# Two students who live on the equator want to estimate the circumference of the earth. The students synchroniz their watches before one student leaves on vacation 600 miles due west of their home....

Two students who live on the equator want to estimate the circumference of the earth. The students synchroniz their watches before one student leaves on vacation 600 miles due west of their home. Describe an experiment that these students can do to estimate the circumference of the earth. In your answer, include realistic results for each of the measurements you describ.

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### 1 Answer

The two students would like to measure the circumference of the Earth. To do this they synchronize their watches at home and then one of them leaves for vacation to a place that is 600 miles due West.

Here is one way to determine the circumference of the Earth. As the two have synchronized their watches, both of them can take measurements at the same time. Each of them has to set up a system to be able to accurately measure the angle at which the Sun's ray are striking the ground. This can be done by using 2 sticks, one of which is perpendicular to the ground and the other points in the direction of the Sun. Assume that they choose a time when the Sun's rays are perpendicular to where one of them is and they make an angle X degrees with the horizontal where the other is situated.

If the circumference of the Earth is D miles, the relation between x and D is: `(x/600) = 360/D`

or `D = 216000/x`

A similar method was used by Eratosthenes of Cyrene to make a measurement of the Earth's circumference for the first time.