arrow_backTutorials - Equation of Time

Equation of Time

The equation of time describes the difference between time kept by an ordinary clock and the apparent solar time, such as a sundial would read. The word equation is used in the medieval sense of "reconcile a difference".

Apparent solar time is not a uniform time scale as the Sun will cross the sky at different rates at different times of the year.

diagram showing the equation of time

The accumulated time difference can reach as much as 16 minutes. The Sun's daily motion in the sky is the result of two components: The rotation of the Earth and Earth's orbital motion around the Sun. It is the Earth's orbital motion that is the cause of the Equation of Time. It can vary by as much as ±12% over the course of a year.

The orbit affects the Sun's apparent angular speed in two ways: Seasonal variations due to the 23.4° tilt (the obliquity) of the Earth's axis and the non-circular (the eccentricity) of the Earth's orbit around the Sun.


There is a way to show the effects of these two components, by taking a picture of the sky at the same time each day, from a fixed camera and combining them into one photo you will get an image like this.

photo of analemma

The figure-8 path that the sun makes in the sky during a year is called the analemma. The north–south component of the analemma shows the Sun's declination, its latitude on the celestial sphere, or the latitude on the Earth at which the Sun is directly overhead. The east–west component shows the equation of time, or the difference between solar time and local mean time.

Lets make our very own analemma, will use the planisphere and use a step size of 7 days, our position will be at the Royal Observatory at Greenwhich. Continue to step forward about 52 times until the figure-8 is complete.

Why don't you try making one for your location.