Measuring the Radius of the Earth

We can measure the radius of the Earth for ourselves, using nothing but a watch!

At sunset, measure the amount of time between which the Sun appears to set from the ground level and from the height of your head (h). When you are standing up, you can "see a little further around the corner" and the Sun takes a little bit longer to set. This picture shows the Earth and the Sun, looking down on the solar system from the top of the North Pole. The Earth is rotating counter-clockwise, so the Sun sets first at ground level and then later at head height. The radius of the Earth is identified as a distance R, and is the angle the Earth rotates through during this time interval T.

 [NMSU, N. Vogt]

At sunrise, measure the amount of time between which the Sun appears to rise from the height of your head (h) and from the ground level. When you are standing up, you can "see a little further around the corner" and the Sun rises a bit sooner. This picture shows the Earth and the Sun, looking down on the solar system from the top of the North Pole. The Earth is rotating counter-clockwise, so the Sun rises first at head height and then later at ground level. The radius of the Earth is identified as a distance R, and is the angle the Earth rotates through during this time interval T.

 [NMSU, N. Vogt]

Here is the relationship between your height h, the time interval T, and the radius of the Earth R, where R and h are measured in centimeters, T is measured in seconds, and T/240 is in units of degrees.

Here are the results for various intrepid members of a previous class who performed the experiment.

T (seconds) h (cm) R (108 cm)
451800.3
271630.8
141522.9
111474.7
121784.8
81609.4

People have measured the radius of the Earth in detailed ways and found it to be 6.4 × 108 centimeters. We did pretty well!