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the measurement of long distances on the scale of continents and
oceans, a more exact figure and closer approximation is necessary.
The first approximation to shape of the Earth is Geoid, the
theoretical shape of the Earth. Imagine that the entire Earth’s surface

is covered by water. If we ignore tidal and current effects on this
‘global ocean’, the resultant water surface is affected only by gravity.
This has an effect on the shape of this surface because the direction of

gravity, more commonly known as plumb line, is dependent on the
mass distribution inside the Earth. Due to irregularities or mass
anomalies in this distribution the 'global ocean' results in an undulated
surface. This surface is called the Geoid. The plumb line through any

surface point is always perpendicular to it. It is therefore a natural
reference for heights – measured along the plumb line. At the same
time, the geoid is the most graphical representation of the Earth’s

gravity field.

Figure 2.3. The Geoid and Ellipsoid Depiction.

The geoid surface is described by geoid heights that refer to a
suitable Earth reference ellipsoid. Geoid heights are relatively small.

The minimum of some – 106 meter is located at the Indian Ocean. The
maximum geoid height is about 85 meter. The geoid is very irregular
and the magnitude of geoidal deformations depend on the variation in
the strength of the magnetic field, and on geologic history.

A rotational ellipsoid is another mathematical approximation to
the earth's shape. It is an imaginary, regular and smooth mathematical
surface over which computation of coordinates becomes very easy. An

ellipsoidal surface can be further approximated by a sphere. An
ellipsoid is a smooth elliptical model of the Earth’s surface. GRS80

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