Geoscience Reference
In-Depth Information
5.3 Relationship Between the Geodetic Coordinate System
and the Geodetic Spatial Rectangular Coordinate
System
5.3.1 Definitions of the Geodetic Coordinate System
and the Geodetic Spatial Rectangular Coordinate
System
The Geodetic Coordinate System is used to describe the geometric position of a
point on the Earth's surface expressed by the geodetic longitude (L), geodetic
latitude (B), and geodetic height (H).
As illustrated in Fig. 5.6 , the geodetic longitude of point P 0 is the dihedral angle
formed between the geodetic meridian plane NP 0 S of an arbitrarily chosen point P 0
and the initial geodetic meridian plane NGS (meridian through the Greenwich Mean
Observatory), denoted by L (initial letter of the German word L
ange). Point P 0 is
the projection of P on the ellipsoid along the surface normal. The geodetic longi-
tude of point P is equal to that of its projection on the ellipsoid P 0 . Longitudes can
either be counted from the initial meridian plane eastward, ranging from 0 to 360 ,
or be measured eastward or westward from the Prime Meridian at Greenwich,
ranging from 0 to 180 east or west, known as east longitude and west longitude,
respectively. East longitudes are given positive values and west longitudes are
given negative values in geodesy. Obviously, all points on the same meridian
have the same longitude.
The geodetic latitude of point P is the angle formed from the equatorial plane to
the ellipsoidal normal PK p , denoted by B (initial letter of the German word Breite).
The geodetic latitude of point P is equal to that of its projection on the ellipsoid P 0 .
Geodetic latitudes are measured southward or northward from the equator to poles,
positively towards the north and negatively towards the south, ranging from 0 to
90 , known as south latitude and north latitude, respectively. Apparently, all points
on the same parallel have the same latitude.
The geodetic height at a point P on the Earths' surface is the distance from the
reference ellipsoid to the point in a direction normal to the ellipsoid, denoted by
H (the distance H between P and P 0 in Fig. 5.6 ). Geodetic heights are measured
from the ellipsoid, which are reckoned positive outward and negative inward.
The geodetic longitude L, geodetic latitude B, and geodetic height H constitute a
three-dimensional geodetic coordinate system. These three coordinate values can
uniquely specify the position of a point on the Earth's surface. If the point is on the
surface of the ellipsoid, obviously H
0, therefore, the position of a point on the
ellipsoid can be uniquely determined by means of geodetic longitude L and geo-
detic latitude B, which is a two-dimensional geodetic coordinate system.
The direction of a curve on the ellipsoid is represented by the geodetic azimuth,
which is the angle between the geodetic meridian and the geodetic line to the object
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