The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 144

fifth of the total mass of the Earth, this irregularity is very small. As a consequence,
the geoid closely approximates a regular figure in general. Geodetic observations
since the eighteenth century have demonstrated that this regular shape is an oblate
ellipsoid of rotation with a bulge at the equator and flattening at the North and South
Poles.
A rotational ellipsoid is a geometric figure obtained by rotating an ellipse around
its minor axis. Figure 4.8 is an ellipsoid centered at the origin O rotating around its
NS axis.
In geodesy, the ellipsoid of rotation that represents the Earth's shape and size is
referred to as the Earth ellipsoid, shortened to ellipsoid. The Earth ellipsoid is
specified by four parameters: the semimajor axis a and flattening f that represent
geometric properties of the Earth; the total mass M of the ellipsoid, which repre-
sents the physical properties of the Earth; and the angular velocity

ω of the ellipsoid

rotating around its minor axis.
Before the 1950s, the geometric parameters of the Earth ellipsoid a and f were
computed using data from astronomical, geodetic, and gravimetric observations in
particular regions. Results were of low precision and could only represent the
geometric figure of some particular regions on the Earth. Since the 1960s, the
four geometric and physical parameters of the Earth ellipsoid have been calculated
using data from global terrestrial geodetic measurements and satellite geodetic
surveys with an increase in precision of two orders of magnitude compared with
that prior to the 1950s. One case in point is Ellipsoid GRS80 (Moritz 2000); the
difference of a is less than 2 m and the relative mean squared errors of f and GM are

10 7 , respectively (G is gravitational constant, M is total
mass of the Earth). Table 4.1 gives the ellipsoid parameters used in China. The
Beijing Geodetic Coordinate System 1954 adopted the Krassowski Ellipsoid, the
Xi'an Geodetic Coordinate System 1980 adopted the Ellipsoid GRS 75, and the
China Geodetic Coordinate System 2000 (CGCS2000) basically adopted the Ellip-
soid GRS80 (GM value of the Ellipsoid GRS80 is defined more precisely). The
parameters adopted by the two international geodetic coordinate systems WGS84
(World Geodetic System 1984) and the ITRF (International Terrestrial Reference
Frame; see Chap. 7 ) are the WGS84 Ellipsoid and the GRS 80 Ellipsoid,
respectively.
On the Earth ellipsoid, the plane that contains the rotation axis (minor axis) of
the reference ellipsoid is called the geodetic meridian plane. The geodetic meridian
is the intersection of the plane containing the rotation axis with the surface of the
ellipsoid. The plane through the center of the ellipsoid and perpendicular to the axis
of rotation is the Earth's equatorial plane. The equator is the intersection of the
equatorial plane with the ellipsoid. A parallel circle (parallel line) is an intersection
of the plane parallel to the equator with the ellipsoid, also termed circle of latitude.
The northernmost point N of the spin axis on the Earth is the North Pole, lying
diametrically opposite the South Pole, S.
The Earth's gravity field and its level surface become rather complex given the
irregular shape of the Earth and the uneven distribution of mass. To facilitate the
study of gravity and the gravity field, the Earth ellipsoid is introduced, which is

10 6 and 3 2