1/8 of the earth's circumference south from the North Pole and asked at what angle above the horizon the inhabitants there would have to look to find the North Star. Discussion followed, with a variety of different quick answers. Ms. B. challenged the groups to use their compasses and protractors to make a drawing that would give them the answers. When the groups had come up with some ideas, she led them in a discussion on how the angle changed as the distance around the earth from the pole changed. They agreed that it got smaller and smaller, going from 90 degrees at the pole to 45 degrees 1/8 of the way around, and 0 degrees at the equator.
The next day, Ms. B. put a graph with the three points the students had found so far on the board. She asked how they could predict the angle of the North Star for two points, A and B, which she added to the graph, one halfway between the 45 degree point and the pole and the other halfway between the 45 degree point and the equator? The students suggested a straight line on the graph which fitted their three points would represent the relationship between the angle and distance around the earth. The students also agreed that this was just a guess. Ms. B. asked how they could be more certain and they decided they could go back to their drawing, use their protractors to put A and B on it, and measure what the angle of the North Star would be.
The result of their graphic investigation confirmed that a straight line seemed to be a good graph for the relationship between the angle formed by the North Star and the horizon and distance around the earth.
Ms. B. then told them that in Columbus' day it was known from ground travel that the distance between a town in Scandinavia where the North Star angle was 67 degrees and another in Italy where the North Star angle was 43 degrees was about 3,000 miles. People who knew what the students now knew could figure out the circumference of the earth. The groups were to take their data to math class where they would have time to figure out the earth's circumference and then proceed to look in the library for the best modern value.
The next day, the class discussed how well they had done in getting a value for the earth's size. In succeeding days they calculated the distance to the moon and its circumference and looked up the same information for the sun. They also learned how modern astronomers calculate distances and size. Finally, using the data, each group designed a scale model of the sun, moon, and earth.