Abstract
In our previous works, we described the projections that make it possible to construct maps of the celestial bodies in planetary scale – the azimuthal and cylindrical projections of different distortion classes. However, for regions in the middle latitudes, it is advisable to use a conic projection, which has not been developed previously. 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. The quasi-conformal conic projection is a projection close to the conformal projection in the neighbourhood of each meridian corresponding to a meridian section. We treat conic projections as projections in which the meridians are a bundle of straight lines emanating from a single point, and parallels are curves constructed in accordance with the selected character of distortion. This definition of conic projections of the triaxial ellipsoid allows us to connect various classes of projections in a system. Thus, cylindrical projections can be considered as a limiting case of conic projections, and azimuthal projections as a special case. For the triaxial ellipsoid as a surface that can be projected on a plane without distortions, we use a direct elliptic cone tangent to the 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
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
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