why is there no spherical solution to the direct geodesy problem? There is!

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I assume 'we' have at least tickled your curiosity w our responses, any alibi's (just curious)? I have one final & hopefully definitive reference from SPON Press

PLANE AND GEODETIC SURVEYING, SECOND EDITION
Aylmer Johnson
CRC Press
© 2014 by Taylor & Francis Group, LLC

8 Geoids, Ellipsoids and Co-ordinate Transforms 101
8.1 Definition of the Geoid 101
8.2 The Need for an Ellipsoid 102
8.3 Orthometric Heights and Bench Marks 106
8.4 Geometry of the Ellipse 108
8.4.1 Defining the Shape of an Ellipse 108
8.4.2 Curvature on an Ellipse 110
8.5 Transformations between Ellipsoids 112
8.5.1 Using a Transform Matrix 112
8.5.2 Making a Transform Matrix 117
8.6 ETRS89 and the International Terrestrial Reference System 118
8.7 Further Properties of Ellipsoids 119
8.7.1 Curvature on an Ellipsoid 119
8.7.1.1 Principal Curvatures 119
8.7.1.2 Curvature in Other Directions 122
8.7.1.3 Average Curvature at a Point 124
8.7.1.4 Mean Curvature of an Ellipsoid 125
8.7.2 Geodesics 125
&
10 Reduction of Distance Measurements 155
10.1 Correction for the Curvature of the Ellipsoid 155
10.2 Correction for Light Curvature 158
10.3 Corrections to Slope Distance Measurements 163
10.4 Final Calculation of Reduced Distance 165
10.5 Slope Distances 167
10.6 Summary 169
&
Appendix C: Worked Example in Transforming between Ellipsoids 211

ALL as apropos

BEST!
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