Eratosthene experiment in Colegiul Tehnic Mihai Viteazul Oradea Romania

1. COMENIUS TEAM of C.T."M.Viteazul"Oradea ERATOSTHENES EXPERIMENT

2. ERATOSTHENES Greek geographer, mathematician and astronomer; Born: 276 BC in Cyrene, North Africa (now Shahhat, Libya); Died: 194 BC in Alexandria, Egypt; In about 240 BC Eratosthenes became the third librarian at Alexandria.

3. Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth. Details were given in his treatise On the measurement of the Earth which is now lost. Eratosthenes compared the noon shadow at midsummer between Syene (now Aswan on the Nile in Egypt) and Alexandria. He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250 000 stadia.

4. We repeated the experiment of Eratosthenes in the different partner-schools looking for own angle of inclination with respect to the equator on the autumnal equinox September 2009. 47 ˚ 03 ́ 50.47˝ N 21 ˚ 55 ́ 02.72˝ E

5. On Tuesday 22th September, between 12.50 local time and 13.40 local time We made around ten readings in total between these times. Ideally it would be nice to take readings every couple of minutes, especially around local noon. We used not only the gnomon but some devices as - QUADRANT. -SOLAR M OT ION DEMONSTRATOR. -GNOMON W ITH APERTURE.

6. QUADRANT SOLAR M OT ION DEMONSTRATOR GNOMON W ITH APERTURE GNOMON

7. S=shadow length G=gnomon length In the first experiment w e got: G 1 = 54 cm S 1 = 58,2 cm tg Z 1 = tg ( S 1 / G l ) = tg (58,2 / 54) = > Z 1 = 46,92 º In the second experiment we got : G 2 = 84 cm S 2 = 89,8 cm tg Z 2 = tg ( S 2 / G 2 ) = tg (89,8 / 84) = > Z 2 = 47,15º In conclusion : (Z 1 +Z 2 ) / 2= 47,035 º Z av =47,035 º

8. . C E =Earth circum f erence d OE =distance Oradea-Equator d OE =5284 km (Google references) C E / 360˚ = d OE / Δ z C E = 40443km C E = 2 π R-> R = C E / 2 π = 40443 / 6.28= 6439.98 km =

9. Our team: