[1] Most satellite-based in situ plasma experiments are affected in some manner by the electrostatic structure surrounding the spacecraft. In order to better understand this structure, we have developed a fully three-dimensional self-consistent model that can accept realistic spacecraft geometry, including both thin ($10 À4 m) wires and long ($10 2 m) booms, with open boundary conditions. The model uses an integral formulation incorporating boundary element, multigrid and fast multipole methods to overcome problems associated with the large range in scale sizes and inherently three-dimensional structure. By applying the model to the Cluster spacecraft, we show that the electric potential structure is dominated by the charge on the wire booms, with the spacecraft body contributing at small distances. Consequently, the potential near the EFW (Electric Fields and Waves experiment) probes at the end of the wire booms is typically significantly above the true plasma potential. For the Cluster spacecraft, we show that this effect causes a 19% underestimation of the spacecraft potential and 13% underestimation of the ambient electric field. We further assess the electric field due to the sunward-oriented photoelectron cloud, showing that the cloud contributes little to the observed spurious sunward field in the EFW data.Citation: Cully, C. M., R. E. Ergun, and A. I. Eriksson (2007), Electrostatic structure around spacecraft in tenuous plasmas,