World Geodetic System of 1984 (WGS 84) definitions

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Besides being a map/chart datum WGS 84 (World Geodetic System of 1984) also defines the shape and size of the ellipsoid of revolution (an oblate spheroid) that is considered to be the best mathematical model of Earth:

Flattening = f =

Semi-major axis = equatorial radius = a =

1/298.257223563  (≈ 3.35 ‰)

6378137.0 m

From these two numbers it is possible to calculate:
Semi-minor axis = polar distance = b = (1−f)a = 6356752.3142 m  
Difference between equatorial radius and polar distance = a−b =      21384.6858 m  
Axis ratio = b/a = 1−f = 0.996647189335  
First eccentricity squared = e2 = 1−(b/a)2 = (2−f)f =

First eccentricity = e =

0.00669437999014

0.081819190842621

 
Arithmetic mean radius of Earth = (2a+b)/3 = (1−f/3)a = 6371008.7714 m  
Surface area of Earth = A = 2πa2+π(b2/e)ln[(1+e)/(1−e)] =

Radius of sphere of equal surface area = &frac12√(A/π) =

510065621.724 km2

6371007.1809 m

<nobr>(= 2π[a2+(b2/e)arctanh(e)])</nobr>
 
Volume of Earth = V = 4πa2b/3 =

Radius of sphere of equal volume = (¾V/π)¹⁄³ = (a2b)¹⁄³ =

1083207319801 km3

6371000.7900 m 

(= geometric mean radius)
Maximum circumference of Earth =

circumference of Earth at the equator =
circumference of parallel of latitude at 0° latitude = 2πa =
Radius of sphere of equal circumference = a



40075.017 km
(see above)
 
Minimum circumference of Earth =

circumference of Earth through the poles =
4 × (distance from the equator to a pole) = 4 × <A HREF="Grid_1deg.htm" TITLE="http://home.online.no/~sigurdhu/Grid_1deg.htm">10001.966 km</A> =
Radius of sphere of equal circumference = 40007863 m/2π =



40007.863 km

6367449.1458 m 



See the <A HREF="Grid_1deg.htm" TITLE="http://home.online.no/~sigurdhu/Grid_1deg.htm">main table</A>.
Difference between maximum and minimum circumference =        67.154 km  
Radius of curvature at the poles = a/(1−e2)¹⁄² =
Radius of curvature in a meridian plane at the equator = <nobr>a(1−e2) = </nobr>
6399593.6258 m

6335439.3273 m

(= a2/b)
(= b2/a)
Difference between maximum and minimum radius of curvature =      64154.2985 m  

Latitude where latitudal widths are equal to equator widths =

(e.g. width of one minute of latitude equals
width of one minute along the equator).

54.14432°
54° 46.858′
54° 46′ 51.5″

(1 min. of lat.    = <A HREF="Grid_10min.htm" TITLE="http://home.online.no/~sigurdhu/Grid_10min.htm">1855.325 m</A>)
(1 min. of long. = 1072.371 m)

If Earth had been a perfect sphere, this would had happened at all latitudes.

Latitude halfway between the equator and one of the poles =
45.78096°
45° 08.659′
45° 08′ 39.5″

(1 min. of lat.    = 1852.243 m)
(1 min. of long. = 1310.811 m)

If Earth had been a perfect sphere, this would had happened at exactly 45° of lati­tude (½ × 90° = 45°).

Latitude where latitudal widths and longitudal widths are equal =

(e.g. width of one minute of latitude equals
width of one minute of longitude).

06.58980°
06° 35.388′
06° 35′ 23.3″

(1 min. of lat.    = 1843.148 m)
(1 min. of long. = 1843.148 m)

If Earth had been a perfect sphere, this would had happened at the equator.

Department of Defense World Geodetic System 1984, Its Definition and Relationships with Local Geodetic Systems: Ficheiro:NIMA Technical Report TR8350.2.pdf