Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 169

surface. Hence, the reference ellipsoid becomes the reference surface for surveying
computations. The points from the physical surface of the Earth are projected
directly onto the ellipsoid along the ellipsoidal normal. As a result, the ellipsoidal
normal becomes the datum line for surveying computations.
The reference ellipsoid has defined the geodetic coordinate system (cf. Sect. 5.3 ).
If two countries or one country at different periods of time have adopted different
reference ellipsoids, i.e., different geodetic coordinate systems, then one coordinate
system needs to be transformed to another in order to make use of each other's
results.
The reference ellipsoid is a mathematically defined surface that approximates
the physical shape of the Earth. As the reference surface for surveying computa-
tions, the reference ellipsoid has played prominent roles in surveying and mapping,
as follows:
1. The reference ellipsoid is used as the reference surface for the determination of
the horizontal coordinates (geodetic longitude and latitude) and the geodetic
height of a point on the Earth's surface.
2. The reference ellipsoid is the reference surface to describe the shape of the
geoid. The vertical distance from the geoid to the reference ellipsoid is called
geoid undulation. The angle between the plumb line and the surface normal to
the reference ellipsoid at a given point is the deflection of the vertical. The geoid
undulation and deflection of the vertical reflect the distance between the two
surfaces and the deviation of the geoid from the ellipsoid, and also characterize
the shape of the geoid.
3. The reference ellipsoid also serves as the reference surface for map projection,
where the reference ellipsoid is used to represent the Earth when discussing the
correlations between two mathematically defined surfaces.
To study global geodetic problems, there needs to be a reference ellipsoid that
best fits the geoid throughout the entire Earth, that is, a general Earth ellipsoid. Its
center must coincide with the center of the Earth. If the study is conducted both
geometrically and physically, then the general Earth ellipsoid can be defined as the
normal ellipsoid that best represents the shape of the geoid.
The normal ellipsoid is the reference surface for studying the Earth's gravity
field in physical geodesy. The reference ellipsoid, on the other hand, is the reference
surface for studying geodetic computations in geometric geodesy. Practically, due
to the same mathematical properties between the normal ellipsoid and the reference
ellipsoid, the normal ellipsoid can be used as both the physical and mathematical
reference surface in geodesy.
Modern geodesy has realized the geocentric orientation of the reference ellipsoid
and has made the reference ellipsoid correspond to the normal ellipsoid. The
orientation of the reference ellipsoid established by the classical geodetic tech-
niques can only approximate the geoid of its home country or region, not the
geocentric orientation. Therefore, the reference ellipsoid and normal ellipsoid
were initially two different concepts.