The Equation of Time

"Sun time" and "clock time"

Sundials tell "sun time". Clocks and watches tell "clock time". Neither kind of time is intrinsically "better" than the other - they are both useful and interesting for their separate purposes.

"Sun time" is anchored around the idea that when the sun reaches its highest point (when it crosses the meridian), it is noon and, next day, when the sun again crosses the meridian, it will be noon again. The time which has elapsed between successive noons is sometimes more and sometimes less than 24 hours of clock time. In the middle months of the year, the length of the day is quite close to 24 hours, but around 1 September the days are only some 23 hours, 59 minutes and 41 seconds long while around Christmas, the days are 24 hours and 31 seconds long.

"Clock time" is anchored around the idea that each day is exactly 24 hours long. This is not actually true, but it is obviously much more convenient to have a "mean sun" which takes exactly 24 hours for each day, since it means that mechanical clocks and watches, and, more recently, electronic ones can be made to measure these exactly equal time intervals.

Obviously, these small differences in the lengths of "sun days" and "mean days" build up to produce larger differences between "sun time" and "clock time". These differences reach a peak of just over 14 minutes in mid-February (when "sun time" is slow relative to "clock time") and just over 16 minutes at the beginning of November (when "sun time" is fast relative to "clock time"). There are also two minor peaks in mid-May (when "sun time" is nearly 4 minutes fast) and in late July (when sun time is just over 6 minutes slow) (These minor peaks have the fortunate effect, in the Northern hemisphere, that the differences are relatively minor during most of the months when there is a reasonable amount of sunshine).

The differences do not cumulate across the years, because "clock time" has been arranged so that, over the course of a four year cycle including a leap year, the two kinds of time very nearly come back to the same time they started. (The "very nearly" is because "clock time" still has to be adjusted by not having a leap year at the turn of each century, except when the year is exactly divisible by 400, so 1900 was not a leap year, but 2000 will be). Even with this correction, we had an extra second added to "clock time" recently.

The reasons for these differences are discussed below, followed by some information on what the differences are at given times of year. 

Why the days are of different lengths

These differences arise from two quite separate causes. The first is that the plane of the Equator is not the same as the plane of the Earth's orbit around the sun, but is offset from it by the angle of obliquity.

The second is that the orbit of the Earth around the sun is an ellipse and not a circle, and the apparent motion of the sun is thus not exactly equal throughout the year. The sun appears to be moving fastest when the Earth is closest to the sun.

These two effects are explained in more detail in a leaflet of the Royal Greenwich Observatory and in Art Carlson's excellent article on the subject at the end of this page.

The sum of the two effects is the Equation of Time, which is the red curve with its characteristic twin peaks shown below. (Many thanks to Patrick Powers for providing this graph from his ownsundial page).

An extensive discussion by Kevin Karney on the Equation of Time, including a discussion of time scales and video presentations on the components of the EoT is available on https://equation-of-time.info

Some people like such information presented in tables rather than in graphs, so two tables are presented for your information below. These are both handy summary tables, which will give you a different view of the Equation of Time, and may help you to remember some key features, for example, that between the end of March and mid-September the sun is never more than 6 minutes away from "clock time", and for the whole of February it is 13 or 14 minutes slow! If you want to know the Equation of Time for every day of the year, there is a table in Appendix A of thebook by Waugh.

Table showing the dates when "Sun Time" is (nearly) exactly a given number of minutes fast or slow on "Clock Time"

Minutes Fast__________________________________ 

16         Nov 11         Oct 27

15         Nov 17         Oct 20 

14         Nov 22         Oct 15 

13         Nov 25         Oct 11 

12         Nov 28         Oct 7

11         Dec 1           Oct 4

10         Dec 4           Oct 1 

9           Dec 6           Sep 28

8           Dec 9           Sep 25

7           Dec 11         Sep 22

6           Dec 13         Sep 19

5           Dec 15         Sep 16 

4           Dec 17         Sep 13

3           Dec 19         May 4         May 27         Sep 11

2           Dec 21         Apr 25         Jun 4             Sep 8

1           Dec 23         Apr 21         Jun 9            Sep 5

The Four Days Watches tell Sun Time - exactly right!

0           Dec 25         Apr 15          Jun 14         Sep 2

Minutes Slow__________________________________ 

1           Dec 28         Apr 12         Jun 19          Aug 29

2           Dec 30         Apr 8          Jun 23          Aug 26

3           Jan 1            Apr 5          Jun 29          Aug 22

4           Jan 3            Apr 1          Jul 4             Aug 18

5           Jan 5            Mar 29        Jul 9            Aug 12

6           Jan 7            Mar 26        Jul 18          Aug 4

7           Jan 9             Mar 22

8           Jan 12           Mar 19

9           Jan 15           Mar 16

10          Jan 18          Mar 12

11          Jan 21           Mar 8

12           Jan 24          Mar 4 

13           Jan 29          Feb 27

14           Feb 5            Feb 19

Table showing the Equation of Time on the 5th, 15th and 25th of each month, together with the average daily change in seconds (given in minutes and second, + = "Sun time" is fast on "clock time"

Eq.of time on the:

                5th           15th           25th      Av. change (secs)

 

January   -5m03     -9m10       -12m12          20 

February -14m01   -14m16     -13m18             5

March      -11m45   -9m13        -6m16            16

April           -2m57   +0m14      +1m56            18

May           +3m18   +3m44       +3m16             4

June          +1m46    -0m10        -2m20           16

July            -4m19    -5m46        -6m24            20

August       -5m59    -4m33        -2m14            11

September +1m05  +4m32       +8m04            20

October    +11m20 +14m01    +15m47            13

November +16m22 +15m28    +13m11           10

December +9m38     +5m09      +0m13           27

A review article by Art Carlson discusses the causes of these variations - click here to open it.

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