Conic projections of the triaxial ellipsoid: the projections for regional mapping of celestial bodies

Maxim V Nyrtsov,Maria E Fleis,Michael M Borisov,Philip J Stooke

doi:10.5194/ica-proc-1-84-2018

Abstract

Abstract. Different distortion classes of the azimuthal and cylindrical projections of the triaxial ellipsoid have been considered in our previous works. These projections make it possible to construct maps of the celestial bodies in planetary scale. However, for regions in the middle latitudes it is advisable to use a conic projection which was not developed until now. In this investigation we describe the development of three conic projections of a triaxial ellipsoid: a conic projection with true scale along meridians, an equal-area conic projection and a quasi-conformal conic projection. In derivation of the projections we use an elliptical cone tangent to a triaxial ellipsoid. The projections are calculated and maps in these projections are created for the first time.

Highlights

Nowadays we have examples of regional mapping of celestial bodies in conic projections
Maps in this atlas were compiled in the Lambert conformal conic projection for the sphere despite the fact that the shape of asteroid is approximated by a triaxial ellipsoid
− conic projection with true scale along meridians; − equal-area conic projection; − quasi-conformal conic projection close to the conformal projection in the neighborhood of each meridian corresponding to meridian section which we call the projection of the meridian section

Summary

Introduction

Nowadays we have examples of regional mapping of celestial bodies in conic projections. Maps in this atlas were compiled in the Lambert conformal conic projection for the sphere despite the fact that the shape of asteroid is approximated by a triaxial ellipsoid. If the compression of shape of a celestial body is more than 40% the difference in the conic projections of sphere and ellipsoid will be significant and the reasonability of using of a triaxial ellipsoid is justified. Angles at the crossing points of meridians on the projection depend functionally on corresponding angles on the ellipsoid and of the cone parameters. This definition of conic projections allows us to connect the different classes of projections of a triaxial ellipsoid in a united system. − conic projection with true scale along meridians; − equal-area conic projection; − quasi-conformal conic projection close to the conformal projection in the neighborhood of each meridian corresponding to meridian section which we call the projection of the meridian section

Derivation of conic projections

Findings

Conclusion