Title Bar - Cosmology

Activity: Measuring the Earth's Curvature

Here is a quick experiment, designed to show that the earth is round and to calculate its circumference. It is easy to do if you are in the right location. Unfortunately, in order to do this experiment properly you must have a clear view of the sunset or sunrise over the ocean. The idea behind the experiment is this: if the Earth is round, then objects which travel away from you along the surface of the Earth will disappear from view at a certain distance. More interesting is that they disappear from the bottom up. Think of a friend walking over a hill. If you watch her from one side of the hill as she walks over the hill, her feet will disappear first and then her legs and body followed by her head. This is one way ancient sailors knew that the Earth must be rounded like a hill. They could see the tall masts of ships long after their hulls as the boats receded far away. To see why this effect occurs, look at the diagram below:

Earth's Rotation during a Sunset

As the Earth rotates, the view from the top of the pink stick changes to reveal the sun or make the sun disappear depending upon which way the Earth is rotating. If the Earth rotates as shown the Sun will disappear. (Note: this diagram is NOT to scale.) Looking at the following diagram you can see that if you watched the sunset from a low point of view and then got up really quickly you might be able to witness the sunset twice in one day.

Viewing the Sunset Twice in One Day

Based on this principle it is possible to calculate the circumference of the Earth:


    • A location where you can clearly view a sunrise or sunset over the ocean
    • A friend to help you measure the height of your eyes while laying down and while standing.
    • A measuring tape or meter stick
    • A stopwatch
    • Pen and paper to record times and heights


    1. Go to a place where you can easily view the sunset or sunrise over the ocean. Be sure to check local weather reports to know the time of day to expect the sunrise or set.
    2. If viewing a sunset, make your first measurement lying down on the ground and your second measurement while standing. If viewing a sunrise, do the opposite. From now on I will explain only the directions for the sunset, please make the necessary adjustments for the sunrise experiment.
    3. Before the sunset, get a friend to measure the height of your eyes while you are lying down and still able to see the horizon where you expect the sunset.
    4. Prepare a stopwatch to begin counting.
    5. Wait for the sunset.
    6. When the last bit of sun has disappeared, start the stop watch and quickly get up and stand in a position that is directly above where your eyes were when you were laying down.
    7. You should be able to see the Sun set again.
    8. Stop the stopwatch when you see the last bit of sun disappear again.
    9. Have your friend measure the height to your eyes in the standing position.
    10. Calculate the circumference of the Earth using the following two equations:
    • [sqrt(2Rh1) - sqrt(2Rh2)]/[2pi * R] = s/S , Where R = The radius of the Earth

h1 and h2= the height of your eyes during the two measurements (h1 should be the bigger of the two heights)

s=the number of seconds between sun sets

S=the number of seconds in one day, which is equal to 60 seconds*60 minutes*24 hours.

This equation is a proportion that assumes the Earth rotates once in 24 hours so that the difference between the distances to the horizon over the whole circumference of the Earth is equal to the ratio of the time between your measurements and a whole day.

    • For example, if you measured 6 seconds in between the sunset when you were laying down with your eyes at a height of 10 cm off of the ground and the sunset when you were standing up at a height of 2m, then you would have to solve the two above equations for the radius of the Earth in terms of h1 and h2 (which are .10 m and 2 m) and the number of seconds in between sunsets:
{[60sec * 60 min * 24 hours
sqrt(2) * (sqrt(h1) - sqrt(h2))^2]/[6sec * 2pi]}^2 = Radius of the Earth

Back | Next

Back Next Table of Contents Click Here for details about distributing the Materials in the Teacher's Guide.