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## The Question

(Submitted January 16, 1998)

I have a question regarding sunrise and sunset. I realize that the winter solstice on 21Dec is the shortest day of the year. Since this date, the days have been gradually getting longer. Sunset has been getting gradually later as expected, however, sunrise continued to come later until the first week in Jan. My question is: what is the cause of this asymmetrical distribution of daylight between sunrise and sunset?

This is due to a phenomenon called "the equation of time".

Solar day is the length of time between one local noon (when the Sun is highest in the sky) to the next. As it turns out, the length of the solar day is not always 24 hrs (its average over the course of a year defines 24 hrs). The solar day would always be 24 hrs if the Sun 'moves' east against the background of fixed stars at a constant rate (for convenience, astronomers have invented 'Mean Sun' to do exactly that). The real Sun moves at a variable rate, however,

• Because of the tilt of the Earth rotation axis relative to its orbit around the Sun (the obliquity), the same reason as for the changing length of daytime hours.
• Because the Earth's orbit is elliptical and so it moves faster at perihelion (around Jan 2) than at aphelion (Jul 3).

Both effects combine to create an offset in the time of local noon (and those of sunrise and sunset) by as much as +/- 16 min: this is the equation of time. Around winter solstice, the daily change in the equation of time happens to be more important than the daily change in the length of the day, causing the phenomenon you so keenly observed.

The equation of time is often represented by a figure 8. That figure is called an 'analemma'. There is an actual photograph of an analemma at http://sundials.org/links/local/pages/dicicco.htm (https://pantherfile.uwm.edu/kahl/www/Images/Weather/Other/analemma.html), which was taken by Dennis di Cicco.

I hope this helps,

Koji Mukai, David Palmer, and Tim Kallman
For the Ask an Astrophysicist Team

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