THE NON-ITERATIVE SOLUTION OF THE DIRECT GEODETICPROBLEM ON MIDDLE AND LONG DISTANCES
: In this paper the practical formulae for solving the direct geodetic problem of both high accuracy (0.0001) and low accuracy (0.01) are derived. These formulae can al- most fit for any long distance, e.g. the half round of the earth. The Bessel's formula and those given in literature  have been extended up to eighth-order terms of e, and the iterative computation procedure has been eliminated by way of the reverse solution of trigonometric series. This paper also gives two small auxiliary tables applicable to these formulae, these tables are suitable for any reference ellipsoid. Finally a rigorous formula (accurate to seventh-order terms of s) is derived for the purpose of solving the direct geodetic problem of middle distance or low accuracy. Under these circumstanccs, many high order terms of that formula can be neglected, thus computation can easily be made.