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2.11 The time equation


Frank L. Preuss


When one measures the true midday time at midday time, when therefore the sun is really the highest above one, therefore the axis of the earth, the position and the sun are all in one plane, then one can detect that the calculated values are not right.

There is for example the fact that the sun moves differently fast, that it is faster at sun nearness in January, and slower at sun farness in July. Astronomical tables for that reason sometimes give perhaps the distance of the sun for every day.

And for that reason the time equation exists, so that one can check these differences there.

Through the time equation one can therefore gain control of the differences between the true sun time and clock time, and check one’s astronomical observations.

The true midday time if of course always the one, when the sun goes through the local meridian.

When a country like China wants to have everywhere in the country the same time, because that is for them more important than to have midday time at about 12 o’clock, then the midday time in the capital might perhaps not be far from 12 o’clock, because it is in the time zone +8, 120oE, but in the far west of the country, therefore at 75oE, 3 time zones further, the true midday time is then at 15 o’clock. One can get used to that, but it saves one to have different clock times in the country.

Australia is in its east west extension smaller than China, but has 3 time zones.

Russia has, from the International Date Line in the east of the country, to Königsberg in the west, from time zone +12 to time zone +2, 11 time zones.

Now follows the time equation and after that an example of its use.



"Sonnenuhr geht vor"  = "Sundial is fast"
"Sonnenuhr geht nach" = "Sundial is slow"

"Die Zeitgleichung"   = "The time equation"


The time equation
Values from the time equation Zone times for Frankfurt With the time equation corrected zone times for Frankfurt Values for Frankfurt from astronomical table Differences between time equation and table
Date Difference in minutes Midday time as clock time Midday time as clock time: column 3 minus column 2 Midday time as clock time Culmi-nation height, angle in degrees Difference in minutes: columns 4 minus column 5, minutes only
17.02.-1412:2512:3912:3927.9o 0
28.03. -812:2512:3312:3042.9o+3
16.04.  012:2512:2513:25 *)50.0o 0
15.05.  412:2512:2113:21 *)58.8o 0
15.06.  012:2512:2513:25 *)63.2o 0
27.07. -712:2512:3213:31 *)59.1o+1
02.09.  012:2512:2513:25 *)47.8o 0
04.11. 1812:2512:0712:0824.5o-1
26.12.  012:2512:2512:2516.6o 0


*) Time is adjusted for DST


The data, where there should be no deviations, are marked yellow. When one therefore measures on such a day at midday the true point of time of midday time, the real midday time should agree with the calculated midday time. One should therefore then get by without a correction through the time equation.

To check the measured midday time, for example for Frankfurt, therefore the mean midday time must once be established. And that is 12:25 o’clock. And then a correction with the help of the time equation must be carried out.

For the 1. October it would be +13 minutes. By these 13 minutes the sun dial is fast. And the mean clock is then by these 13 minutes slow. And then one would get a midday time of 12:12 o’clock.

The astronomic table gives the value of 13:14 for the time and 36.6o for the angle at Solar Noon, therefore at sun midday. The time is there the summer time; the difference is therefore 2 minutes. With such differences one must therefore put his faith in the table or calculate the value oneself.

And then one must not forget that the laws of nature were created by God and can therefore also be changed by him.

"The earth rotations are therefore driven out from the inside, but regulated through counter powers, until excessive influence from the inside results in earth tremors and eruptions, so that the laws of nature remain so long irrefutable, until I myself dissolve them through my will, when the end of the earth has come." See B.D. Nr. 4998.

The simplest way to check such values is to build a sun observatory from two A4 pages oneself, and to measure the time oneself.

One can also make it still easier; one just measures the distance from a shadow casting point to its shadow every few minutes. The further midday comes, the smaller the distance becomes, and the further midday moves away, the greater the distance becomes. The shortest distance gives one the true north direction and the true midday time. One can therefore use every shadow giving point as sun observatory.




This is the end of "2.11 The time equation"
To the German version of this chapter: 2.11 Die Zeitgleichung



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