Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 174

Fig. 5.6 Geodetic
coordinate system and
geodetic spatial rectangular
coordinate system

observed, measured clockwise from the north meridian, ranging from 0 to 360 .
This angle is denoted by A.
In Fig. 5.6 , the origin of the geodetic spatial rectangular coordinate system
(geodetic Cartesian coordinate system) is situated at the center O of the ellipsoid,
and the line of intersection between the initial geodetic meridian and the equatorial
plane is the X-axis. The Y-axis is perpendicular to the X-axis on the equatorial plane.
The Z-axis is the spin axis of the ellipsoid, and the right-handed coordinate system
O-XYZ is thus formed. The position of point P is represented by X, Y, and Z.
Definitions of geodetic and astronomical coordinate systems (cf. Sect. 2.1.3 ) are
similar, although also different:

1. They have different reference surfaces and datum lines. The geodetic coordinate
system uses the reference ellipsoid as its reference surface. Its datum line is the
ellipsoidal normal, whereas the reference surface and datum line for the astro-
nomical coordinate system are the geoid and the plumb line.
2. Geodetic coordinates are defined mathematically, whereas astronomical coordi-
nates have physical meaning, influenced by the irregularity of the plumb line.

3. λ are determined by theodolites directly, whereas L and B are calculated

from observed quantities at some given point, including directions, distances,
coordinate differences, etc.

and ˆ

5.3.2 Expressions of the Ellipsoidal Normal Length

As shown in Fig. 5.7 , we establish a rectangular plane coordinate system, with axes
x, y, and z, within a meridian plane or ellipse. Draw the normal PK P through point P,
and the angle between the normal PK P and the x-axis is B. Through point P draw a
line TP tangent to the meridian, and the angle between the tangent line TP and the