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The discovery of the largest trans-neptunian object 2003 UB313 (dwarf planetEris) was made more than 5 years ago, but the question on the true relation ofthe sizes of Pluto and Eris (and according to of their densities) remainsdebatable in view of a sizable scatter of their size's estimates obtained bythe various methods. Here, we first used a semi-empirical approach to deducethe expression linking the orbital parameter eccentricity to the physicalproperties of the trans-neptunian dwarf planets and have applied it todetermining the mean size of these planets. In doing so is proved that the meanEris' size should be about 9 % larger than of Pluto's. Based on the publishedphotometric data and the derived mean diameter the possible estimates of theminimum and maximum diameters of Pluto and Eris on the assumption of adeviation their form from spherical are provided. The probable reason for anoccurrence of such an aspherical form of these dwarf planets is brieflydiscussed.

On the relation of the sizes of trans-neptunian dwarf planets Pluto and Eris