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05-MassEarth

# 05-MassEarth - 5 Mass and Radius of Earth PreLab Name...

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5. Mass and Radius of Earth – PreLab Name: Section: Date: Finding the Radius of Earth Long before Columbus many people already knew the Earth was not flat. The first recorded measurement of the size of Earth was made by a Greek named Eratosthenes in 240 BC. Eratosthenes measured the angle the sun made at noon from two different positions in Egypt. Using some simple geometry he measured the radius of Earth to within kilometers of the presently accepted value. His experiment was as follows. When the sun was directly overhead in one location he measured the angle the sun made (using shadows) at the other location. Knowing the distance between the two places (Aswan and Alexandria), he used the geometry to calculate the radius of the Earth. Earth Sun (Not to Scale) θ Distance Between Aswan and Alexandria Sun θ

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Once you measure the angle and the distance between the cities, the geometry problem is rather simple. We know that if we go all the way around the Earth the Sun's position must change by 360 degrees. Whatever fraction of angle (out of 360) the sun has moved from location to location must be equal to the fraction of the circumference of Earth we've traversed. ( Θ Between Cities)/360 = (Distance between Cities)/(Circumference of Earth) or... Circumference of Earth = (Distance between Cities)* 360 / ( Θ Between Cities) Eratosthenes knew the distance between Alexandria and Aswan was 800km and that the Suns angle was 90 in Aswan. He measured the Suns angle to be 82.8 degrees in Alexandria.
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