Sunday, December 8, 2013

If the shortest day is Dec 21st, why is the earliest sunset weeks before?

A recent post at EarthSky explains a confusing fact: the earliest sunset of the year is NOT on the shortest day of the year--December 21st--but weeks earlier.

The days shorten until December 21st or so, due to the earth's revolving around the sun to the point at which the earth's tilt has the northern hemisphere tilted as far as possible away from the sun.  It would be reasonable to expect that the days would shorten equally at both "ends"--so later sunrises and earlier sunsets--but that turns out to be wrong.
On the right is the situation we're approaching: notice that
much of the northern hemisphere in darkness, so that our daylight hours are few.

I first discovered this years ago as a junior high school science teacher.  I liked to get out of the book sometimes, and do big outdoor things.  One favorite was to make the school yard into a giant sundial using the flagpole as a gnomon.  (My hope was that such a tall pointer would make a shadow you could watch move just standing there for a few minutes, but the shadow turned out to be too indistinct to work well.)  I wanted to use the shadow to establish the exact direction of south by looking at the shadow at "local noon"--the time when the sun is directly over your meridian, that is, your longitude line.  I figured to find that time as the half-way point between sunrise and sunset.  (That didn't work as planned, owing to the definitions of sunrise and sunset!)  It was in studying the newspaper almanac day after day that I became confused by the seeming lack of a pattern in the times. 

Note: I've discovered that the explanation below (as well as the EarthSky post referenced above) has errors. I will fix these in a post later in January. (Edited 1/3/14)

EarthSky describes the reason for the mismatch this way: "The time difference is due to the fact that the December solstice occurs when Earth is near its perihelion – or closest point to the sun* – around which time we’re moving fastest in orbit. Meanwhile, the June solstice occurs when Earth is near aphelion – our farthest point from the sun – around which time we’re moving at our slowest in orbit."

That explanation is good, but has gaps I think need filling.

First, why should the speed of the earth in its orbit around the sun affect sunrise and sunset times?  For convenience, let's count a day as being from one solar noon to the next.  (The Royal Navy used to do this.)  We think of the 24-hour day as the result of the earth's rotation on its axis, but in fact the sun is also moving about one degree of its 360 degree annual trip around the sun in that same day.  That means that the earth not only has to rotate one degree MORE than 360 degrees on its axis in order for our location to return to pointing at the sun--that is, back to solar noon.  As long as the earth kept a steady speed in it's orbit, all would be well.  But instead the earth speeds up a bit as winter approaches, and begins slowing again after early January.  Because it is going more than one degree around the sun in December, the earth must rotate farther to bring it around to the same solar noon, making everything (all things being equal) a bit later.  The opposite occurs when the earth is at its slowest, in June and July.  This effect combines with the shortening days of fall to create the odd timing of sunrises and sunsets.

Here's an animation that makes the below clearer.

Imagine you are standing on earth where the left-pointing arrow begins. From "Day 1" to "Day 2" your location has rotated 360 degrees PLUS an additional amount to point back toward the sun, since the earth has moved a bit further around the sun.
At least one more question occurs: why does the earth change speed in the first place?  That has to do with the elliptical shape of earth's orbit, and a law first discovered by Johannes Kepler centuries ago (soon after Copernicus and Kepler established that the earth revolved around the sun, instead of the reverse).  Earth's orbit is an ellipse (oval) that is not quite circular, with the sun a bit nearer to one end of the oval.  Kepler discovered that planets move slowest when they are farthest from their parent body, and fastest when closest.  To be precise, any orbiting body sweeps out equal areas of its orbit in equal times.  (You can think of these areas as pie-slices of the whole orbit: it will take a wider pie slice to cover the same area when the wedge is shorter.) 

Enough for now.  More about the "reasons for the seasons" soon!

*This surprises a lot of people, who assume that summer is warm because the earth is closer to the sun, while winter is colder because it is farther--but the opposite is true.  It turns out that the difference in earth-sun distance from summer to winter is not very great, and the reason for the seasons lies elsewhere, as I'll explain at the solstice in a couple of weeks.

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