There is still debate over the size of the base length unit used by Eratosthenes. There are many challenges to overcome, including that the original writings were lost.
- There was a tool called Gnomon , that can be used to measure the angular inclination of the sun at noon. This acts as a clock, but it can also be used to measure differences in shadow projection at different places of the earth
- Eratosthenes used the distance between Alexandria and Syênê (see: 20210124124525 ) and calculated the angle of the Sun at the solstice. Syênê lies close to the tropic, which means a vertical rod casts no shadow. Known the angle and the distance, it is possible to calculate the circumference.
- There are several sources of error in the measurement, for instance the shadow is not sharp, Alexandria and Syênê are not on the same meridian, the verticality of a rod to measure the angle of the sun can’t be guaranteed. Taking everything into account, it may be possible to estimate the error on the measurement. However, there are errors that counter balance, making the measurement of Eratosthenes extremely precise just by chance (1% deviation).
- There are numeric considerations to take into account. The measured value of 250.000 stades is not divisible by 60, and therefore some authors rounded it to 252.000 stades.
- There are different accounts for these measurements, which could have different impacts on history. See: 20210124131152 .
[ @dutka1993 “Eratosthenes' measurement of the earth reconsidered” ] is a good starting point for bibliographic notes, need to further explore the other work.