Introduction: Erathostenes Apparatus
Recently I heard a lot of weird theories regarding Earth, so I have decided to make simple apparatus to repeat Erathostenes experiment conducted over 2200 years ago. I designed and 3D printed simple apparatus which I called 'Erathostenes apparatus' and you can use it to prove that Earth is a sphere and you can measure radius of Earth with pretty good accuracy.
- 30cm ruler
- M3 x 20mm bolt with nut
- 3D printer
- Philips screwdriver
Step 1: Experiment Principle
The experiment is simple. Erathostenes placed vertical rod in Syene at noon of the summer solstice so it didn't cast the shadow. The same size vertical rod was placed in Alexandria and it cast a shadow. The difference between those 2 locations was about 7 degrees. Knowing the distance between Syene and Alexandria, Erathostenes was able to calculate radius of Earth.
The experiment I designed is not super accurate, but in the age of internet and smartphones the results can be obtained immediately. You will need two exactly the same pieces of apparatus in two different locations.
On the same day and at the same time 2 people can move the rod so it won't cast a shadow and then measure the angle. Further the two measuring point will be, the greater the difference in the angles will be measured.
You can do it another way by placing the ruler and set up the rod the way, it will cast the same length shadow in both places and then read the angle. This is the method me and my friend used, as you can take multiple readings and calculate the average reducing the error significantly.
Step 2: Apparatus Assembly
- First you need to 3D print all the pieces
- Drill 3mm hole through the protractor centre and place it in the 3D printed cover
- Glue the top cover and then glue the case with protractor into the base
- Use M3 bolt and mount the rod (tighten the nut, but make sure you can still move it slightly)
- Glue the small 3D printed pointer into the rod (there is small slot for that)
Step 3: Setting Up the Apparatus
- Place the device on level ground and you can use spirit level to check if it's reasonably levelled
- At first you have to point the apparatus toward the Sun. The easiest way to do that is to keep rotating the plate until the shadow cast by protractor is parallel to shadow cast by the rod (see picture above)
- Move the rod so it won't cast any shadow. It's quite tricky and there is an error involved as the rod and the screw have certain thickness
- After that place the ruler or tape measure under the rod on the base
- Now you can start moving the rod so it will cast certain length shadow and measure the angle
- Record your readings in a table
NOTE: Remember to do that experiment with your friend or family member that lives quite far from you. The longer the distance the more accurate calculation will be.
Step 4: Taking Readings
My friend from Havant, UK made this apparatus and so did I. I'm based in Heywood, UK and we are about 320km apart. I know the distance because I drove to visit him few times and I tried to use most direct route as possible. Of course the distance I measured never will be super precise, but I took the average from 3 trips and then I compared it with Google maps. Based on that I estimated the distance between 320km to 330km.
As you can see on the pictures above we did video call and we took few readings from two different locations (Havant and Heywood), but on the same day and at the same time. The results are in table (see picture above).
Step 5: Radius Calculations
After taking reading, I calculated the average angle difference between the two locations. Having that you can use proportions to estimate the circumference (or radius L=2*Pi*R) of the Earth.
I also calculated the error and, although it's quite significant, the radius of Earth we calculated is within that error.
I'm very pleased with the results and the best thing about this experiment is that anyone can verify my calculations and find out radius of Earth themselves.
The final results: R = 6153m +/- 800km while the real value is R= 6371km
Participated in the