Moon Shadow

Columbus sailed the ocean blue in 1492.

But when it came to proving his claim,

He didn't have a clue.

- Wishes to remain

Anonymous

These days, if you need to know where you are on Earth, a handful of artificial satellites can pinpoint where you stand to within a few feet.

On Sept. 26, another kind of satellite - the moon - can help you do something similar. Beginning at 9:12 p.m. Eastern Daylight Time, a brilliant hunter's moon will silently slip into the darkest part of Earth's shadow. During this eclipse, which will appear as a full eclipse in North America and Western Europe, our planet's natural satellite will slowly turn from bright white to a dark orange or even dark red, and back again.

Using two simple homemade instruments, you can turn the eclipse into a contest to see if you can beat Christopher Columbus in finding your latitude and longitude (no fair peeking at a map!).

Columbus: I'm in China?

On two different trips to the New World, Columbus used a half-hourglass, a list of sunrise and sunset times, and the moon's vanishing act to figure out how far west he had traveled. Twice he tried to measure where he was when he arrived. Twice he blew it - big time. He thought he'd landed in China, where he wanted to go. Instead, he landed on a tiny island in the Caribbean.

A few years ago, two professors in Youngstown, Ohio, had local public-school students try the technique that Columbus used. The students hit the mark. The astronomy professors, Warren Young and Richard Pirco of Youngstown State University, designed the low-tech half-hourglass at the heart of the project.

Where did Columbus go wrong? He stumbled over those imaginary lines across Earth's surface known as longitude.

Since ancient times, geographers knew that finding your spot on a map would be a whole lot easier if you imagined a network of lines running north and south (longitude) and east and west (latitude) around Earth. Mathematicians already had come up with the notion to divide a circle's edge into 360 equal parts known as degrees of arc. Knowing that Earth was round, too, you could describe your location with the two numbers that identify where latitude and longitude lines cross.

Ptolemy (say "TALL-uh-mee") was a math whiz and a primo geographer who lived in Alexandria, Egypt. He's also the guy who got it wrong when he said the sun traveled around Earth. He used latitude and longitude lines in his world atlas, around AD 150. He not only drew the lines on his maps, but his atlas also listed major locations and gave their latitudes and longitudes.

The motion of the sun, moon, and planets across the sky helped Ptolemy pick the starting point for measuring latitude: the equator. There, these objects in the heavens appear to pass almost directly overhead.

The starting point for longitude, known as the prime meridian, had no such natural anchor. By international agreement, the prime meridian today passes through Greenwich, England, on its way from the North Pole to the South Pole. But Ptolemy ran his prime meridian through the Canary Islands. Since then, the prime meridian has been the Carmen Sandiego of cartography: It's been to the Cape Verde Islands, Copenhagen, Jerusalem, St. Petersburg (Russia), Paris, and Philadelphia, to name a few.

Rocking clocks a problem

Knowing where you were was easier on (or near) land. There were well-worn trade routes with cities, mountains, and rivers for landmarks. If you sailed beyond sight of land, however, you had a problem - no landmarks.

Figuring latitude was easy. You could measure the angle between the horizon and the North Star, for instance.

Longitude was trickier. You knew that because Earth turns once every 24 hours, you could use time to measure how far east or west of the prime meridian you were. If Earth turns 360 degrees in 24 hours, it turns 15 degrees in one hour, or 1 degree every 4 minutes. Two clocks, one set to the time at the prime meridian and one reset daily to local time by using the sun's highest point in the sky as noon, would do the trick. Find the difference between the two clocks, and you could figure your longitude. If the clock was accurate enough, you could find your longitude down to minutes (1/60th of a degree) and seconds (1/60th of a minute) of arc.

But clocks of Columbus's day didn't fare well on ships. The rolling and pitching at sea made the clocks run faster, slower, or not at all. The first truly useful shipboard clock, or chronometer, was invented and refined from 1730 to 1770. So mariners kept track of time on cruises using a half-hourglass. On sunny days, the "clock" could be reset by observing when the sun was at its highest point in the sky - noon.

But early explorers still had to use "dead reckoning" to navigate. They'd sail south until they reached the latitude of their destination, then turn and sail along the latitude line as best they could. Using primitive techniques to determine their speed, they would basically guess how far they'd traveled. Columbus was an excellent dead-reckoning sailor.

Once you reached land, you could use sunset times contained in your nautical almanac, the half-hourglass you used to mark time aboard ship, and some well-known naked-eye astronomical event to determine longitude. This is what Columbus did when he used full eclipses of the moon in 1494 and 1504 to try to prove that he had landed in Asia.

How Chris got crossed

Some say Columbus got his longitude wrong (by more than 20 degrees each time) because he misread his sunrise/sunset charts. Others say he was so sure that he was in Asia that when he got the right answer, he thought it was wrong. He reworked the math until he got the answer he wanted.

As if that weren't enough, he scrambled his math again when he translated map information from Arabic to something he could use. This mistake left him thinking the circumference of the earth was 6,000 miles less than the best estimate at the time. So when he converted his wrong longitude calculations into distances using the wrong circumference for the earth, he came to the wrong conclusion.

Peter N. Spotts

*Any questions or comments? You can e-mail me at:

spotts@csps.com

Finding Your Whereabouts The Old-Fashioned Way

A few days before the lunar eclipse, use your homemade quadrant to determine your latitude. Aim it at the North Star, and read the number on the protractor under the weighted string. Subtract your reading from 90 to get your latitude. (For example, if the weighted line on your quadrant falls on 50 degrees, subtract 50 from 90 to arrive at your latitude: 40 degrees North.)

To find your longitude, you need to find the difference between local time and the time at a standard longitude. Today, the standard, or 0 degrees longitude, runs through Greenwich, England. Sunset at your location and a celestial event like a lunar eclipse are common "markers" to determine the time difference.

On Sept. 26, the day of the eclipse, use the table below to find the time for sunset. (Note: All chart times are in standard, not daylight-saving time.) Use the entry for the latitude closest to the one you found. Columbus consulted almanacs for this, and once he knew his latitude, he also had an accurate sunset time.

Using your homemade half-hourglass, see how much time passes between sunset and the start of the eclipse. Add this interval to the sunset time. This is your "local mean solar time" for the eclipse. (You could time it with a watch, but that's so un-15th century!)

Here's an example: Say you live in Youngstown, Ohio. You sight on the North Star with your quadrant and it reads 49 degrees. Subtract 49 from 90, and 41 is your latitude.

Reading from the table below, you know that sunset will be at 5:49 p.m., Eastern Standard Time, on Sept. 26 at 40 degrees N. latitude. So on the day of the eclipse, start timing with your half-hourglass at 6:49 p.m. Eastern Daylight Time. You decide to use the start of the eclipse as your "marker," so you stop timing when you see the first bit of dark shadow on the moon. You find that an hour and 59 minutes has gone by since sunset.

Add that time to the sunset time, and you get 7:48 p.m. This is the mean local solar time for the onset of the eclipse. From the table below, you find that the starting time for the eclipse at Greenwich is 1:12 a.m. The difference between the two times is 5 hours, 24 minutes. Convert the minutes into a decimal fraction by dividing 24 (minutes) by 60, and you get 5.4 hours.

Since you know that the earth turns once every 24 hours, and that a circle is divided into 360 degrees, you divide 360 by 24 to find how many degrees of longitude the earth rotates each hour. The answer: 15 degrees per hour. Multiply 15 d.p.h. by the number of hours between the two starting times for the eclipse (5.4) and you get 81 degrees longitude.

Check your answer with a map.This approach isn't likely to give you a precise match. If you come within 2 degrees, you're an ace! And if you are less than 23 degrees off, you can still count yourself a better astronomer than Columbus!