Plasma and field measurements on board magnetospheric spacecraft can be influenced by the spacecraft potential and emitted particles such as photoelectrons and secondary electrons. There exist contradictory requirements for, on one hand, minimizing the spacecraft potential and, on the other hand, minimizing perturbations in the sheath and contamination by spacecraft-generated electrons. Assessment and mitigation of such effects therefore require improved quantitative modeling of the spacecraft electrostatic sheath. In this paper a fully self-consistent model of the plasma around an electron-emitting central body in a spherically symmetric geometry is used to analyze the electrostatic sheath around an idealized magnetospheric spacecraft. Although the model is too simplistic to allow detailed comparisons with observations, it helps to analyze the phenomenon of potential barrier occurrence and some global characteristics, which can be relevant to conductive magnetospheric spacecraft like Geotail or Cluster. It is shown that nonmonotonic potential with negative potential barrier can exist all around a positively charged spacecraft even in the case of realistic illumination pattern. The magnitude of the potential barrier in regions of the magnetosphere with large Debye-length plasma is found to be as large as a few volts negative for small positive spacecraft potential but that it quickly vanishes when the potential is increased by a few volts. Furthermore, the location of the potential barrier is found to be much more variable than previously predicted.