Equation of Time - Analemma

Elliptical Orbit Effect

We begin this section by making two assumptions:

  1. The Earth is not tilted on its axis.
  2. The observer is standing on the equator.

The Earth does not travel around the Sun in a circle, but in an ellipse. If the Earth were to orbit the Sun in a circle, with the Sun as its centre, the Earth's speed around the Sun would be constant. We can think of this as the Earth's average speed. However, because the Earth's orbit is elliptical, the speed of the Earth varies throughout the year. The speed of the Earth is fastest when it is closest to the Sun, in January, and slowest when it is furthest away from the Sun, in July. In other words, in January, it will be moving faster than average, and in July, it will be moving slower than average.

Let's look at the animation. Note that the effect due to the Earth's elliptical path has been greatly exaggerated in the animation.

Notice that the green coloured Earth travels around the Sun in a circle. Its speed never varies. The blue coloured Earth travels around the Sun in an ellipse. Its speed is greatest in January, when it is closest to the Sun. Its speed is slowest in July, when it is furthest away from the Sun.

Although our clocks say that the day is 24 hours long, it only takes the Earth 23 hours 56 minutes to make a complete revolution about its axis in a day. Hence, at the end of 24 hours, the Earth has actually rotated 361, instead of 360. If we superimpose 2 Earths, one having rotated around the Sun for 24 hours in a circular path and the other in an elliptical path, we will get the picture in Figure 15. Earth A travelled in a circular orbit at a constant speed. Earth B travelled in an elliptical orbit, so in January, it was traveling faster than average.

elliptical effect
Figure 15

After 24 hours, if you were standing on Earth A looking at the Sun, it would appear to be directly overhead. If you were standing on Earth B looking at the Sun, it would not appear to be directly overhead. Earth B has not quite rotated far enough relative to the Sun. If you were looking at your watch on Earth B and comparing its time to the position of the Sun, it would appear that the Sun's position would be slightly to the east. After another 24 hours, Earth B is still continuing to move faster than average. This error in time will accumulate and the Sun will continue for a time to appear to move further and further east in the sky, again, in comparison to what your watch reads at noon.

The difference continues to accumulate until around 2nd April, when the speed of Earth A and Earth B are the same. At that time, the position of the Sun in the sky will have reached its maximum "offset" to the east. The time difference between the Sun and your watch will be almost 8 minutes. From 2nd April to 3rd July, the Sun will drift back toward the west. Then from 3rd July to 2nd October, the Sun continues to drift west until it reaches its maximum "offset" in the west. Then from 2nd October until 2nd January, the Sun drifts back toward the east until it reaches its starting position on 2nd January.