Equation of Time

In Astronomy by Brian Koberlein5 Comments

In our modern age, we measure time by clocks calibrated to an international standard.  With the exception of the occasional leap second, each day is exactly 24 hours long.  So you might figure that the time between noon on Monday and noon on Tuesday is likewise 24 hours, but things are not quite so simple.

If we consider “noon” to be the time at which the sun is highest in the sky (which we can measure by a sundial), rather than “when the clock reads 12,” then the time between successive noons is not quite 24 hours.  Relative to our clock, our sundial will seem to run a bit fast on some days, and a bit slow on others.  To relate sundial time to clock time, we therefore need a correction known as the equation of time.  I’ve plotted this equation in the figure below, and it shows the correction factor needed at various times of the year.

eoftThe reason for this correction is because of two factors.  The first is that Earth’s orbit is not quite a perfect circle but rather a slight ellipse.  For part of the year, it is a bit closer to the Sun than its average distance, and for part of the year it is a bit further away.  While the Earth rotates on its axis at essentially a constant rate, the Earth’s speed around the Sun is not constant.  Instead, it orbits a bit faster when it is closer to the sun and slower when farther away.  Because the Earth is orbiting the Sun, the Earth has to rotate about a degree more than 360 degrees to go from noon to noon.  On days when it moves faster, it has to rotate a bit more than that, and on days when it moves more slowly, it has to rotate a bit less.

The second factor is due to the tilt of the Earth’s axis.  Because of this tilt, the Sun appears higher in the sky during the Summer months and lower in the Winter months.  This means from one noon to the next, the Sun is a bit higher or a bit lower depending on the season.  That daily shift means the time at which the Sun is highest in the sky (noon) is a bit early or a bit late.

The combination of these two factors creates the equation of time you see above. It is the ebb and flow of the celestial clock as our home rounds the Sun.


  1. Somewhat related: How do tides play into the Earth’s rotation around it’s axis and length of the day? Do tides serve as “friction”? As the Earth’s glacial ice sheets continue to melt, there will be a redistribution of weight on the Earth, and also more water to be pulled by the Moon and Sun. Plate tectonics will also accommodate the redistribution of weight. How will this all contribute to the length of a day?

    1. Author

      Tides do serve as friction, and is part of the reason why the Earth’s rotation is gradually slowing down. Things like the melting ice sheets and tectonics can affect the rotation as well. However all of these are very small contributions, and only matter on geologic time scales.

  2. While the orbiting of the Earth always contributes a positive addition to clock time to get sundial noon time, the overall graph having both positive and negative corrections implies that the tilt of the Earth plays a bigger role in this correction. Can you please explain how both positive and negative corrections are required?

    1. Author

      The Earth’s motion in its orbit is faster at times and slower at times, while the rotation of the Earth is basically constant. So the length of time from noon to noon is longer and shorter. Days are marked relative to the “average” day, hence the need for both positive and negative corrections.

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