Components of a geographic coordinate system
The details
of a geographic coordinate system vary according to the earth model you're
using. For instance, a sphere and a spheroid have different shapes, so they
can't coincide spatially at every latitude-longitude value. The same goes for
two spheres with different radii.
A
geographic coordinate system has three components:
·
an
angular unit of measure
·
a
prime meridian
·
a
datum, which includes a spheroid
About
the components
The angular unit of measure is usually degrees,
in which the unit represents one part in 360 of a circle. But it may also be grads,
in which the unit represents one part in 400 of a circle.
The prime
meridian defines the zero value for longitude. (It isn't necessary to
define a zero value for latitude, since this is always the equator.)
The datum
specifies the sphere or spheroid. Actually, it does a little bit more than
that, but we'll talk about the rest in the next module.
A sphere is
defined by the length of its radius. A spheroid defined by the length of its
semi-major and semi-minor axes, or by the length of
the semi-major axis and the flattening value. (Flattening, or the oblateness of the spheroid, is the ratio of the semi-major
to the semi-minor axis.)
Common spheres and spheroids
The most commonly used radius for the earth is 6,371
kilometers. This is the default sphere used by ArcGIS® for sphere-based map
projections.
Of the
twenty or more spheroids defined for the earth since 1800, several are still in
use today. The WGS84 spheroid, determined by satellite, is becoming a global
standard, but a huge amount of spatial data—digital and non-digital—is based on
other spheroids. Here are the dimensions for a few widely-used spheroids. You
can see that the differences among them are not that big:
Name |
Date |
Semi-major axis |
Semi-minor axis |
Flattening Ratio |
WGS84 |
1984 |
6,378,137 |
6,356,752.3 |
1/298.257 |
GRS80 |
1980 |
same |
same |
same |
WGS72 |
1972 |
6,378,135 |
6,356,750.5 |
1/298.26 |
International |
1924 |
6,378,388 |
6,356,911.9 |
1/297 |
Clarke 1866 |
1866 |
6,378,206.4 |
6,356,583.8 |
1/294.98 |
How to calculate flattening
Let the semi-major axis (equatorial radius) = a; the
semi-minor axis (polar radius) = b; and the flattening = f.
The equation to calculate flattening is f = (a – b) / a.
Taking the Clarke 1866 spheroid as an example:
(6,378,206.4 – 6,356,583.8) / 6,378,206.4 = 0.0033900753
Since flattening is usually expressed in the form 1/f, you
divide the quotient into 1:
1 / 0.0033900753 = 294.978
Geographic
coordinate systems in ArcMap
Any spatial data you add to ArcMap™ is associated with
a particular geographic coordinate system (