Measurement Of Radius Of Earth

Purpose

To demonstrate how the radius of the earth can be measured using trigonometry.

Equipment

Optical board, disc with tabs, and meter stick.

Setup Time

5 min.

Images

e2-02

Description

A disc of radius R with two radial tabs, as shown, is mounted on the optical board and illuminated by a parallel beam of light, as if the earth were being illuminated by the sun. The equatorial tab must have its shadow along the horizontal diameter of the disc. Measure the length b of the upper tab, the length a of its shadow, and the distance S along the surface between the two tabs. By geometry: S/R=a/b, or R=bS/a. Compare the result of this calculation with the direct measurement of the radius R of the disc. ◙◙

References

Lecture Demonstration Information Sheet. Zachary H. Levine, How to Measure the Radius of the Earth on Your Beach Vacation, TPT 31, 440-441 (1993).