The 2005 World Year of Physics celebrates the centennial of Albert Enstein's "Miracle Year." LIGO Hanford Observatory recently moved the physics spotlight back from Einstein -- about 2100 years back -- and repeated Eratosthenes' measurement of the earth's circumference. Area residents gathered at LHO under mostly clear skies on June 18 to undertake the task. Collaborators in San Francisco and Fairbanks, Alaska assembled their shadow makers and transmitted their data by phone. The group successfully completed the job over the course of several midday hours.

Step 1: Build the shadow maker. Each team ensured that their device pointed to the earth's center by attaching a string and a bob to the upper portion of the stick then aligning the stick with the string. Shadow measurements then followed.

Step 2: Find the solar noon shadow. Investigators at each location identified the minimum shadow length. We usually think of noon as the time of the sun's peak ascension, but solar noon differs from clock noon because of daylight savings time and because the time of the sun's highest point varies across the width of a time zone.

Measuring at 20-minute intervals, the LHO participants realized that the shadows were still diminishing at 12:45. Just as the teams filed out of the auditorium for the critical 1:00 PM measurement, the sun disappeared behind a large cloud. Fortunately one team squeezed in a measurement with only seconds to spare and confirmed that the shadow had started to lengthen. The teams then reverted to their 12:45 value for the minumum.

Step 3: Measure the angle formed by the shadow. At the top of the stick the shadow covers an angle that forms an interior angle of a parallelogram. The vertex of the equal and opposite angle lies at the earth's center, and this angle covers a portion of the earth's surface.

The teams re-created the dimensions of their minimum-shadow triangles on the floor with string. By placing paper under the angle between the hypotenuse and the adjacent side and using a protractor, participants measured the angle of interest. The hosts did not provide scientific calculators (did Eratosthenes have one?), and one mathematically inclined group used a table of trigonometric values to identify the angle by its tangent.

Step 4: Calculate the circumference. The groups attained very good precision for the angle, arriving at an average of 23° with an uncertainty of 1°. Modesto Tamez from the Teacher Institute at San Francisco's Exploratorium reported an angle of 13.5°. Later in the afternoon (due to the lateness of solar noon in Alaska), former Tri-City Astronomy Club member and Fairbanks resident Larry Bowman reported an angle of 46°, a difficult measurement due to cloud cover. By taking the differences between pairs of angles, by finding the mileage between the pairs of locations and by realizing that the earth's surface covers 360°, participants computed a simple proportion to find the mileage of the circumference. Reportedly Eratostheses instructed a servant to walk from Alexandria to Syene (over 700 km) to measure the distance. Not wishing to walk to either San Francisco or Fairbanks, the LHO groups utilized third-party estimates of the distances between the latitudes of the cities.

The Richland-San Francisco data produced a circumference of 23,000 miles or 37,000 km. The Fairbanks-Richland data yielded 20,000 miles or 32,000 km. Greater confidence was assigned to the San Francisco result due to poor Fairbanks shadows as reported by Larry. The value that Ertosthenes obtained is questioned since the unit of 'stadium' that he used lacked a clear standard. If his stadium was 157m (a likely possibility according to scholars) then his circumference was about 25,000 miles or 40,300 km. Today's accepted value for the polar circumference is very close to 40,000 km, or 24,800 miles.

The process of successfully measuring a quantity so large with a device so simple seemed remarkable and highlighted the importance of cleverness and clear thinking in science. Participants came away with a heightened respect for the Greeks' expression of these attributes. Perhaps in the future we'll attempt the distance to the moon, or the distance to the sun. When's the next eclipse?