How to calculate the radius of the earth
There are several methods to estimate the earth’s radius, however, the most famous method is one that Eratosthenes used in the age 300 B.C., which is the first method dated by history and the way for calculating the radius of the earth is measuring differences in the angle of the rays of the sun at two separate points of the earth. Now, we explain how you can estimate the radius of the earth, too, by using the Eratosthenes method.
The first step is to fix two random locations of the earth, we call these locations to place 1 and place 2 to avoid confusion, and record the distance. We denote by x the distance between place 1 and place 2. Next, insert a rod measuring one meter into the ground at place 1 in a sunny spot and tack one end of a piece of string to the top of the rod. Do the same in place 2. Make sure both rods are one meter long and are at a 90-degree angle to the ground, that is, they are perpendicular to the ground.
The second step is to measure the angle of the shadow of your rod, do this when the sun is overhead and the shadow is smallest, for example at the noun is an excellent time. Place the end of the string at the end of the cast shadow and keep it taut to avoid measurement errors. Use the protractor to measure the angle made by the string and the rod. At the exact same time do the same in place 2. Now, subtract the two measurements obtained to get the difference in the angle between the two places, we denote this number by the symbol.
The third step is to calculate the measure of the line that joins place 1 and place 2 and goes around the earth, we call this measure the perimeter of the earth and we denote this measure by the letter c. One can calculate c using x
and as follows. Let r be the radius of the earth, then from the perimeter formula, one obtains that c=2r. Finally, since the circle has 360-degrees we have that
In view of the rule of three,
The above equation provides the value of the r, as an example, in the case of the Eratosthenes x=800 km and =7,2- degrees, therefore r=6265,9 km. Thus, following these easy three steps, one can estimate the radius of the earth.
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