The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 161

Fig. 4.13 Grids based on
longitude and latitude lines

Normal height is needed in topographic mapping and engineering construction.
Traditional leveling is labor-consuming and inefficient, whereas GPS leveling can
provide the ellipsoidal height. The grid model of height anomaly should be known
while using GPS measurements to replace leveling, and then the ellipsoidal height
can be converted into the normal height. At present, leveling has gradually been
replaced by GPS measurements in height connection surveys for aerial photogra-
phy, project completion surveys, pipeline surveys, etc. Therefore, the establishment
and refinement of the grid model of height anomalies have obvious economic
benefits.
The grid model of geoid height is established in the same way as that of the
height anomaly.

Review and Study Questions

1. Derive the formula for the gravitation of a body of mass.
2. What is the potential function of force?

fm
r and write
down the integral formula for the gravitational potential of the Earth.
4. Prove that the centrifugal potential is Q

3. Prove that the gravitational potential of a mass point is V x;y;z

Þ ¼ ð

2

¼ ω x 2 y 2 .

5. What is harmonic function? Write down the general form of the gravitational
potential of the Earth.
6. Explain the physical meaning of zero and first-degree terms of the gravitational
potential coefficient.
7. What roles do level surface and plumb line play in field survey?
8. What is the geoid and its role in geodetic survey?
9. Explain the concepts of normal ellipsoid, normal gravity, spheropotential
surface, and gravity anomaly.
10. Explain the reason for the existence of the theoretical misclosure of leveling
loops.
11. Explain with formulae the concepts of orthometric heights and normal heights.

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