Just over 2000 years ago, a Greek scientist measured the circumference of the Earth, and got to within a few per cent of the actual value. And all that he used was a stick, a ruler and some simple geometry and mathematics.
Of course, the Earth is not a perfect ball. The Earth spins on its own north–south axis once every day.
This makes it bulge outwards a little at the equator. Measured at the equator, the average diameter of the Earth is about 12,756.2 kilometres. That's about 42.6 kilometres greater than the diameter measured across the poles.
As a result of this greater distance, as well as the spin, the 'suck' of gravity is slightly weaker at the equator than at the poles, but only by about five parts per thousand.
So if you weigh 50 kilograms at the South Pole, you weigh less at the equator: 250 grams less, or a quarter of a kilogram less.
The guy who used just a stick and some maths to measure the circumference of the Earth was Eratosthenes. He was a Greek who lived in Alexandria in the third century BC.
Eratosthenes spread himself over many fields. As well as being an astronomer, geographer and mathematician, he was also a poet and athlete.
Besides working out the circumference of the Earth, he also calculated the tilt of its spin axis. He also devised a system of latitude and longitude, and a calendar that included leap years.
His colleagues called him Beta (the second letter of the Greek alphabet) because they reckoned he was the second best in almost any field.
Now Eratosthenes had been told by travellers of something wonderful in the Egyptian town of Syene (Today known as Aswan, near the giant dam on the Nile).
This town was not on the Equator, but instead, was on the Tropic of Cancer. The story went that on just one day of the year, the summer solstice, the light of the Sun would reflect off the water in the bottom of a well.
This would happen for only a few moments around midday. That meant that on the summer solstice, the Sun was vertically overhead, and that Syene was on the Tropic of Cancer.
So on the day of the summer solstice (June 21), Eratosthenes set up an experiment in his home town of Alexandria.
He set up a stick to be perfectly vertical, and measured the smallest shadow that it threw around midday. This was easy to do, because the Greeks (and their friends in the Middle East) had been playing with geometry for a long, long time.
The shadow was about 7.2° away from the stick. Now 7.2° is about one-fiftieth of the 360° that make up a circle.
So that meant that the distance between Syene and Alexandria was one-fiftieth of the circle that makes up the Earth.
If you draw this out on paper, you can immediately see this is true, from simple geometry.
Eratosthenes needed just one more piece of information. He had to find the north-south distance between Syene and Alexandria. This came to about 5000 stades (one stadia is the length of the foot race in a stadium). Or as we now know it, about 800 kilometres.
If 5000 stades was one-fiftieth of the circumference of the Earth, then the full circumference was 250,000 stades.
But while the theory is lovely and simple, once you actually do the experiment, a few errors creep in.
First, Syene was not exactly at the Tropic of Cancer, it was slightly north of it. So the Sun was not exactly vertical on the day of summer solstice.
Second, Syene was not exactly south of Alexandria, but a little off to one side. So the measured north–south distance between them was a little wrong.
Third, the Sun is not a point infinitely far away, so its rays are not exactly parallel. Indeed, over the distance between the Earth and the Moon, they diverge by one-sixth of a degree.
Fourth, it's really difficult to keep your accuracy when you have to pace out a distance of 800 kilometres.
Fifth, how big was a stadia back then? How many ruined stadiums do you have to average?
The Greek historian, Herodotus (c. 484 BC – c. 425 BC) reckoned that one stadia was 600 feet. But how big is a foot?
Depending on the purpose of the measurement, and which culture measured it, a stadia could range between 157 metres and 209 metres.
Anyhow, depending on these and other factors, Eratosthenes got to within 0.5–17 per cent of the true value of the Earth's circumference. That's got to be some kind of a world record for using just a stick.
Is it not interesting?
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