ИСТИНА

New method for solving the inverse geometric problem about reconstruction the form of a triaxial ellipsoid by its projection onto the picture plane (limb) is developed. The method is based on a rotation matrix with three special angles that are maximally adapted to restore the ellipsoidal shape for direct use of positional observations. The geometric properties of the limb are investigated and the theorem is proved: the area of the limb will be maximal (minimal) when the projection of the rotation axis of ellipsoid on the picture plane coincides with the small (large) axis of this limb. A system of eight equations is derived for finding the spatial shape of the dwarf planet Haumea, as well as the inclination of its ring and the orbits of the satellites. These equations take into account all information on the Haumea's photometry, its limb and ring. For each value of the photometric parameter, we calculated the shape and density of the ellipsoidal Haumea model, and its orientation with respect to the ring and satellite orbits. The limitations from below for elongation of the model, and from above on average density are received. With increasing the photometric parameter the model stronger deviates from the Jacobi ellipsoids. We found that the orbit of Hi’iaka as well as the Haumea’s ring does not coincide with the Haumea equator, and that both satellites have prograde motion. The most probable characteristics of the Haumea system are obtained and the results are compared with the studies of other researchers.