Quandaries
and Queries
Assuming that a North-South line has been established, you set up two camps that are 67 miles apart. You now set up poles at each camp perpendicular to the ground. On a certain day at "noon" the pole at the South camp casts no shadow, while at the North camp a shadow is cast. The shadow makes an angle of 89 degrees with the horizontal. What is the radius, diameter, and circumference of this planet?
Hi Kelly,
I assume the question means to say that the LINE FROM THE BASE OF THE NORTH STICK TO THE SUN makes an angle of 89 degrees with the horizontal. Just draw a picture -- at both positions the stick points directly away from the center of the planet. In the south, the stick points directly toward the sun; in the north, an arrow pointing toward the sun is parallel to the stick in the south, which means that the angle between the two sticks is 1 degree. We therefore know that one degree along the planet's surface equals 67 miles. from that you get the planet's radius. (I think that you'll find that your planet has the same radius as does earth, because here on earth, one degree equals about one mile along the surface).
Chris