT) .

On February 12 a [solar] day is exactly 24 long and the solar noon in London is about 12:15. From then until the middle of May all the days are shorter than 24 hours long and the solar noon drifts backward.

The Science Geek

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5. that is so cool. Thanks

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6. Very interesting. I knew that the sun stared rising earlier in January but it’s such a small increment that it takes almost until mid-January to notice. I also knew, somewhat, about having to add leap-seconds that culminate in a full day every 4 years. But the rest was new to me. Thanks for the continuing education post.

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1. Thanks for your kind comment and glad you’re enjoying my blog. What you said isn’t quite right about leap seconds :).

It takes roughly 365 ¼ days for the Sun takes to return to the same position in the cycle of seasons as seen from Earth. We call this period of time a solar year.

If all years had exactly 365 days then the calendar year would slowly run ahead of the solar year at the rate of roughly ¼ day sper year. So, in about 400 years from now, the seasons would have drifted by about 100 days. Spring would start at the end of June, the Summer solstice, or longest day, would be at the end of September, the Fall equinox would be at the end of December. To prevent this happening we add an extra day (February 29) every four years, when this happens it is a leap year. The rule is that if the year is divisible by 4 then it is a leap year (e.g., 2008, 2012, 2016). Because the number of days in a solar year is actually slightly less than 365 ¼ (it is 365.242 to three decimal places), we have the further rule that a century year e.g. 1900, 2000, 2100,2200 must be divisible by 100 to be leap year. So 2000 was a leap but 2100 and 2200 won’t be.

Leap seconds arise for a similar reason as leap years. The length of a mean solar day (the average day measured by measuring the rising and setting of the Sun) is actually around 24 hours 0.002 seconds. This means that in 500 days the solar day would drift out from the actual day by 1 second. To prevent this happening we add the occasional extra leap second . When these are needed they are added on June 30th or December 31st.

The Science Geek

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1. Fascinating…..really fascinating. If sun set at 1500hrs or took longer….probably till 2000hrs or even 1900hrs in my country (Kenya), everyone would start “repenting” as ‘we’ await our journey to heaven. Thumbs up Sciencegeek……..

In your response to frncnseal585, I seek clarification on “we have the further rule that a century year e.g. 1900, 2000, 2100,2200 must be divisible by 100 to be leap year. So 2000 was a leap but 2100 and 2200 won’t be”…..why would 2100 not be leap yet it is divisible by 100?

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1. I made a mistake in my original reply to frncnseal585. In fact in the Gregorian Calendar (which we virtually all countries in the world use) a century year e.g. 1900, 2000, 2100,2200 must be divisible by 400 to be leap year.

Thanks for highlighting this 🙂

The Science Geek

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