Equation of Time - Analemma

Introduction

The text and graphics in this section is based on the analemma website by Bob Urschel. The flash animation have been created for this project.

If you record the position of the Sun in the sky at the same time everyday, say sometime around noon, you would notice that the Sun takes a rather strange path. You might notice that at certain times throughout the year, the Sun is not only moving north and south as you would expect with the change of seasons, but also slightly east and west. This figure-of-8 path that the Sun makes in the sky is called the analemma. On some days, you might notice that the Sun is not in the sky where, according to the time on your watch, you would expect it to be.

The difference in time between what your watch reads and the position of the Sun is called the equation of time. If you are on the northern hemisphere and the Sun's position is to the east of where your watch indicates it would be, the equation of time is negative. If the Sun is to the west, the equation of time is positive.

An easier way to see this effect is to find a place where the Sun shines on the ground at noon all year round - winter, spring, summer and autumn. Then place a rod about 3 feet tall into the ground, making sure that it will not move throughout the year.

On the first day of each month, at the same time everyday, place a mark on the ground with another shorter rod (you will need 12 of these) where the Sun makes a shadow with the tip of the longer original rod. At the end of 12 months, you will see that the 12 short rods make a figure-of-8 pattern which is similar to the one shown in Figure 14.

analemma
Figure 14

There are two independent reasons why the Sun takes this strange path.

  1. The Earth is tilted on its axis 23.5 in relation to the plane of its orbit around the sun.
  2. The Earth does not orbit the Sun in a circle, but in an ellipse.

It is simply the sum of these two effects that causes the analemma.

With the aid of a few diagrams and animations, we hope that the analemma can be easily understood.