Buy F&SF • Read F&SF • Contact F&SF • Advertise In F&SF • Blog • Forum

August 1999
 
Book Reviews
Charles de Lint
Elizabeth Hand
Michelle West
James Sallis
Chris Moriarty
 
Columns
Curiosities
Plumage from Pegasus
Off On a Tangent: F&SF Style
 
Film
Kathi Maio
Lucius Shepard
 
Science
Gregory Benford
Pat Murphy & Paul Doherty
 
Coming Attractions
F&SF Bibliography: 1949-1999
Index of Title, Month and Page sorted by Author

Current Issue • Departments • Bibliography

Science
by Pat Murphy & Paul Doherty

The Shadow Knows

Gordon Van Gelder, the editor of this magazine, is a clever man. When he asked us to write for Fantasy & Science Fiction, he wanted us to write four columns a year. He cleverly set our deadlines on dates that we, as scientists who spend our time observing the natural world, could not possibly forget. He said, "Let's make your columns due on the solstices and equinoxes."

Very clever. We haven't forgotten a deadline yet.

In honor of that astute decision, we decided to write this column about about the solstices and about the movement of the sun as perceived from the earth. We're going to suggest that you spend some time watching shadows, a way of indirectly observing the movement of the sun across the sky. These observations can put you in touch with natural patterns that humans have been watching for thousands of years--but that most of us modern folks have come to ignore. Along the way, we'll talk about time--we just can't avoid it.




I'm not lazy; I'm a scientist

We'll start with an observation you can make on a sunny afternoon, while lounging around in a hammock or kicking back in a poolside bar. Take a look at the shadows around you. Find a place where a shadow, maybe the shadow of a building or a fence, makes a straight line. Mark that line somehow--with a rock if you're on the grass, a chalk line if you're on blacktop, or a swizzle stick if you are sipping daquiris by the pool.

Guess where the shadow will be in 15 minutes and mark your guess in the same way you marked the shadow. ("Hey, could we have some more swizzle sticks over here? Oh, sure--put 'em in another round of daquiris.")

In 15 minutes, check your guess. You may be surprised at how quickly the shadow moved. That is, you may be surprised at how quickly the sun moved. Or, to be even more accurate, you may be surprised at how quickly the earth is spinning--about 1000 miles per hour at the equator.

Right now, for simplicity's sake, we're going to talk about the movement of the sun. We know and you know (and Galileo knew) that the sun isn't really moving across the sky. But according to Paul, physicists have to be adept at jumping from one point of view to another. According to Pat, so do writers. So we're going to stay on earth (at that poolside bar, maybe) and tell our story from that frame of reference for a while.

Next time you spend the day outside, pay attention to the movement of the shadows as they move with the sun. The sun rises more or less in the east (more on that "more or less" later) and sets more or less in the west. So the shadows point more or less west in the morning and more or less east in the afternoon.

An interesting aside here: if you watch the movement of the shadow on a sundial over the course of a day, you'll notice that it moves in a clockwise direction. Coincidence? We don't think so! Early clockmakers designed clocks to mimic the familiar sundial. Those readers who are fond of alternate history stories might consider what might have happened if we used clocks based on sundials that had been developed in the Southern Hemisphere where shadows move the other way!

Shadows are at their longest at sunrise and sunset. When are they at their shortest? Noon, you say? Well . . . more or less. You see, unlike sunrise and sunset, the concept of noon relates to human time-keeping--and that gets a little tricky.




Does Anybody Really Know What Time It Is?

If you are telling time by the sun, noon is defined as the time when the sun is at its highest point in the sky. The important words in that sentence are "if you are telling time by the sun." That is, if you are using solar time. Chances are, you are telling time by that device strapped to your wrist. And the time on your wrist watch isn't solar time; it's what's called standard time. You can blame that on the railroads.

Back before 1883, people used solar time. Each community kept its own time, basing that time on the sun's position in the sky. Since the sun is always moving across the sky, noon where you are is at a slightly different time than noon at a place a few miles to the east or west. Back before 1883, noon in one town would be four minutes later than noon in a town fifty miles to the east.

In 1883, to regulate time for the sake of railroad schedules, the United States adopted standard time, designating time zones and requiring all communities within a time zone to keep the same time—even though that standard time doesn't quite match solar time.

If you are smack dab in the middle of your time zone, the sun will be at its highest point at noon. But if you are at one edge of your time zone, solar time may differ from standard time by as much as 40 minutes.




What About the Solstice?

If you spend some time watching shadows, you'll notice that the position and length of a shadow depend not only on time of day--but also on the time of year. That's because the sun's position at a certain time is different in different seasons. And that, of course, brings us to the solstices.

What's the longest day of the year? Any good Druid could tell you the answer to that one. The longest day is the summer solstice (June 21 or thereabouts) and the shortest day is the winter solstice (December 21 or thereabouts).

As a knowledgeable fantasy reader, you probably even know of some of the fantasy connections for these dates. The summer solstice is associated with Midsummer's Night Eve, when witches and fairies and other supernatural forces are in control. In The Hobbit, the keyhole that lets Bilbo, Thorin, and the dwarves unlock the passage into the dragon's lair opens on Durin's Day, the first day of the last moon of autumn on the threshold of winter.

You know the length of a day changes over the course of a year, but have you ever really paid much attention to the position of the sun--other than squinting when the summer sun comes in your window too early or complaining when the days get too short? Well, here's your chance.

For those of you with a lot of patience, here's an activity that takes a year to complete. You need a south-facing window, a pocket mirror, some small Post-Its, and a lot of patience. Choose a time of day when you'll be home at least once every couple of weeks for the next year. Put your little mirror on the window sill and position it so that it reflects a spot of sunlight on the wall or the ceiling. Cover most of the mirror with masking tape, leaving only a 1/4" square exposed.

If you can, fasten the mirror in place so no one moves it by accident. Pat stuck hers down with some stuff called "museum putty," that's sold in California under the brand name Quake Hold™. You folks who are sensible enough to live far away from the fault zone will have to come up with your own methods.

Note the time and date on a Post-It, and stick the Post-It to the wall or ceiling where the spot of light reflecting from your mirror falls. A week later, at the same time, do it again. And a week later, do it again. Repeat for an entire year. (We warned you that you'd need patience.)

As you do this, you need to use standard time. If you move your clock forward (or back) to adjust for daylight savings time, change the time that you make your weekly mark by an hour.

Keep it up, and at the end of a year, the Post-Its will form a figure eight on your wall. The marker from mid-December will be at one end of the eight and the marker from mid-June will be at the other. This pattern is called the analemma, which is Latin for "sundial." The analemma is a visual record of the sun's changing position over the course of a year.

This is the same figure 8 you see on earth globes—usually in the middle of the Pacific Ocean. It is also known as the equation of time. Each planet has its own shape for the analemma. On Mars, the analemma is the shape of a teardrop.

Pat is in the middle of doing this activity. (On earth, not on Mars.) As we write this column, she has Post-Its all over the ceiling of her sunporch. She started back in December and we're writing this in March, so she's not even halfway done yet.

If you (like most of us), prefer instant gratification, then you probably have access to the World Wide Web. In that case, we suggest you visit www.skypub.com/spc/staff/dic.html. On that web site, you find Dennis di Cicco's award- winning, year-long photograph of the analemma made in the late 1970s. But to convince yourself that Dennis didn't cheat and do this in a darkroom, you still might want to try the experiment with a mirror and Post-Its. Depends on how trusting you are. (According to Paul, scientists must be professional doubters. But he's not the one with Post-Its all over his ceiling, so go figure.)




So why already?

You want to know why the analemma is a figure-eight, rather than a tear-drop or an oval or a circle? You fool! Pat wanted to know why, once upon a time. Days later, after much explanation with circles and arrows and too many diagrams and too much math, she decided she didn't want to know the whole story.

We're going to give you the short version of why the analemma is a figure-eight. If you must understand every last detail (which Pat claims is enough to make a person's head explode), we recommend you visit www.analemma.com, a thoroughly detailed Web site with animations and full discussion of why the sun does that.

We'll start you off with an easy question: where does the sun rise? Did we hear you say "east"? Sorry. It's an easy question, but the answer is tricky. We warned you about that earlier, remember?

If you were to watch the sun rise each morning over the course of an entire year, you'd see that the sun doesn't always rise in the same place. In the summer, in the Northern Hemisphere, the sun rises a little bit north of due east. The date on which it rises the farthest north of due east is June 21, the summer solstice and the longest day of the year. In the winter, in the Northern Hemisphere, the sun rises a little bit south of due east. The date on which it rises the farthest to the south is December 21, the winter solstice and the shortest day of the year.

Suppose you watched the path of the sun on the winter solstice and on the summer solstice. On the summer solstice, the sun rises much higher above the horizon at noon than it does on the winter solstice, taking a longer path across the sky. On the winter solstice, the sun never gets as high in the sky.

Okay, now we're going to have to do one of those shifts in viewpoint that physicists and writers like. Instead of staying on earth, we need to take a look at the solar system from the outside, examining the earth's orbit.

The sun's path across the sky changes with the seasons partly because the earth's axis (the imaginary line through the earth around which the planet spins) is tilted with respect to the earth's orbit around the sun. As the earth orbits the sun, the North Pole (the point where the axis intersects with the earth's Northern Hemisphere) always points in the same direction, pointing near Polaris, the North Star. (The direction of the Earth's axis does change over a 26,000 year cycle, which means that the analemma evolves with time. But we're not going to get into that here.)

Because the earth's axis is tilted, during a portion of the earth's orbit, the earth's Northern Hemisphere is tipped toward the sun. That's when it's summer in the Northern Hemisphere. The North Pole is tipped toward the sun and the sun shines on a greater area of the Northen Hemisphere. As the earth spins, places in the Northern Hemisphere stay in the sunlit area longer, and the days are longer.

At the other extreme of the earth's orbit, the earth's Northern Hemisphere is tipped away from the sun. That's when it's winter in the Northern Hemisphere. The sun shines on a smaller area of the Northern Hemisphere, and the days are shorter.

The earth's tilt affects the position of the sun in the sky—and so does the shape of the earth's orbit around the sun. You might think that the earth always traveled about the same speed on its way around the sun. That would be the case if the earth's orbit were circular—but it's not. The earth's orbit is an elliptical, which means that sometimes the sun is closer to the earth and sometimes it's farther away. The difference in distance is only about 3% of the overall distance. That may not seem like much, but it makes a difference to the speed of the Earth.

Suppose you took the average speed of the earth --about 30 kilometers per second. If you checked the planet's speed when it was closer to the sun (which happens in January), you'd find it was a little faster than that average. When the earth was farthest from the sun, in July, you'd find that it was moving a little slower than average.




Meanwhile, Back on Earth

That's what all this looks like from outside the solar system. How does all this affect what you see on the planet Earth?

Paul says that the analemma would be easier to understand if there were no atmosphere on the earth. Without the atmosphere to scatter the sun's light, we could see the stars during the daytime, and we'd be able to see the sun's movement against the background stars. (Of course, if there were no atmosphere we couldn't breathe. But we'd understand the analemma. Pat says that seems like a small consolation.) Anyway, if we could see the sun moving against a background of stars, we'd see that the sun moves on a regular path through the stars, a path called the ecliptic.

Suppose you could see the stars when the sun is out. Suppose you're watching the stars at around noon in mid-May. The sun is in the constellation of Scorpio, perhaps near the star called Antares. Just before noon the next day, 23 hours and 56 minutes later, you check on the position of Antares. Antares will be back in the same place in the sky. The sun, however, won't yet have reached its highest point in the sky. That will take about four more minutes. From your point of view on earth, the sun is lagging four minutes behind the stars.

Add together the time it takes for Antares to return to its original position and the four minutes that it takes to get the sun back to its original position. You get 24 hours or one average day. Very tidy, isn't it?

Each day, the sun lags behind the stars. Over the course of months, this accumulating difference means that different stars rise at different times. In the Northern Hemisphere, for example, Scorpio is a summer constellation--you don't see it in the night sky during the winter. The difference between the sun's movement and the stars' movement has shifted the rising time for the stars that make up Scorpio so that the constellation is up during daylight hours.

Why do the sun and Antares move across the sky at slightly different rates? Ah, that takes us back to outer space. The earth is spinning, and that's what brings Antares back to its starting position. But the earth is also orbiting the sun. That's why it takes an extra four minutes (or so) for the sun to get back into position.

No doubt you caught that weasely little "or so" in the previous sentence. It doesn't always take the sun exactly four minutes to get back into place. After all, the earth isn't always orbiting the sun at the same speed. From your point of view on earth, that means that the time it takes the sun to return to a particular place in the sky isn't always the same. In early January, when the earth is nearest to the sun, the sun moves farther from one day to the next. It takes longer for the earth to overtake the sun and return it to the same place in the sky. It can take 8 seconds longer each day. These 8 seconds add up from day to day, and the sun begins to lag behind. In June, when the sun is farthest from the earth, the sun takes less than four minutes to return to its original position.

But that's not all. Remember the earth's tilt? Over the course of the year, the position of the noontime sun moves up and down in the sky, because of the earth's tilt. Consider the position of the sun at noon. Maybe you've been told that the sun is overhead at noon. That's not necessarily so. (Sorry. Someone's been telling you fibs.) In fact, if you are in North America, the sun is never directly overhead. For the sun to be directly overhead, you have to be in the tropics, the belt around the earth between the Tropic of Cancer at 23.5 degrees north latitude and the Tropic of Capricorn at 23.5 degrees south latitude.

On the summer solstice, when the North Pole is tilted 23º 21' toward the sun, the sun is directly overhead on the Tropic of Cancer. Six months later, on the winter solstice, the South Pole is tilted toward the sun and the sun is directly overhead on the Tropic of Capricorn.




Putting It All Together

From our earth-based viewpoint, the movement of the sun changes in two ways over the course of the year. The daily path of the sun moves up and down in the sky, and the time it takes the sun to reach its noontime position changes, with the average time being four minutes.

Those of you who are familiar with electronics may have seen Lissajous figures, very cool patterns that appear on an oscilloscope screen when you have two signals out of phase with each other. Paul says of the analemma: "It's a Lissajous figure with the sun moving up and down in the sky once a year and ahead of and behind the rotation of the earth twice a year." Pat agrees that makes a certain amount of sense: after all, you have two movements that are out of phase and that could certainly create a figure 8. But she says that we have already caused the heads of our audience to explode and we should stop now.




But Wait! There's More!

For those of you who are still with us, here is one more question. You know that the winter solstice is the shortest day of the year. On what day of the year does the sun rise latest? Or, for those of us who prefer not to be up at dawn, on what day of the year does the sun set earliest?

Did you say the winter solstice? Not a bad guess, but wrong, nevertheless. Though the winter solstice is shortest day, but it's not the day when the sun rises latest or sets earliest. The exact date of the latest sunset depends on your exact latitude, but around here the earliest sunset is around about December 7 or so. The latest sunrise is around about January 4. And the winter solstice is December 21, somewhere between the two.

Weird. To understand why this happens, you need to apply the concept of analemma rise and analemma set. And that's something that Paul says makes his head hurt. So we'll stop here, with Pat cheerily putting Post-Its on her ceiling and Paul puzzling over analemma rise. Then maybe we'll have another round of drinks by the pool and watch a few shadows move. After all, it's science.

To contact us, send an email to Fantasy & Science Fiction.
If you find any errors, typos or anything else worth mentioning, please send it to sitemaster@fandsf.com.

Copyright © 1998–2014 Fantasy & Science Fiction All Rights Reserved Worldwide

Hosted by:
SF Site spot art