An ellipsoid is a mathematical model of the shape of the earth. Mathematically, it is a 3-dimensional shape formed by rotating an ellipse around the shorter of the two axes. The earth's shape is approximately ellipsoidal because the centrifugal force at the equator distorts it slightly. The figure below is enormously exaggerated; the earth would appear to be spherical at the scale of the image.
An ellipsoid is described by two numbers. In the figure below, a is the semi-major axis or equatorial radius, and b is the semi-minor axis or polar radius. When used in calculations, other numbers derivable from a and b are more convenient, and so sometimes an ellipsoid is specified in terms of those other quantities.
f is the flattening, and is defined to be (a - b) / a.
e is the eccentricity, and is defined as e^{2} = 2f - f^{2}.
[http:/images/bmwiki/ellipsoid.png]
An ellipsoid is independent of a ["datum"], but a datum will always specify which ellipsoid is to be used. Various ellipsoids have been used to approximate the shape of the earth. A few are listed below.
Ellipsoid |
Date |
a |
b |
flattening |
Description |
WGS 84 |
1984 |
6,378,137.0 |
6,356,752.3 |
1/298.257223563 |
Used by the WGS84 datum and the NAVSTAR GPS system. The ellipsoid is very nearly the same as the GRS80. The minor difference in the flattening has no effect on practical calculations. |
GRS 80 |
1980 |
6,378,137.0 |
6,356,752.3 |
1/298.257222101 |
Used by the NAD83 datum. |
Clarke |
1866 |
6,378,206.4 |
6,356,583.8 |
1/294.978 |
Used by the NAD27 datum, and for older maps within the U.S. |
Airy |
1830 |
6,377,563.4 |
6,356,256.9 |
1/299.325 |
Used by older maps within Great Britain |
Bessel |
1841 |
6,377,397.2 |
6,356,079.0 |
1/299.153 |
Used by older maps within Central Europe |