Question

On a fake planet, you find that on a certain day at noon no shadow is cast. At the same time your friend sees a shadow due to the Sun being 12 degrees away from the Zenith. Knowing the distance between you and your friend is 500 km, what is the circumference of this fake planet

Answer 1

In 250 BC, Eratosthenes measured the circumference to be about 24,500 miles:

by this method, 12 deg = 12 / 360 = 1/30 of the planet's surface\

30 * 500 km = 15,000 km in circumference, about 9,200 miles