**CARTOGRAPHIC
PROJECTIONS FOR SMALL BODIES OF THE SOLAR SYSTEM**

Maria E. Fleis *(maria@geocnt.geonet.ru*), Michael M. Borisov *(bom@geocnt.geonet.ru)*,

Michael V. Alexandrovich (*m-indigo@yandex.ru*),

Philip Stooke (*philatwestern@hotmail.com*),

Kira B Shingareva (*Kira.Shingareva@mtu-net.ru*)

First, spherical or near-to-spherical models were used for celestial
bodies mapping. It was suitable for the Earth, the Moon, Mars and other large bodies.
Many small celestial bodies are of quite irregular shape, and their minimum and
maximum radii differ by more than ten per cent. Morphographic projection was
developed for mapping of such worlds. This projection transfers spatial data
directly from physical surface to the map plane and shows the bodie’s shape. A
different approach consists of using triaxial ellipsoid as a mathematical
surface for primary data transfer from physical surface. Different cartographic
projections were devised for this ellipsoid. Triaxial ellipsoid composed
projection, devised for the Phobos map, was later used with morphographic
projection for the Deimos map.

But some small bodies have essentially regular shape and unusual
revolution axis position provided by none of natural physical means. To all
appearance, this is the sequence of bodies’ formation randomness. Eros asteroid
has shape near to ellipsoid of revolution, but the proportion between major and
minor axes and ellipsoid revolution axis position differ from conventional
ones. Revolution axis of ellipsoid is perpendicular to revolution axis of body
and Eros could be considered as a triaxial ellipsoid with equal polar and
equatorial radii. But an attempt to use triaxial ellipsoid composed projection
for Eros map showed that the projection is not suitable for this celestial
body. The reason is that major axis is more than twice longer than minor one,
so eccentricity, conventionally used as small value in series, is closer to 1
than to zero. Composed projection of “upturned” ellipsoid of revolution
consising of transverse cylindrical conformal and transverse azimuthal
projections is proposed in the report. **The
formulae of new cylindrical conformal projection and new azimuthal projection
are devised for the case of matching ellipsoid revolution axis with major (not
minor, as usual) axis of ellipse. Formulae are obtained without approximations
and are true even for eccentrisity close to 1.** We intend to devise such
formulae for equal-area projections. Approximate formulae of equidistant projections need serious
revision. Since longitude and latitude for celestial bodies are used to be
defined in planetocentric coordinate system, it’s possible to transform datasets
from normal to transverse coordinate system using known formulae. Formulae of
obtained projections and an application for calculation of rectangular
coordinates of point sets will be published in Web.