Chapter 3, Problem 50EAP

Method of Eratosthenes II. You are an astronomer on planet Tirth, which orbits a distant star. It has recently been accepted that Tirth is spherical in shape, though no one knows its size. One day, you learn that on the equinox your sun is directly overhead in the city of Tyene, located 400 kilometers due north of you. On the equinox, you go outside and observe that the altitude of your sun is 86°. What is the circumference of Tirth? (Hint: Apply the technique used by Eratosthenes to measure Earth’s circumference.)