## Equation of Time

Due to factors associated with the earth's orbit around the sun, the earth's orbital velocity varies throughout the year, so the apparent solar time varies slightly from the mean time kept by a clock running at a uniform rate. The variation is called the equation of time (ET). The equation of time arises because the length of a day, that is, the time required by the earth to complete one revolution about its own axis with respect to the sun, is not uniform throughout the year. Over the year, the average length of a day is 24 h; however, the length of a day varies due to the eccentricity of the earth's orbit and the tilt of the earth's axis from the normal plane of its orbit. Due to the ellipticity of the orbit, the earth is closer to the sun on January 3 and furthest from the sun on July 4. Therefore the earth's orbiting speed is faster than its average speed for half the year (from about October through March) and slower than its average speed for the remaining half of the year (from about April through September).

The values of the equation of time as a function of the day of the year (N) can be obtained approximately from the following equations:

ET = 9.87 sin(2B) - 7.53 cos(B) - 1.5 sin(B) [min] (2.1)

Jan Feb March April May June July Aug Sept Oct Nov Dec

Jan Feb March April May June July Aug Sept Oct Nov Dec

Day number

FIGURE 2.2 Equation of time.

Day number

FIGURE 2.2 Equation of time.

A graphical representation of Eq. (2.1) is shown in Figure 2.2, from which the equation of time can be obtained directly.