Uno sviluppo accurato della latitudine conforme in termini della latitudine geodetica

This paper puts forward an approximate expression of the conformal ellipsoidal latitude in terms of the corresponding geodetic latitude and of the even powers of the first eccentricity with coefficients trigonometric polynomial of the geodetic latitude. From the equality of two different developments of the isometric latitude, suitably cut off, it is first obtained - by successive approximations - the difference between the conformal latitude and the corresponding geodetic one, and finally the approximate expression of the conformal latitude. Because of the high degree of eccentricity powers (up to the 12th) and of the sine function of geodetic latitude (up to the 11th), the expression is extremely accurate, so it is possible to achieve an approximation in the order of a (double) precision eps with which the numerical data in “Floating Point” using electronic computers and various programming and computing languages are represented and processed. Numerical examples in order to verify the accuracy of the expression are reported. The approximation, that can be obtained with a lower computational cost compared to other expressions reported in geodetic and cartographic literature, and the specific form of this conformal latitude development are necessary for the application reported in a successive article, in order to implement a new calculating method of the Gaussian cartographic coordinates in wide time zone of longitude and with adequate accuracy.