In a recent Ask Fuzzy, we drilled a hole through the Earth and jumped in to see what would happen. The 84-minute trip to the far side and back has been giving us time to muse on how a tiny human can figure out the size of something so large.
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It turns out this problem was solved in a surprisingly simple but clever way by the Greek mathematician Eratosthenes. This week marks the summer solstice in the northern hemisphere, which is the anniversary of when in 240BC, the answer occurred to him. He read a text in the library at Alexandria that described the position of the sun at midday on the solstice.
Syene in southern Egypt is located on the Tropic of Cancer, while Alexandria is 800 kilometres further north. Eratosthenes learnt the sun was directly overhead in Syene, but angled at 7.2 degrees in Alexandria. That meant that it was a 50th of the way around the full 360-degree lap of the globe. A simple multiplication told him that the Earth is about 40,000 kilometres at the circumference. His answer was remarkably good, although there are doubts about the length of the "stadia" used in his day. His estimate was also off slightly because he didn't have a good way of measuring distance.
Eratosthenes did an excellent job calculating the Earth's circumference, but the idea that the Earth is round goes back to Aristotle. One clue is the curved shadow you see during a lunar eclipse. Another clue is similar to Eratosthenes' observation that the angle of the sky depends on where you are.
We now know the Earth is not quite spherical, but flattened at the poles in an "oblate spheroid". The spinning planet causes a slight midriff bulge, but the effect is small, only about one part in 300.
From Darwin's time, it's been speculated the Earth might be expanding or contracting. Since then, we've learnt about the shifting tectonic plates, which might also be involved. To find out whether that is happening, a NASA-led international team used sophisticated techniques from satellite data. That information allows geologists to calibrate movements due to processes such as volcanoes and earthquakes.
The expression says the world gets smaller every year, but it isn't much – the radius shrinks by 0.1 millimetres per year.
Response by: Rod Taylor, Fuzzy Logic
The Fuzzy Logic Science Show is 1100am Sundays on 2xx 98.3FM. Send your questions to AskFuzzy@Zoho.com Twitter @FuzzyLogicSci
