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 the 1st of 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 accumulate 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.

The sum of the two effects is the Equation of Time, which is the red curve with its characteristic twin peaks shown below. 

below are some useful 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", for the whole of February it is 13 or 14 minutes slow.

The table below shows the dates when "Sun Time" is (nearly) exactly a given number of minutes fast or slow on "Clock Time".

Minutes fast 

Minutes 
Dates
16
Nov 11, Oct 27
15
Nov 17, Oct 20 
14
Nov 22, Oct 15 
13
Nov 22, Oct 15 
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!
 

Minutes 
Dates
0
Dec 25, Apr 15, Jun 14, Sep 2


Minutes Slow

Minutes 
Dates
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

 

Below is a 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
-5:03
-9:10
-12:12
20
February
-14:01
-14:16
-13:18 
5
March
-11:45
-9:13
-6:16
16
April
-2:57
+0:14
+1:56 
18
May
+3:18
+3:44
+3:16
4
June
+1:46
-0:10
-2:20
16
July
-4:19
-5:46
-6:24 
20
August
-5:59
-4:33
-2:14
11
September
+1:05
+4:32
+8:04
20
October
+11:20
+14:01
+15:47
13
November
+16:22
+15:28
+13:11
10
December
+9:38
+5:09
+0:13
27