I want to design an experiment to show (in an educational context) how we can measure the radius of the Earth without using modern technology in order to demonstrate the engineering achievements of those who did it so long ago, and to show some practical uses for the maths involved.
The methods I know how to do this are:
- Place a stick vertically in the ground and another one many kilometers North of it and measure the shadow of both at exactly noon.
- Know the height of a mountain by a large lake or the sea and measure the distance you have to go until it disappears.
- Watch the sunset lying down and then stand up and watch it again, measuring the time difference between them and know your height.
The first two are impractical to do with the kids, but the third one shows potential. However, is there a way to do this during the day using shadows cast by buildings, or must the shadow come from the horizon? How could I design some simple equipment to allow me to do this experiment and calculate the radius of the Earth during the day?
Note: I am happy to use a digital stopwatch as the kids can easily see how people in the past might have used a mechanical clock to do the same thing (including measuring the length of a full day).