The analemma and the Equation-of-Time are a result of the sum of the effects of the Earth’s elliptical orbit around the sun and the tilt of the Earth’s axis in relation to the plane of its orbit around the sun. The following chart shows the effect of this summation.

This chart shows the position of the true sun in the sky throughout the year. The y–axis on the chart represents the declination of the sun in the sky for one year, going from –23.45° in the winter to +23.45° in the summer. The x–axis represents the difference in time from what your watch reads to the actual position of the sun in the sky.

This chart also demonstrates why even though the longest day of the year is around June 21st, the latest sunset occurs a few days after that. At the top of the chart we can see there is more lateral motion of the sun than motion downwards. In otherwords, when your watch reads that the sun should have set, the true sun will have drifted slightly to the east (up). The opposite effect occurs in the winter. While the shortest day of the year is around December 21st, the latest sunrise does not occur until several days after that.

Let’s go back inside the celestial sphere and watch the path of the true sun making the analemmic curve. The speed of the true sun on the ecliptic now reflects its elliptical orbit around the sun, moving faster in January and slower in July.

And finally, a view from the sun looking back towards the Earth.
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Earth's TIlt - Math Summation - Math