Suppose you are an alien living on a fictitious war-like planet Myrmidon and you want to measure its size. The sun is directly shining down a missile silo 1000 miles to your south, while at your location; the sun is 36 degrees straight overhead. What is the circumference of Myrmidon? What is its radius?Can I please have an explanation on how to get to the answer?
In 240 B.C, Eratosthenes calculated the circumference of the Earth. The same method he used there can be applied here (plus you can google this if you needed additional explanation). We assume the sun is far enough away that the rays of light can be treated as parallel. A little geometry shows that you are separated from the missile silo by 1/10 the circumference of the planet so the planet's circumference if 10,000miles. To get the radius you divide this by 2pi.
Assuming the sun is an infinite distance away, (so that it's rays are hitting the planet are all parallel - yes, I know this is impossible), the difference between you and the silo is 36 degrees - that's 1/10 of a circle of 360 degrees. So the circumference of the planet is 10,000 miles. To find the diameter, divide 10,000 by Pi and you get 3,183 miles. Since the radius is 1/2 of the diameter, the radius would be 3183 / 2 or 1,591 miles.
