This scenario is based on the method devised more than two thousand years ago by Eratosthenes and involves two groups who, at the same time, in two different cities that are approximately on the same meridian, at least 200 km apart, measure the length of a gnomon's shadow and exchange the results. By exchanging information on social media, communication can take place "live" and be more engaging. The web can be used several times and in a diversified manner during the activity, to get to know the other group, to agree on the operations to be done, to take information relating to the difference in latitude, to process and interpret experimental data, etc.
Materials
two and three meters long a stick (gnomon) to be placed vertically on the ground between
a GPS device (the one of a smartphone works fine)
Google Earth Pro
A social media like Whatsapp or Tweet and a videoconferencing software like Google Meet or Microsoft Teams
Useful tips
Which gnomon?: As a gnomon we can use whatever "salvage" pole we can find (pipes, wooden slats, road sign supports - they can be bought and are resistant - etc). the important thing is that they are as straight as possible.
Height of the gnomon: The ideal measurement of the height of the gnomon is - according to our experience - between two and three meters: a longer gnomon oscillates, resulting in a further source of error, if instead it is too short the inaccuracy in the measurement of the shadow becomes unacceptable the gnomon must be positioned so that to the south of it (the area where the shadow is cast around noon) there is free space and above all as flat as possible to allow you to measure the length easily and with the greatest possible accuracy of the shadow!
Cross-cutting objectives
This interdisciplinary scenario (trigonometry, astronomy, cartography, etc.) reproduces the method to measure the Earth’s radius ideated by Eratosthenes more than 2.000 years ago. It involves two classes in two different places at least 200 km far each other, and approximatively laying on the same meridian. Each group measures the length of the shadow of a vertical stick named gnomon and exchange the result with the other group.
From the length of the shadow of the gnomon is possible to determine the height of the Sun in the two different places; they can determine the angle of incidence of the solar rays in the two places and then the angle at the centre of the Earth.
Previous knowledge of the participants:
• Euclidean geometry (similarities between angles)
• Trigonometric expressions (in particular the concept of arctangent)
• Notions of general geography (meaning and use of geographic coordinates)