Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 252

Example

The solutions of long-distance geodetic problems are vital and useful in navigation
and long-distance missile launching. We hereby provide the block diagram and
instance of computation for approximate solutions in meters. Likewise, we can also
program the block diagram for approximate solutions in hectometers and produce
precise solutions (precise solutions or approximate solutions in hectometers)
according to the formulae.

Block Diagram

The block diagram of computation for the solution of the direct geodetic problem is
shown in Fig. 5.48 .

Computations

A sample computation for the solution of the direct geodetic problem is provided in
Table 5.10 .

5.6.5 Computations of Bessel's Inverse Solution
of the Geodetic Problem

Steps for Solution

Project the Ellipsoidal Elements onto the Spherical Surface

1. Given B, find u
u can be obtained from:

e p tan B 1 1 tan u 1 ﾼ

e p tan B 2 1

: ð 5 : 102 Þ

tan u 2 ﾼ

2. Given l, find ʻ

In the inverse solution, given the longitude difference l on the ellipsoid, the
corresponding longitude difference ʻ on the spherical surface is still unknown.

To compute , m, and

M since all of them are involved in the reckoning of the correction terms. The
accuracy required is not high and generally approximations made twice will be
satisfactory.

ʻ given l, from ( 5.92 ), obviously we first need to calculate ˃