WOLFRAM|DEMONSTRATIONS PROJECT

Calculating the Earth's Circumference at Any Date from Any Location

​
latitude
ϕ
1
​(°)
44.13
longitude
λ
1
(°)
1.25
Standard Time Zone
1
DST
latitude
ϕ
2
(°)
29.
longitude
λ
2
(°)
77.7
Standard Time Zone
5.5
DST
year
2011
month
2
day of month
10
zoom
February 10 2011
declination δ = - 14° 51' 12"
solar time (noon)
12: 0' 0"
location
1
latitude
ϕ
1
= 44° 7' 48"
longitude
λ
1
= 1° 15' 0"
zenith at noon,
θ
1
= 58° 59' 0
local time 13: 0' 26"
location
2
latitude
ϕ
2
= 29° 0' 0" ​
longitude
λ
2
= 77° 42' 0"
zenith at noon,
θ
2
= 43° 51' 12
local time 12: 24' 38"
We verify that
θ
1
=
ϕ
1
- δ
θ
2
=
ϕ
2
- δ
ϕ
1
-
ϕ
2
=
θ
1
-
θ
2
= 15° 7' 48
​
The Earth's circumference is determined from
θ
1
​,
θ
2
​, and
D
12
.
circumference =
D
12
360
θ
1
-
θ
2
= 1682 × (360 / 15.13) = 40030 km
This Demonstration generalizes Eratosthenes's calculation of the Earth's circumference. The solar zenith angles
θ
1
and
θ
2
are measured at noon, on the same day, at two different locations. Knowing the distance
D
12
between the parallels of the two locations, the Earth's circumference is given by:
D
12
360

θ
1
-
θ
2

or
D
12
360
θ
1
+
θ
2
,according to whether or not the locations belong to the same hemisphere.
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.