# Locating a Point On the Earth

Giving a complete description of the location of a point on the Earth requires a lot of information--more than some might imagine. It requires three general pieces of information in addition to the point's coordinates.

• The terrestrial reference system (the geodetic datum)

• The coordinate system

• For all but ECEF (Cartesian) coordinates, a reference for the height measurement.

# Terrestrial Reference System

The terrestrial reference system (TRS) is a set of rules that define the relationship between a point's location and the coordinates that describe it. A TRS is also known as a geodetic datum and includes

• Rules that define the origin of the coordinate system (or systems) and in what directions the axes point

• An ellipsoid model, which approximates the shape of the Earth

# Coordinate System

There can be any number of coordinate systems in which one may describe the location of a point on the Earth. The systems described below are the most common.

## Earth-Centered, Earth-Fixed (ECEF) Coordinates

The ECEF coordinate system is a three-dimensional Cartesian coordinate system. Its origin is at the center of Earth's mass, its x and y axes coincide with the plane of zero latitude, and the z axis coincides with the Earth's rotational axis. The x axis also passes through the point of zero longitude (the prime meridian).

You might be tempted to believe that the ECEF coordinate system is independent of the TRS. Don't. There is almost always a translational or rotational difference (or both) between the ECEF coordinate system in different TRSes.

## Geodetic Coordinates

Geodetic coordinates are the longitude, latitude, and height of a point.

In cases where a spherical Earth model is used, the latitude is sometimes referred to as the authalic latitude.

## Projected Coordinates

A projection coordinate system is one in which a portion of the round Earth is depicted on (usually) a flat surface. A projection coordinate system defines an origin and an orientation relative to ECEF or geodetic coordinates.

Coordinates in a projected coordinate system describe point locations in terms of easting and northing from the coordinate system's origin.

# Describing Height

In geodetic or projected coordinate systems, there is a height component. The height component is normally referenced to one of three possible baselines.

• The ellipsoid. A height referenced to this baseline is called the ellipsoid height.

• Mean sea level, which is described by the geoid. A height referenced to this baseline is called the orthometric height, or height above the geoid.

• A vertical datum, which normally declares a specific point to be at a known height above mean sea level

Chuck Taylor -- (Copyright) -- (Contact)