The stationary Vlasov-Poisson system modeling the interactions between plasma and a satellite in a three-dimensional framework without reemission is studied. The case of a sphere and a general object shape in a Maxwellian plasma are considered. An analytical expression of the space charge is available in the first case under an approximation. The asymptotic behavior of the space charge and the electrostatic potential are studied. On the basis of this analysis, an optimal relaxation iterative algorithm is built for the solution of the Vlasov-Poisson model. In the second case the space charge in the whole space is computed using a stationary algorithm based on a Lagrangian method.