The tropic of Cancer is 23.5 degrees north of the equator. On any given day a vertical stick on the equator casts no shadow while one at the tropic of cancer does. Calculate earth's circumference...

The tropic of Cancer is 23.5 degrees north of the equator. On any given day a vertical stick on the equator casts no shadow while one at the tropic of cancer does. Calculate earth's circumference using this information

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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This question is very similar to what Eratosthenes did to calculate the circumference of Earth, way back in 3rd century BC in Greece. We can think of Earth as a sphere and then any two points of its surface will subtend an angle at its center. Knowing the angle and the distance between the two points, we can use the analogy of arc of a circle to determine the circumference of the sphere. We are given the angle between Tropic of Cancer and the Equator as 23.5 degrees, but not the distance. We can assume that value to be about 2600 km. We can use unitary method to calculate the circumference of Earth. If 23.5 degrees is equal to 2600 km, then 360 degrees (complete circle) is equal to a distance of:

Circumference = `360/(23.5) xx 2600 km = 39830 km`

or, the circumference of Earth is about 40,000 km. 

This circumference will yield a diameter of about 12,678 km. In reality, the diameter of Earth is 12,742 km, so we got a pretty good estimation of Earth's circumference. 

Hope this helps.

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