In order to describe one's position on Earth, a person needs a
simple surface which can be described mathematically. Since the
18th century, measurements have existed which prove that the Earth
does not look like a perfect sphere, but rather is flattened at
the poles. The appropriate mathematical description is an ellipsoid
of revolution. An ellipsoid of revolution is produced by rotating
an ellipse about one of its two axes. One defines the ellipsoid
by describing the ellipse and the axis of rotation. The ellipsoid
of the Earth has as axis of rotation the small axis of an ellipse
whose precise dimensions are established at international scientific
congresses. Technological progress has made it possible to define
these dimensions with everincreasing accuracy.
Depending on the country or the continent where one is working,
one chooses a geodetic datum which minimises the deviation from
the geoid. The geodetic data are different each time, and their
centre does not coincide with the Earth's centre of mass.
As spatial measurements developed, it was necessary to define global
geocentric reference systems. The most widely used system is the
WGS84 (World Geodetic System 1984). This is the reference system
used for the GPS.
Once the datum is defined, one can describe a point on the surface
of the Earth in either of two ways : by employing geocentric Cartesian
coordinates, or by using geographical coordinates.
Cartographers and navigators have long since grow accustomed to
locating a point with the aid of geographical coordinates expressed
in longitude l and latitude j.
The longitude l is the dihedral angle
formed by the meridian of a point with the meridian of Greenwich
and counted from this original meridian, positively towards the
east and negatively towards the west.
The latitude j of a point is the angle
formed by the vertical of the point with the plane of the equator.
Latitudes are counted from the equator, positively towards the north
and negatively towards the south.
The longitude and the latitude make it possible to define a point
on the ellipsoid. To situate a given point, one must also define
its position with a third parameter, called the ellipsoidal height
h.
One can also describe the location of a point by its geocentric
Cartesian coordinates. Such a positioning system locates the points
in X, Y and Z with the centre of the ellipsoid as origin.
