We begin this section by making two assumptions:

1. the Earth's axis is NOT tilted 23.5° in relation to the plane of its orbit.
2. you, the observer, are standing on the equator.

The Earth travels around the sun in an ellipse. If the Earth were to orbit the sun in a circle, 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 farthest 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 following animation.

show movie
Notice that the green colored Earth travels around the sun in a perfect circle. Its speed never varies. The blue colored 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 farthest away from the sun.

Now let's look at another animation.

show movie
The animation represents 24 hours of time. Earth "A" travels in a circular orbit at a constant speed. Earth "B" travels in an elliptical orbit, so in January it is traveling faster than average. At the end of 24 hours, each Earth has rotated approximately 361 degrees. Let's look at their positions more closely. We will superimpose the orbits - one on top of the other.
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 appear NOT 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 farther and farther east in the sky, again, in comparison to what your watch reads at noon.

Keep in mind that all of these examples have been greatly exaggerated. At the time in January when the Earth is closest to the sun and orbiting the fastest, the actual angle between looking directly overhead and where the sun actually is, is only about .03 degrees. It takes the Earth slightly less than 8 seconds to rotate this angular distance to where the sun will appear directly overhead.

The most important thing about all of this to remember is that the difference accumulates each day. It continues to accumulate until around April 2nd when at that time the speed of Earth "A" and Earth "B" are the same. At that time the position of the sun in the sky will have its maximum "offset" to the east. The time difference between the sun and your watch will be almost 8 minutes. From April 2nd until around July 3rd the sun will drift back toward the west. Then from July 3rd to October 2nd the sun continues to drift to the west until it reaches its maximum "offset" in the west. Then from October 2nd until January 2nd, the sun drifts back toward the east until it reaches its starting position on January 2nd.
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Introduction Elliptical Orbit - Math