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# Treebeard's Stumper Answer16 Jan 98

Wintertime Blues

It might be some relief for the wintertime blues that the days have been getting longer ever since the Winter Solstice on December 21, the shortest day of the year. But the sun rose a bit later each day even after the solstice. Sunrise on the solstice was at 7:02, but sunrise on January 9th wasn't until 7:07. This is made up by even later sunsets, so the total amount of daylight has been growing. Just this week the sun finally started rising a bit earlier each morning. Why isn't the shortest day of the year also the latest sunrise?

Why does the sun rise later, even after the shortest day? There is a difference between clock time and sun time. We think of noon as the middle of the day, when the sun is highest. But this is rarely true by the clock. Even when we correct for time zones, the days are irregular, a bit shorter or longer by as much as 16 minutes in a complicated pattern known as the equation of time. This is caused by the tilt of the Earth's axis and the fact that the Earth's orbit is not quite a circle. At this time of year, the days are getting longer, but they're also getting later, taking the sunrise with them.

Here are a few actual sunrise and sunset times from the local Santa Barbara newspaper. Note how the sun rises later each day from the Winter Solstice on December 21 until January 8, and then starts rising a bit earlier each day. Despite this, you can see that the daylight period is consistently getting longer. For each date I've also figured the "center" of the day, the midpoint between sunrise and sunset. This is true solar noon, the time when the sun crosses the imaginary meridian line that goes across the top of the sky from north to south. dt is the equation of time, how many minutes solar noon differs from clock noon. (These numbers are slightly different from the "official" values, possible because Santa Barbara is a bit east of the 120 degree longitude line at the center of our time zone. Dunn Middle School in Los Olivos is almost exactly on the line.)

datesunrisesunsetdaylightcenterdt (min)
21 Dec7:024:539:5111:57.5-2.5
26 Dec7:044:569:5212:00+0
1 Jan7:065:009:5412:03+3
8 Jan7:075:069:5912:05.5+5.5
16 Jan7:055:1310:0812:09+9
22 Jan7:035:1910:1612:11+11

The sun rises a bit later after the solstice by the clock, but in fact it always rises earlier in relation to true solar noon. Sunrise and sunset are symmetrical with respect to sun time but not clock time. It seems a stumper that the earliest sunset is about 2 weeks before the solstice and the latest sunrise is about 2 weeks after the solstice, but this is a problem with our too-regular clocks, not the sun itself. The stumper is just an artifact of clock time.

The equation of time for the entire year is available on almost any globe. Look for the analemma, the mysterious stretched out figure 8 that's usually printed in the empty part of an ocean somewhere. Find a date around the outside of the figure, and its distance from the center line gives the time in minutes that the Sun is either behind or ahead of the clock.

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