next up previous contents
Next: Dynamic height and dynamic Up: Geostatics and Dynamics: The Previous: Changes in the reference

Geometrical spacing of the equigeopotential surfaces in the sea and the air

In order to accurately express the configuration of the equigeopotential surfaces in the sea and air relative to the sea level geoid we can make use of Eqs. (66) and (26):

or

The value is 0.00259 as deduced from pendulum measurements; has the value cm for the sea; and has the value 980.62 cm/sec . The variable z is vertical distance measured upward along the plumbline from the sea level geoid reference.

Eq. (91) applies accurately to the gross distribution of throughout the practical limits of the sea and atmosphere. At very great distances away from the earth's surface (say, greater than 100 km) Eq. (91) is not accurate since Eq. (26), upon which Eq. (91) is based, no longer accurately describes the variation of g with elevation. For great positive values of z the development given in Article 2.07 corrected for the effect of the variation of with latitude must be used.

The elevation of a particular equigeopotential surface in the sea or atmosphere can be evaluated from Eq. (91). If the binomial expansion is employed in evaluating the quadratic roots and second order terms neglected, we find

This holds within the practical limits of the sea and atmosphere as does Eq. (91).


next up previous contents
Next: Dynamic height and dynamic Up: Geostatics and Dynamics: The Previous: Changes in the reference

Steve Baum
Mon Dec 1 08:50:29 CST 1997