Expert: Courtney Seligman - 1/21/2011

Question
Beginning at the winter solstice. Why do the change in sunrise and sunset differ. In Seattle, after 30 days, sunrise is 4 minutes earlier, and sunset is 30 minutes later. Why the difference?

Answer
Added note, in response to feedback: I'm sorry that my answer wasn't as clear as it could have been. However, my statement that the Sun is moving northward in January is correct, in the sense that although it moves eastward every day (relative to the stars) it also moves north and south during the year (which is the cause of the seasons). In late December, it is as far south as possible (the exact date when it is furthest south defining the Winter Solstice, around the 21st of December). So as December turns to January, the Sun is moving eastward (as usual, though a little faster than usual) but also northward, relative to its southernmost position. This makes the days longer, so as it moves north(east)ward, it should rise earlier and set later (for Northern Hemisphere observers). In your original example, by mid to late January the Sun is up over half an hour longer than in late December, which should cause it to rise 17 minutes earlier and set 17 minutes later, if there were no other complications. The complication discussed in the original answer (that sundial time runs about 13 minutes "slow" because of the Sun's faster than normal eastward motion) shifts things so that it doesn't rise that much earlier, and sets much later.

Again, I apologize for not making things as clear as they could have been; but I find that if I try to explain things in too much detail at the start, all I do is confuse people.
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That's because our clocks are based on the average motion of the Earth around the Sun, and the corresponding average motion of the Sun among the stars. On the average, the Earth moves 360/365 of a degree around the Sun each day (there being 360 degrees in an orbit, and 365 days in a year), which is a little less than a degree per day. But in early January we are closer to the Sun than usual (in fact, we are closest to it the first week of January), and moving around it faster than normal -- about 61/60 of a degree per day, which is a little more than a degree per day. As a result, the Sun seems to move eastward among the stars over 3% faster than normal at that time of the year. This causes the daily westward motion of the Sun to lag behind its average motion, and makes the Sun rise and set later than you'd expect.

Using your example, in mid to late January the actual motion of the Sun is running about 13 minutes behind the average motion which we use to set our clocks. If not for the change in the time it is up, it would rise and set 13 minutes later; but because it is moving northward, it is up longer. This shifts the time error so that sunrise is earlier, but not as early as you might expect; and sunset is even later than you would expect.

As a final note, if you look at old globes (or reproductions of old globes), there is usually a funny looking figure 8 off the west coast of South America. This is a graphic representation of the "analemma", and was supposed to allow the owners of such globes to correct their watches and clocks for the "error" made by sundials as a result of the Sun's non-uniform motion among the stars (although of course a table of corrections by date would do the same thing more accurately). So if you look up the analemma, you should be able to read more about the non-uniform motion of the Sun, and its effect on the difference between Apparent Solar Time (which is what is kept by a sundial) and Mean Solar Time (which is what we use to set our clocks).