Calculating the Earth's Circumference at Any Date from Any Location
Calculating the Earth's Circumference at Any Date from Any Location
This Demonstration generalizes Eratosthenes's calculation of the Earth's circumference. The solar zenith angles and are measured at noon, on the same day, at two different locations. Knowing the distance between the parallels of the two locations, the Earth's circumference is given by:
θ
1
θ
2
D
12
D
12
360

θ
1
θ
2
D
12
360
θ
1
θ
2
The Earth is, of course, assumed to be a perfect sphere. Actually, it is slightly oblate, with the equatorial radius approximately 21 km greater than the polar radius, but this contributes a negligible correction.