High School Students Measure New Value for Earth’s Radius to Celebrate World Physics Year

Andrew Blum gives some pointers to students in his high-school class in Clinton, Mississippi as they work on the Eratosthenes project.

Has the radius of Earth mysteriously grown by about 3%? According to data taken by 183 high-school classes participating in a World Year of Physics project, "Measure the Earth with Shadows", the radius of Earth is 6563 km, compared to the accepted value for the mean radius of 6371 km.

Of course, no one is claiming the size of Earth has actually changed. "Most of the data submitted was remarkably good," said Jennifer Fischer, the APS project leader. "It is nice to see that measurements taken by so many groups, sometimes in less than ideal conditions, came so close to the right answer."

The data were submitted by high school classes all around the US, as well as some in Canada and Mexico, working in pairs. Each pair measured the angle of the sun, in the same way that the Greek philosopher Eratosthenes did more than 2000 years ago in Alexandria, Egypt–by comparing the length of an object to the length of its shadow, measured at local noon.

Eratosthenes made his measurement on the summer solstice, and had the additional knowledge that on that day the sun was directly overhead at a location a known distance south of Alexandria, on the Tropic of Cancer. This enabled him to compute the Earth’s radius. In the current experiment, each pair of high schools used the known north-south distance between them and the angle of the sun at each location to determine the radius.

For various reasons, about one-sixth of the schools were unable to work with their assigned partner school, but they did the measurement anyway, on the vernal equinox, using the knowledge that the sun is directly overhead at the equator on that date.

"The Eratosthenes Project really gets kids to think in a special way," Fischer said. "Most kids learn in school that the Earth is round, but they never really picture it in their heads as if they were in outer space. This project forces you to imagine the solar system as if looking down on it from the outside. Learning to think imaginatively and creatively like this is an important part of physics."

Rebecca Messer, a physics teacher in Northfield, Minnesota, wrote in an email "My students were thrilled to be part of this experiment and were very diligent in their measurements. We ran 5 stations; they each used a level to plant their dowel and to level the horizontal when they measured the shadow lengths."

The class of physics teacher Brent McDonough in Edmonton, Alberta, had two US partners, one in Henderson, Nevada and the other in Calexico, California. "We had a great time working with all three schools and have even exchanged email photos of each class and posted them on our school website with a report of the project," McDonough said.

The project’s influence has spread to the southern hemisphere. An Argentine physicist, Silvia Ponce Dawson, writes "I’ve found the Eratosthenes project that you’ve launched on the occasion of the World Year of Physics really fascinating and I would like to have it done in my country too." As a first step, she has translated the APS teacher’s guide for the project into Spanish.

Participating students each received a World Year of Physics pin, and their classes received a commemorative certificate. More details of the project, including the teacher’s guide and a map showing the distribution of participating US schools, can be found on the World Year of Physics website.