Question

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?

Answer 1

6000 km The difference between 23 and 47 is 47-23 = 24 degrees. Since there's 360 degrees in a full circle, that means that the distance between the two observers was 24/360 = 1/15 of the circumference of the world that they're standing on. So just multiply 400 km by 15, giving 15*400 = 6000. So the circumference of the world, those two observers are on is 6000 km.