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

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 (meters) Semi-minor axis (meters) 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 (
GCS), distinguished by its unique set of components—especially by its datum. Commonly-encountered geographic coordinate systems are GCS_WGS84, GCS_North_American_1983 (NAD83), and GCS_North_American_1927 (NAD27). You'll learn more about these systems in the next module.