(b) Refer to Table 1-2, and note that equations (1), (2), and (3) use the gravimetric method to

obtain the components of the deflection of the vertical (ξ and η). If the astronomical coordinates and

azimuth have been observed, the geodetic coordinates can be computed. The largest computed

difference in position between astronomic and geodetic observations is approximately 1,000 feet. The

average difference between the computed positions is somewhere in the neighborhood of 300 feet.

These differences in position look very small. However, we are looking for a precise position;

consequently, the geodesist must indicate the exact pinpoint position, not an approximation. This is

especially critical at the initial point of any weapons system since any deviation will influence the final

location of the impact area.

(c) The Laplace equation (5) in Table 1-2 is important because it gives the relationship

between the azimuth and longitude differences without knowing the components of the deflection of the

vertical. In survey networks this fundamental relationship is used as a check to determine the accuracy

of the observed geodetic and astronomic data.

(d) The astro-geodetic deflections of the vertical are only relative since the deflections of the

vertical are computed with respect to a specific ellipsoid. If the ellipsoid is changed, the deflections of

the vertical also change (Figure 1-17). It is necessary to assume a specific orientation of the reference

ellipsoid with respect to the geoid before computing the astro-geodetic deflections. This orientation is

fixed by the initial values of the datum point from which the geodetic coordinates were computed. Any

change in these initial values, therefore, changes the deflection of the vertical at each point.

Consequently, the astro-geodetic deflections of the vertical have the same restrictions as the geodetic

positions. They are related to the geodetic datum.