Recently V-3s core level XPS of freshly evaporated vanadium clusters on graphite exhibited the appearance of a satellite structure; the spectrum was then interpreted by the effect of surface magnetic moments on vanadium. In this paper we extend a previous electronic structure model calculation to the case of vanadium adatoms upon graphite with the help of the Hartree-Fock approximation. The outcoming results are used to discuss the origin of the satellite structure in V-3s core level XPS for a V-adatom upon graphite.