It is possible to do this experiment any time of the year, but if you want it to be easy, then you need to wait for June 21st, noon. At this date (and it has to be noon), you need to stick a vertical pole in the ground, and see how long the shadow is. To make it exact, measure the length of the shadow and the length of pole that is sticking out of the ground. If the pole is 2 feet tall, and the shadow is 1 foot long, then draw on a piece of paper the pole bieng 2 inches tall and the shadow being 1 inch long. Use a ruler. Then whip out your calculator and we'll do some simple trigonometry. If you have a scientific calculator, first divide the shadow's length by the pole's height. When you have that number, press a button titled 2nd, then press the one titled TRIG. You now have your angle.
If you don't have a good calculator, or you just are too lazy to figure this out, don't worry, it isn't very hard. First you need to graph the pole and shadow length according to their actual size. For example, you may have 1 cm be equal to a square length on a sheet of graph paper. Then, use a ruler to create a line from the end of the shadow (point B) to the top of the pole (point A). Then get out the protractor and place the center point of the protractor on point A, and the line between point A and B should be parallel to the protractor. The hypotenuse, if the line is stretched far enough, will point to the angle number on the protractor. Simple, but I prefer the calculator.
Divide 360 degrees by that angle, and you have the amount of times that the angle goes around the earth. All you need to do now is to find the distance from where you are to the equator, then multiply that distance by the number of times that the shadow's angle went into 360 degrees. It is easy to find your distance from the equator by knowing that each latitude is 69.171 miles. All you need to know is your latitude, which, if the expriment is done on summer solstice, is equal to the angle you found earlier in the experiment.
See what other people have done, expressed in a chart below.
There are many schools around the world that study Eratosthenes and his experiment. Here is a table showing one school's math class and their results, using the crude tools Eratosthenes used. (actual latitude of location: 24 degrees).
Group
Shadow Length in cm
Pole Height in cm
Angle
Earth's circumference based on calculations (in miles)
Percentage miscalculated
Group 1
31
62
26.56
22,728.72935
8.58% short
Group 2
51
109
25.07
24,087.42
3.11% short
Group 3
117
249
25.1678
23,993.48669
3.485% short
Group 4
29.5
61.6
25.59
23,597.621
5.08% short
Group 5
25
51.5
25.893
23,315.8183
6.22% short
Group 6
10.5
20.5
27.1213
22,265.26457
10.44% short
Group 7
25.5
62
22.356
27,011.21981
8.6% more
This is a great experiment and you can see how close you get to
the actual distance of the earth, which is 24,859.82 miles.
If you want to see a visual of what we did, click here.
to figure this out, don't worry, it isn't very hard. First you need to graph the pole and shadow length according to their actual size. For example, you may have 1 cm be equal to a square length on a sheet of graph paper. Then, use a ruler to create a line from the end of the shadow (point B) to the top of the pole (point A). Then get out the protractor and place the center point of the protractor on point A, and the line between point A and B should be parallel to the protractor. The hypotenuse, if the line is stretched far enough, will point to the angle number on the protractor. Simple, but I prefer the calculator.
