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Where on earth will the Sun rise earliest

A few months ago on my way to work I was listening to a popular morning program on a local AM radio station. It was a Friday morning and the weatherman was winding down his report with his daily trivia question. Callers-in had been solving his weather riddles all week and the weatherman, determined not to go 0-5 for the week, came up with the following stumper:  

"Where on earth will one be (on land) to be the first to witness the sunrise in the year 2000?"

One-by-one, the gloating weatherman shot down his audience's guesses to his vexing riddle, and by day's end the weatherman went home triumphant, 1-4. Of course the weatherman was referring to the New Millennium, and what he really meant was the year 2001, but no matter, the question can pretty much apply to any year, and to be first to witness the actual dawning of the New Millennium has got to be something to write home about.

Indeed it is a fairly tough riddle, one that might stump an unwary geographer or astronomer, even a cartographer, but as we'll see, we can home in on this elusive piece of real estate, if not quite pinpoint it, with nothing but—a globe. Yes, the underrated and underappreciated globe, commonly relegated to a den, or some room in need of an air of studiousness and refinement, is a repository for a wealth of information. Besides giving us the more mundane information such as the names of countries, oceans, and so forth, a well-labeled globe can serve as our tour guide as we ride our whirling planet through its orbit around the sun. By "well-labeled," I mean a globe with added features, including the ecliptic. The ecliptic shows the path of the sun, moon, planets, and the stars of the zodiac as the Earth goes around the Sun. It is the curving line that intersects the equator at the vernal and autumnal equinox, and diverges farthest from the equator at the summer and winter solstices. (More about the ecliptic, equinoxes and solstices further on.) As an added bonus, other features may be present, such as the analemma, and—I had to look this one up—the equinoctial colure. (If you're thinking that what follows is going to be an inscrutable treatise laden with technical jargon—take heart! Scroll down and I think you'll find most the words below in boldface are familiar.) With our globe, we can now narrow our item of interest to a sufficiently small area, maybe the size of Toledo, and then turn to a more detailed map to pinpoint the piece of land in question.

We have two main things to consider for us to reckon where the sun will rise earliest. First, along which particular north-south meridian on our spinning planet in its journey through space around the Sun will January 1 first take place? For example, on January 1, when it is 1:00 AM in London, it is 8:00 PM on December 31 in New York. London has seen the year 2001 before New York. We know as we travel west we lose one hour for every time zone we pass through. The Earth is 360 degrees around and there are 24 time zones around the Earth, thus each time zone spans a 15º arc of longitude. Syracuse, NY, where I live, lies roughly 75º west longitude. California, three time zones away, thus 45º west of Syracuse, lies about 120º west longitude. If we travel beyond California through another four time zones we reach the International Date Line. The International Date Line is where differences in time, owing to the rotation of the Earth, are reconciled. If on Friday, December 31, 1999, we were to travel from Alaska across the International Date Line into Siberia, it would become exactly one day later—Saturday, January 1, 2000. It is here, somewhere just west of the International Date line, where one will first see the sun rise in the year 2000. So we must be somewhere on or just west of this12,500 mile-long semi-circular imaginary line (the 12,500 mile-long semi-circle that completes the circle on the other side of the Earth is the Prime Meridian) to first witness the sunrise on January 1. But where?

This is our other main consideration in reckoning where on earth the sun will rise earliest. We've narrowed the location down to its line of longitude, or meridian, we now need to find the approximate line of latitude at which the event will occur so we can then home in on our site. Earth’s axis tilts about 23º 27' from vertical, or 23º 27' from a perpendicular to the plane of the Earth's orbit around the sun. If not for this tilt, the Sun would rise and set at the same time for everyone along any meridian around the Earth, from the North Pole to the South Pole as it does on the vernal and autumnal equinox, and as it does on the equator every day throughout the year. But because of the Earth’s tilt, all celestial objects rise and set at different times at different points along any meridian. The tilt further complicates things because although its angle is always the same with respect to the plane of the solar system, it continuously changes with respect to the Sun. This can easily be seen if you take your globe, dust it off, and revolve it around an object simulating the Sun while you make sure its axis always points in the same direction. Imagine light from the Sun cast onto the rotating earth as its tilt is ever-changing with respect to the sun as it journeys around the Sun—you can see why we have our change of seasons.  This continuous change in the Earth's tilt with respect to the Sun is the Sun's declination. At the solstices the Sun's declination is 23º 27'; at the equinoxes it is 0º.

So we have to imagine where, north or south along this 180º line of longitude from pole to pole, the Sun will rise earliest in the day. Where, in other words, will we be just west of the International Date Line when the Sun rises just after midnight, December 31, 1999?

We can figure this out by looking at our handy-dandy globe again. Set it on a flat surface and rotate the base of the fixture so that the North Pole is farthest away from an imaginary light source (the Sun). This simulates winter in the northern hemisphere; summer in the southern hemisphere. For illustrative purposes, let's consider Alaska. You’ve heard of Alaska’s nickname, “land of the midnight sun?” That’s an apt description—but only in summer. Around December 21, the day of the winter solstice, winter begins here in the northern hemisphere. On this day the Earth’s 23º 27' tilted axis is directed away from the Sun, thus it is the day of the year with the shortest period of daylight. On December 21 the Sun never rises in the region between the North Pole and 66º 33' north latitude. We get this number by subtracting the sun's declination—23º 27'—from the north celestial pole—90º, which is a point in space the Earth's axis points to. This imaginary circle around the earth at 66º 33' north latitude where the Sun is split in half by the horizon at noon during the winter solstice is called the Arctic Circle. Look at the globe and you’ll notice that the Arctic Circle runs right across the very top of the globe. Rotate the globe (itself) until Alaska is on top. The globe is now positioned so that somewhere in Alaska, it is noon, December 21. (Noon is the instant in time when the Sun is highest in the sky; due south in bearing.) Imagine standing outside at noon in Fort Yukon, Alaska—which happens to lie on the Arctic Circle—and gazing at the Sun. You will see the Sun straddling the horizon, the upper limb of the Sun above, the lower limb below (actually, as I'll explain later, that's not quite so). It is exactly 90 degrees from your zenith, a point in the sky directly above your head. If you were to stand a few miles to the north the Sun would never rise all day long; if you stood a few miles to the south it would briefly arc just above the horizon and then disappear in a few minutes. This is the phenomenon that will help us solve our problem—except for one thing—we’re in the wrong hemisphere!

While we in the northern hemisphere on December 21 are shivering on our winter solstice, folks down under in the southern hemisphere are basking in the sun on their summer solstice. With the globe still in the same position look on the bottom for the Antarctic Circle (66º 33' south latitude). If we were to bore a hole on top of the Earth in Fort Yukon straight down through the very center of the Earth, the hole would emerge at the bottom of the earth directly on the Antarctic Circle. It is noon at the beginning of summer where the hole begins in Fort Yukon, but where the hole emerges on the Antarctic Circle it is midnight at the beginning of winter. The Antarctic Circle has the opposite effect as that of the Arctic Circle as you travel north or south of it. At midnight, a few miles to the south of the Antarctic Circle, the Sun will shine all day long. It will approach the horizon at midnight, but it will not quite touch it. A few miles to the north of the Antarctic Circle the Sun will briefly dip below the horizon, disappear, and rise a few minutes later. It is this brief dipping below the horizon around midnight that is the key to solving our riddle.

Let’s pause to review the question. Where on earth will one be (on land) to be the first to witness the sunrise in the year 2000? We know that we must be somewhere on or just west of the International Date Line, and since we are interested in sunrise just after midnight, we can rule out any place in the northern hemisphere because it is winter there and the days are too short. We can’t be below the Antarctic Circle because the Sun never sets between the Antarctic Circle and the South Pole on the summer solstice, so without a sunset there can be no sunrise. We must be on it, or just north of it, where the Sun sets just briefly enough for us to see it rise. And the briefer it is, the earlier it is. So we are looking for a point on earth that is on or just barely west of the International Date Line (it has to be Saturday, January 1—not Friday, December 31) and on or just barely north of the Antarctic Circle, where the Sun rises from its brief arc below the horizon.

Now that we've narrowed the location down to a fairly small area near the junction of the International Date Line and the Arctic Circle, it's time to consider a couple of confounding factors that may affect our reckoning. But first we need to define "sunrise." The World Almanac defines it as the instant the upper limb of the Sun touches the horizon. By this definition we can't see a sunrise until the Sun has risen after having been completely below the horizon. We've been discussing the position of the Sun with respect to the horizon while standing on the Antarctic Circle at midnight during the Southern Hemisphere's summer solstice. But the year 2000 begins on January 1—ten days after the summer solstice. The Earth has begun to tilt back a little toward the Sun in its journey around the Sun. In the ten days since the solstice, the Sun has moved from a declination of 23° 27', to one of  23° 7'—a 20' change. This 20' difference in declination means that on the Antarctic Circle at midnight on January 1, instead of the Sun's being split in half by the horizon as it would on the solstice, it will be 20' lower in the sky. The Sun's disk subtends an arc of about 31'. This now puts the top of the Sun 4.5' below the horizon. So far, so good, because this would mean we would have a sunrise. But we have another confounder. Atmospheric refraction. Atmospheric refraction bends the image of the Sun above the horizon an average of 34' of arc. This has the opposite effect of raising the image of the Sun back up to where the top of it is now 29.5' above the horizon. Thus, at midnight on the Antarctic Circle on the solstice, the top of the upper limb of the sun's disk will appear about 30', or half a degree above the horizon—so no sunrise on the Antarctic Circle. We therefore need to be at least 30' north of the Antarctic Circle, or at at least 66° 3' S latitude to see the sunrise. We've now pinpointed our target: 180° E longitude by 66° 3' S latitude.

Look at the globe and you'll see that this is not an area where you're likely to see a queue of tourist buses. In fact, even the most detailed atlases just flood-fill several thousand square miles of ocean in the region "aqua blue" and move on. To satisfy the conditions of the question we need to sight land. Turning to the Hammond Atlas of the World, as we travel west away from the International Date Line, the first land we come across that is at least as far north as 66° 3' S latitude is on the continent of Antarctica at a point near the Dibble Iceberg Tongue. The U.S. Naval Observatory has pinpointed the position at 135° 53' E.  Here, we are sure to witness a sunrise. But—is it necessarily the first sunrise?

That will be subject to the whim of our old friend atmospheric refraction. Recall that atmospheric refraction bends the image of the Sun an average of 34' of arc. Atmospheric refraction is variable to such an extent that sunrise and sunset times cannot be predicted with any better precision than to the nearest minute. In regions near the poles where the Sun just skims the horizon this effect is greatly magnified because of the shallow angle with which the sun moves with respect to the horizon. Because of this unpredictability, it is possible for a sunrise to occur as far north or south of our targeted latitude as 25 miles, so the best we can do is assign a probability of seeing a sunrise in an area that lies reasonably close to our latitude of 66° 3' S.

As we scanned west along the Antarctic Circle away from the International Date Line we went over a tiny group of islands off the northern shore (ha-ha) of Antarctica called the Bellamy Islands. The Bellamy Islands, inhabited only by the hardiest of creatures, are remote outposts in a surreal world of perpetual twilight. They comprise three islands: Sturge Island, Buckle Island, and Young Island. A topographical map indicates that the northern shore of the northernmost Island lies at about 66° 13' S latitude. That's about 10' too far south of our 66° 3' limit. Such a distance, however, may not be outside our consideration when the laws of chance, owing to atmospheric refraction, come into play. This lonely little island, surrounded by frigid seas, under the looming shadow of the great Antarctic continent, is the site where there's about a 15% chance* to see the first sunrise of the millennium. But it's a crap shoot. So if our reckoning is correct, and the weather cooperates—Young Island may be, by pure fortuity, the solution to the vengeful weatherman's riddle.

You’d better hurry and book your flight now, for the remote, wind-swept Bellamy Islands may become the site of a most unlikely tourist trap—a gathering of globe-trotting celestial adventurers who live only to experience the magic of solar eclipses and the ghostliness of the Aurora—thrill-seekers who on that fateful day may be the first to behold the Dawning of the New Millennium!

*This probability follows a normal distribution where one standard deviation equal to 18 kilometers (11.2 miles). Ten minutes of arc across the Earth equals about 11.5 miles, which is a little over one standard deviation. Recall that one standard deviation equals an area under the normal curve on both sides of the mean of about 68%, and the area under the curve of the right tail equals about 16%.  Thus the z score of 11.5 = 11.5/11.2/1 = ~ 15%.

SOURCES

A globe with the ecliptic.
The World Almanac.
Chartrand, Mark R. III  Skyguide  New York: Golden Press, 1982.
Berman, Bob  Secrets of the Night Sky  New York: W. Morrow, 1995.
Hammond Atlas of the World  Maplewood: Hammond, Inc., 1997.
U.S. Naval Observatory Astronomical Applications Dept. http://aa.usno.navy.mil/AA/

Special thanks go to my good friend Bruce McClure, whose infectious enthusiasm for astronomy inspired me to write this, and whose advice concerning the more knotty aspects of the discussion helped make it more clear, and above all, justify its conclusion.

Stephen Daniels

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