III. Eratosthenes experiment

CHALLENGE for proving or disproving a spherical Earth 

Difficulty: Easy/Moderate

The technical setup is very simple!
Programming knowledge is not necessary, but may help. 
Cost: $$
Requires collaboration in a team with members from different locations.

Read the entire text. The task (challenge) is at the bottom.

Since 2005 several schools around the world have been doing a simple science experiment: Measuring the sun's altitude at noon using just a simple gnomon (vertical sundial) and a ruler for measuring the shadow. This project (eratosthenes.eu) has been documented here and all results can be found here. 

An interesting task is to plot the results and see if we can find clear evidence of a spherical Earth or a flat Earth. So I picked the measurement series of November 2023 and selected measurements from November 29 and 30. There are obvious gaps in some data series for some schools, this can be due to school vacations maybe, or just bad weather for longer periods. But at the end of November, I found several measurements. So let’s put all this together. In this folder you find a toolkit project where you have the data collected in ODS format (can be read into Excel and converted to a CSV file), together with a README file and a simple Python program that generates two graphs: One for a spheric Earth and the other for a flat Earth. 

Note that you don't need to understand the program code supplied, but you can of course use it if you wish. The plotting could also be done using paper and pencil with the help of a protractor. 

Now let's inspect the results. Let’s first take a look at a flat Earth. To the left, we see the stations in Europe (Greece, Albania, Romania, and France). In the middle is one station in Puerto Rico, and to the right one station in Brazil. At the left end we have the North Pole, and the South Pole (or “Ice Barrier”) to the right. 

It is obvious from the graph above that the location of the Sun can not be deduced. All lines should intersect at one much more definite point, but in the graph above we can easily see at least 4 possible locations for the Sun (being 1000s of km apart). Even with an assumed error of 1-2 degrees for each measurement you cannot deduce a common intersection point. This is a strong contra-indication of the Earth being flat. Where is the Sun? 

Now take a look at the corresponding graph where we fit the data to a spherical Earth: 

In this picture you can easily see that the lines are almost parallel. This indicates a very distant sun and is the model supported by science today. The actual exact distance to the Sun cannot be measured using this simple experiment however, to do this you need much more advanced instruments, but it is interesting to see that the almost parallel sun rays can be found using this very simple backyard experiment which can be repeated by anyone working in collaboration with a team where members are located at different locations. The experiment was first performed by Greek scientist Eratosthenes in 230 BC, but he only had access to two measuring points, so he could not prove Earth's sphericity. He was able though to calculate the Earth's circumference given the assumption the Earth is spherical. But in this experiment as shown above we have seven measuring points, which results in the clear failure of the attempt to fit the results to a flat Earth (first picture). 

Our experiment is very simple, using bottles/simple sticks, etc. The accuracy is not extraordinary, and you can see the lines are not exactly parallel, but it is quite good anyway. It is not far-fetched to assume an accuracy of 1-2 degrees for each measurement. 

CHALLENGE: Repeat this experiment and see for yourself which Earth geometry fits your data best. If you get results that may indicate a difference from what is taught by ordinary science you should take contact with your local university or the International Astronomical Union with your findings. 

Good luck! 

But wait! There is a bonus challenge if you want to dig deeper.