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Earth’s circumference

Earth’s circumference. Eratosthenes. He invented a system of latitude and longitude. He was the first to calculate the tilt of the Earth's axis He also created the first map of the world incorporating parallels and meridians He was the first person to calculate the circumference of the earth.

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Earth’s circumference

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  1. Earth’s circumference

  2. Eratosthenes • He invented a system of latitude and longitude. • He was the first to calculate the tilt of the Earth's axis • He also created the first map of the world incorporating parallels and meridians • He was the first person to calculate the circumference of the earth Eratosthenes of Cyrene was a Greek mathematician, geographer , poet, athlete, astronomer, and music theorist.

  3. History Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. He find out that a circumference is about of 46,620 km, i.e. 16.3% too large.

  4. Purpose • Find the circumference of the Earth without using modern inventions • Verify Eratosthenes's theory.

  5. Hypothesis • I think that my results will differ from real results.

  6. Materials • Stick • Sun • Ruler • Calculator • Friends abroad 

  7. Process • Our school and others schools (from project LULATS) measure shadows in daylight. • We send each otherresults • We chose Spain’s results.

  8. What we need? C - Earth’s circumference L – distance between Taurage and Madrid Y – angle z1 z2 – the angles of elevation of the sun C z1 z2 Tauragė L y Madrid

  9. Formulas z1 z2 y

  10. How find the angle of elevation of the sun? • We need a stick • Stick’s shadow at noon • An angle between a stick and its shadows

  11. Our results Stick length Shadow lelngth 98 cm 98,5 cm 92 cm 108 cm • 139 cm • 140cm • 127 cm • 133 cm

  12. Our Angle a = 54.81° a = 54.87° a = 54.08° a = 50.92 ° b a(average) = z1 = 53.67° a b= 36.33°

  13. Madrid Results Spain time12:0013:0014:0014:13 Solar time10:0011:0012:0012:13 length70,5051,0040,5039,00 • Stick’s length – 100cm • Shadow’s length – 40.5 cm • Angle 22.04° Madrid is in a different geographic longitude. So we need to add two hours and then we will get right result.

  14. Distance between Madrid and Taurage H = 7.95 cm L= 200*7.95= 1590 km

  15. Calculating… L = 1590km z1 = 36.33° z2 = 22.04°

  16. Radius R Rreal= 6378,137km

  17. Why don’t we use just a map? 55.15° y = 55.15° - 40.24° = 14.91° 40.24°

  18. Calculating…

  19. Radius R Rreal= 6378,137km

  20. Results

  21. Findings • Eratosthenes's theory has been reasserted. • We got almost the same result without leaving Taurage • We can easily find Earth’s circumference, when we know two different cities’ geographic latitudes.

  22. Thank you for your attention

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