The Equation of Time determines the difference between solar time and the local time seen on your watch or phone. It is relevant if you want to accurately use a sun clock to tell the time of day. The sun's position in the sky varies slightly throughout the year. If the sun's position is noted in the sky at the same time of the day every day it will create an elongated figure eight called an analemma.
There are two reasons for this variation of the sun's position. The first is due to the earth's orbit. The orbit is an ellipse not a circle. As a result the earth moves faster in some parts of the orbit than others. This effect has a period of one half of a year and adds as much as 9.9 minutes to the discrepancy between solar time and watch time. This effect is called the Orbital Eccentricity.
Most of the information here came from SquareCirclez.
The mathematics of the Orbital Eccentricity can be reduced to the following equation for the elliptical orbit contribution to the Equation of Time. The equation returns the minutes of variation and d is the day of the year.
The second contributor to the Equation of Time is the earth's tilt, 23.44°. This factor is also cyclical with a period of one year. Its maximum contribution to the difference between solar and local time is 7.7 minutes. This is known as the Effect of Obliquity. Without these two effects the sun would appear in the same position in the sky every day at the same local time.
The mathematics of the Effect of Obliquity can be reduced to the following equation for the tilt's contribution to the Equation of Time. The equation returns the minutes of variation and d is the day of the year.
Adding these two equations together produces the Equation of Time.
This equation can be graphed by the button below.
The print needs to be 2 1/2" X 3 1/2" to 2 1/2" X 4".
A screenshot was taken of the graph. This opened in Gimp and the image was flipped horizontally. The size was then readjusted. The file was exported as a png. This file was saved in the cloud.