How Big is the Earth?
How big around is the Earth?
Most of the time when we think about astronomy, we think about the night sky. Then we talk about the
huge masses of stars, the even greater masses of galaxies and their distances that we measure in light years. But how do we know that things are so big if we can’t go there? How did we start measuring such vastness?
The question of the earth’s size kept mathematicians and astronomers busy for hundreds of years. They reasoned that if they could determine how big the Earth is, then they could begin to measure distances to the Moon, and to the Sun. Or, if they knew the length of one side of a triangle and the two adjacent angles, they could work out the other dimensions.
One of the first people who tried to answer such questions was a librarian living in Egypt about 2,200 years ago. His name was Eratosthenes (e-ra-TOS-the-neez); he was a Greek from Libya. Eratosthenes went to school in Alexandria (where he must have studied Euclid’s geometry) and then Athens before he was called back to be in charge of the Alexandrian library. That’s when he put his geometry to work on a couple of facts he knew. Those were the distance between Alexandria and Syene (Assuan), and the difference between the angles of the Sun’s shadow in both places on a given day. He hoped he’d solved not only the question of how big the Earth is, but the bigger question of how to measure it.
What Eratosthenes did you can copy. (Maybe you can be a bit more accurate; he got the figure about a third again too big.) Of course you can look the answer up in a textbook or on Internet. But suppose you’d like to puzzle it out for yourself, using ideas and facts similar to those he used.
These are the facts you need: 1) you need to find the distance from where you are to a place that is due south of you. To make it easy, let’s use the point on the equator. For this you need to know your longitude. (These two points on the great circle run from the North Pole to the South and back again, cutting through your location.) 2) You need to know your latitude. Eratosthenes didn’t know either his latitude or his longitude because they hadn’t yet been calculated. Already you’re two steps ahead of him. (If you don’t know these two facts, one place to look is <http://geography.about.com/cs/coordinates/>.)
With these two numbers, you need to use the algebraic equation that Eratosthenes reasoned out to determine the relation between distance and altitude: D/d=A/a. What these letters mean are that “D” is the unknown circumference of the Earth; “d” is your distance from the equator; “A” is the number of degrees in a great circle; and “a” is your latitude. Substitute the figures and solve the problem.
Or, if you want to make it a little harder for yourself, and do it closer to the way Eratosthenes did, you can measure the angle of the Sun’s shadow where you are on the spring equinox when the Sun is at its height. For this you need to know the date of the equinox. If you decide to try this experiment before March 19, you might want to be a part of a worldwide science and math Eratosthenes Experiment. If so, look it up at www.youth.net/eratosthenes/welcome.html/ <http://www.youth.net/eratosthenes/welcome.html/> Professor James D. Meinke of Baldwin-Wallace College in Berea, Ohio is the head of the project. The address will give you the information you need to start your experiment. Perhaps some of you have noticed that this equation makes several assumptions: that the Earth is perfectly round, that light travels in a straight line, and that the line of a shadow can be measured accurately. Considering these, it’s remarkable that Eratosthenes came as close as he did in his answer. Sources: www.youth.net/eratosthenes/welcome.html/ <http://www.youth.net/eratosthenes/welcome.html/> <http://math.rice.edu/~ddonovan/Lessons/eratos.html> www.phys-astro.sonoma.edu/observatory/eratosthenes/ <http://www.physastro.sonoma.edu/observatory/eratosthenes/>