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 Eratosthenes of Cyrene was a Greek mathematician, geographer , poet, athlete, astronomer, and music theorist.

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.

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

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

Materials Stick Sun Ruler Calculator Friends abroad 

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

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

Formulas z1 z2 y

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

Our results Stick length Shadow lelngth 139 cm 98 cm 140cm 98,5 cm

Our Angle a(average) = z1 = 53.67° b= 36.33° a = 54.81° a = 54.87°

Madrid Results Stick’s length – 100cm Shadow’s length – 40.5 cm Spain time 12:00 13:00 14:00 14:13 Solar time 10:00 11:00 12:00 12:13 length 70,50 51,00 40,50 39,00 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.

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

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

Radius R Rreal= 6378,137km

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

Calculating…

Radius R Rreal= 6378,137km

Results Name With shadows With a map Real results Angle 14.29° 14.91° Earth’s circumference 40055.98km 38390.38km Radius 6378.34km 6113.1km 6378,137km

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.

Thank you for your attention