# Problem solved using Eratosthenes theorem

Drawing on Eratosthenes' method, if two observers are due north and south of each other and are separated by 400 km, what is the circumference of their spherical world if they see the same star on their meridian at altitudes of 23 degrees and 47 degrees respectively, and at the exact same time?

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#### Solution Preview

Estimating the circumference of a body based on Eratosthenes' method:

Two observers positioned at S1 & S2 on a North-South meridian see a star (observed at the same time) at altitudes of 47 deg and 23 deg respectively. If their physical separation S1-S2 is 400 km what is the circumference of their world.

First we can assume that the starlight is ...

#### Solution Summary

Determining the circumference of an observers world using angles of inclination of two stars and Eratosthenes theorem