Eratosthenes' Too-Big Earth & Too-Tiny Universe
Abstract
Sostratos' legendary lighthouse on Pharos Island in Alexandria's harbor is proposed as what enabled Eratosthenes to displace the prior 1-significant-digit crudity of Aristotle & Dikaearchos with 3-significant-digit precision in Earth-circumference, 256000 stades. Bishop Eusebius' testimony that Eratosthenes' distance to the Sun was 4080000 stades shows, in the Greek tradition of setting solar distance as a power of 10 in Earth-radii, that Eratosthenes' Earth-radius was 40800 stades, which multiplied by 2π matches the circumference cited. Reverse calculation fails, so the primary empirical datum was radius, which is what the Pharos provided by the visibility of its flame down the Mediterranean coast from Alexandria over the intervening sea, since Earth-radius is found by dividing the visibility-distance's square by twice the Pharos' height. Ancient testimony indicates the height was c.300', but if Sostratos' tallest-ever lighthouse was made exactly 300' or 1/2 a stade, then the equation's denominator is unity so squaring the visibility-distance in stades equals Earth-radius in stades: squaring visibility-distance 202 stades yields 40800, conventionally rounded. It is emphasized that 40800 stades is 19% or about 6/5 higher than Earth's actual radius, and Poseidonios-Ptolemy's 180000-stade circumference is 5/6 too small. Atmospheric refraction affects the Pharos-flame method by 6/5, while shrinking by 5/6 circumference found by the double-sunset method of gauging the Earth's-girth (AmJPhys 47:126-128). So the 2 standard ancient values cited differ by 40% but are explained by airbent light to within 1% each, using the standard 185-meter stade, while the ever-wheelspinning ad hoc search for oddball stades to explain the ancient errors don't match either value so exactly.
- Publication:
-
DIO
- Pub Date:
- March 2008
- Bibcode:
- 2008DIO....14....3R
- Keywords:
-
- Sostratos;
- Eratosthenes;
- Eusebius;
- Earth radius;
- Earth circumference;
- atmospheric refraction;
- double-sunset;
- Pharos;
- Alexandria lighthouse