a. If the shape of the earth was exactly that of an ellipsoid of revolution, the measurement of one

arc on the surface of the earth should give its dimensions. In practice, numerous arcs from different

areas of the earth are used to obtain a truer ellipsoid figure. As previously pointed out, astronomic

observations are referred to the geoid. This causes errors in arc measurements, which must be

eliminated by using gravity anomaly corrections and gravimetric computations. By mathematically

removing the effects of the deflection of the vertical at the ends of the measured arcs, a more refined and

truer ellipsoid can be determined.

b. Measurements can be solved to find both the size and the shape of the earth. Reductions are

often accomplished by the use of the flattening value obtained by some other method. This simplifies

the arc problem to one in which only the size of the earth is sought.

(1) The shape of the earth (not its size) can be obtained from gravity anomalies. Since the

theoretical gravity formula depends on the assumed flattening of the earth, gravity anomalies are used to

find the gravity formula which best satisfies certain assumptions about the structure of the earth's crust.

The flattening that corresponds to this corrected gravity formula can be found by working backwards.

(2) Artificial earth satellites can also provide a good means of measuring the flattening of the

earth. This method will assume greater importance as tracking techniques with special geodetic

satellites improve.

c. To determine the size and the shape of an ellipsoid for use in a WGS, many methods should be

used based on as large a group of observations as possible. Failure to do this would result in an ellipsoid

appropriate for a small area of the earth but not necessarily an adequate reference for the entire earth.

to a group of specific initial quantities that form a geodetic system or datum. Since the relationship

between geodetic positions remains true only so long as they are on the same geodetic datum. Positions

derived from different datums are not directly comparable in computations. Consequently, the desired

data, such as distance and direction, will be different. The difference will depend on the errors in the

initial quantities of the datums.

a. Since a datum can be defined as any numerical or geometrical quantity or set of such quantities,

a datum is a starting point. In geodesy, the following two datums must be considered: a horizontal

datum that forms the basis for the computations or horizontal control surveys in which curvature is

considered and a vertical datum to reference heights.