Les deux variations que nous venons d'évoquer s'ajoutent l'une à l'autre pour donner cette fameuse "courbe d'équation du temps", qui est donc la somme de deux courbes élémentaires des figures 3 et 4. Elle est représentée figure 5.
- from June to September as the sun's speed increases, it edges ahead of so-called "mean" time. This difference is most noticeable around the middle of this period (towards the end of July).
- from September to December as the sun's speed decreases, it loses its lead and rapidly drops behind (in November).
- from March to June, it drops back once more.
If we plot this changing relationship between solar and mean time during the course of one year, we obtain a sinusoidal curve every 6 months, as shown in figure 3 :
The Eccentricity variation
Also known as the "equation of the centre".
In addition to the perturbation we have just examined, a second variation results from the fact that the earth's annual revolution around the sun describes not a circle but an ellipse, with the sun as one of its two centres. Since this ellipse is only slightly flattened off, it is however an acceptable approximation to regard it as a circle in which the sun is not quite in the centre, but slightly "eccentric". This "eccentricity" leads to an irregularity in the speed of the earth. According to the laws of stellar mechanics, the closer the earth is to the sun, the greater its speed and the further away it is, the slower it moves.
This variation of eccentricity that takes place within the duration of a year means the sun appears to us to be ahead of, or behind, mean time. In autumn, when the earth is furthest from the sun, it decelerates and the sun seems to be behind mean time. In early spring however the earth moves closer to the sun, accelerates and the sun moves ahead of mean time.
When juxtaposed, the two variations we have just looked at produce the famous "equation of time" curve, which is the sum of the curves shown in figures 3 and 4. It is illustrated in figure 5.
In addition to these two phenomena, there exist other sources of perturbation but they are so much smaller as to be not worth examining here.
"Antide Janvier, 1751-1835, Horloger des étoiles"
L'Image du Temps, 1995