Eratosthenes…

I was marking a Winchester paper a while back that had a question about Eratosthenes. Winchester don’t often make mistakes in their papers but on this occasion they spelled it Eratothsenes throughout. I realised that this meant it could be spelled using the elements – ErAtOThSeNeS (erbium, astatine, oxygen, thallium, selenium, neon and sulphur). Sadly the correct spelling is Eratosthenes which requires including tritium as an element to spell it ErAtOsTHeNeS (erbium, astatine, osmium, tritium, helium, neon and sulphur).

Tritium is not really an element. It is an isotope of hydrogen. An isotope is a form of an element that has extra neutrons in its nucleus. Hydrogen, the simplest element, has only a proton in its nucleus orbited by a single electron. Tritium has two additional neutrons in the nucleus, but still the single electron, making an atom of tritium three times as heavy as an atom of hydrogen. It is radioactive which means that one of its neutrons breaks down to form a proton and an electron. When tritium decays an isotope of helium (called helium-3) is produced containing two protons, one neutron and two electrons. There is not much naturally occurring tritium but there is a little in the upper atmosphere where cosmic rays can interact with nitrogen to form a carbon atom and an atom of tritium.

Anyway, none of that has anything to do with Eratosthenes (276 BC to about 195 BC) who managed to calculate the circumference of the Earth to a remarkable degree of accuracy. It is often said that “people used to think the world is flat” but it seems that many of the people who had really thought about it were well aware of its ball-like shape from a fairly early stage.

Eratosthenes knew that at local noon, at the summer solstice on the Tropic of Cancer, the Sun’s rays would seem to be directly overhead (i.e. at 90 degrees to the ground). On the same day, in his home town of Alexandria he took a vertical stick and measured the angle of the Sun at its highest point as 83 degrees. In other words, 7 degrees south of vertical; he therefore deduced that the distance between Alexandria and the Tropic of Cancer was 7/360 the circumference of the Earth. All he needed to know was the distance and he could calculate the circumference of the Earth.

There seems to be some dispute in the literature about how he measured the distance between the two places. He used stadia as his units of distance, but a stadion in one place was not always the same as a stadion in other parts of the world. I have seen it said that he worked out the distance by timing how long it took a caravan of camels to travel from Alexandria to Syene (on the Tropic of Cancer). He settled on about 700 stadia per degree and so a final circumference of 252,000 stadia. Depending on how his stadia were defined (which we do not know for sure), his final figure was likely to have been between 39,690 km and 46,620 km. Modern methods of measurement put the circumference of the earth at about 40,008 km so he did not do too badly.

We now also know that the Earth is not spherical but is an oblate spheroid because it bulges outwards at the equator. I posted an excellent video explaining about the seasons and what Eratosthenes did here from June 2011. Have a look at it because it is really good!

Questions…

1. What formula relates distance to time and speed?
2. What could you have done to ensure that your measurement of the distance using a caravan of camels was as reliable as possible?
3. Why do we have seasons on Earth?
4. How long (in metres) would a stadion have had to have been for his result to be accurate by modern standards?
5. Read the post People As Molecules and come up with some suggestions of your own.