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The Circumference of the Earth: Eratosthenes and GPS


Northern position P2:
latitude Φ2 = 51° 36.795' N (7° 57.468' E)
Southern position P1:
latitude Φ1 = 51° 36.784' N (7° 57.467' E)

Eratosthenes (276 BC - 195 BC) was the first person to calculate the circumference of the Earth. He knew that on the summer solstice at local noon in the Ancient Egyptian city of Syene (S) the Sun would appear exactly at the zenith. He also knew, from measurement of the shadow on a vertical gnomon, that in his hometown of Alexandria (A), the zenith angle of the Sun was 1/50th of a circle (7°12') on the solstice noon. He concluded that the meridian arc distance from Alexandria to Syene (5000 stadia, about 800 km) must therefore be 1/50 of the total circumference of the Earth (40,000 km).

Eratosthenes Syene Alexandria

Source: Wikipedia

Instead of the Sun we use a GPS receiver to measure the angle φ (difference of the latitudes) belonging the length of the meridian arc s (20 m) from P1 to P2:

earth circumference diameter radius

earth circumference formula

GPS latitude difference: φ = Φ2-Φ1 = 51° 36.795' - 51° 36.784' = 0.011' = 0.000183°

Circumference of the Earth L = 20m*360°/0.000183° = 39,300 km
Radius of the Earth R = 6,250 km

The GPS display resolution is 0.001', the error of the result about 10%.

The measurement in my garden simulated by Google Earth:

google earth


Google Earth latitude difference: φ = Φ2-Φ1 = 51,61325° - 51,61307° = 0,000180°, s = 20,00 m
L=40,000,000 m
R=6,366,000 m

Earth Shape Applet

Web Links

Eratosthenes (Wikipedia)

Updated: 2011, Aug 26