Investigations of the shape of the Earth and Eratosthene´s method to measure the size of the Earth Timo Suvanto Heureka

Introductory section and preparatory phase Short Description: Students will measure the angle of the Sun to calculate the size and the circumference of the Earth. Keywords: Sun, angle, Earth, radius, circumference, horizon, Eratosthenes, flat Earth Target audience: Teacher Age range: 10 – 18. The level of mathematical treatment depends on the age of students. Even the youngest ones can understand the basic idea of the method. Context: School and science museum Time required: Pre Visit – 2 hours, Visit – 1 hour, Post Visit – 2 hours

Introductory section and preparatory phase Technical Requirements: Sun (shining), stick, measure of length, calculator, another measurer far enough, telephone. Author’s background: School teacher; museum educator Connection with the curriculum: Earth’s size, measuring, the shape of Earth, history of science Learning Objectives: Students learn to measure the length of Sun´s shadow and use trigonometry to calculate the height of the Sun on the sky.

Introductory section and preparatory phase Guidance for preparation: The teacher should prepare a small presentation with the proposed pictures, videos and relative material. The students’ worksheets should be printed and handed to the students prior to the visit. In the portal of previous Cosmos-project is much useful material for this purpose. This is a good opportunity to show the continuity and permanence of Cosmos- project.

Pre Visit – Teaching Phase 1: Questions Eliciting Activities – PROVOKE CURIOSITY How can one know, that the Earth is a ball and not a pancake? How big is the Earth? How the size of the Earth can be measured? What is proper way to tell the size of the Earth?

Pre Visit – Teaching Phase 1: Questions Eliciting Activities – DEFINE QUESTIONS FROM CURRENT KNOWLEDGE Give some examples to prove that the shape of the Earth is a ball. Which ones of these are something, you can see with your own eyes? Which ones are connected to the modern techology?

Pre Visit – Teaching Phase 2: Active Investigation – PROPOSE PRELIMINARY EXPLANATION OR HYPOTHESES Teacher gives to students hints, how they can make investegations about the shape of the Earth. The investigations can be made by own eyes or using material from Internet. –When a ship is at the horizon, its lower part is obscured due to the sphericity of the Earth. –The shadow of Earth on the Moon during the partial phase of a lunar eclipse is always circular, no matter how high the Moon is over the horizon.Moonlunar eclipse –Travelers going south see southern constellations rise higher above the horizon.constellations

Pre Visit – Teaching Phase 2: Active Investigation – PLAN AND CONDUCT SIMPLE INVESTIGATION Teacher gives to every student one method to study. If a lunar eclipse is present, that would be a happy coinsidence. If somebody will travel to south, that is also usefull. If school is near the sea, the third method is useable. If nothing is not possibly in practice, students use their investigations virtual in Internet.

Visit - Teaching Phase 3 Creation – GATHER EVIDENCE FROM OBSERVATION Students will make the measurements with help of the teacher and sciences centre guides. The calculations can be made either at the same time or later. Sometimes the students are not familiar to the trigonometry needed. The measurements can make also using protactor, if the students are too young to understand geometry.

Visit - Teaching Phase 4 Discussion – EXPLANATION BASED ON EVIDENCE Teacher gives explanations using suitable material. For instance these ones. TEACHER’S GUIDE Cosmos-project of Eratosthenes Eratosthenes method

Visit - Teaching Phase 4 Discussion – CONSIDER OTHER EXPLANATIONS Teacher devides the students to the two group. Another is the supporters of flat Earth, another of round Earth. Both groups will argue only for their own point of view and against others point of view. Teacher will deside, if the Earth is flat or ball, but only using argumential justifications.

Visit - Teaching Phase 4 Discussion – CONSIDER OTHER EXPLANATIONS This is a very nice experiment, how two schools or science centres can co-operate. The height of the Sun varies so little near midday and on successive days, that measurements can made ”flexibly” conserning the time. Because ”right results” are known in advance, another partner can be also virtual (for instance, if the days are different)

Post Visit - Teaching Phase 5 Reflection – COMMUNICATE EXPLANATION Students are asked to do the exercise that is given in the application they have used. Divided into groups, they are asked to make a short presentation about Eratosthenes method and present their measurements. Some can do the same thing about the shape of the Earth. Discuss, what possibly went wrong in teaching or investigations or calculations. teachinginvestigationscalculations

Usefull material and links Teacher´s guide Cosmos-portal About Eratosthenes Finnish example Nice video by Carl Sagan Some problems during Visit-phase Eratosthenes-Quiz