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The Interball-2 spacecraft travels at altitudes extending up to 20 000 km, and becomes positively charged due to the low-plasma densities encountered and the photoemission on its sunlit surface. Therefore, a knowledge of the spacecraft potential <font face="Symbol"><b>F</b></font><sub>s</sub> is required for correcting accurately thermal ion measurements on Interball-2. The determination of <font face="Symbol"><b>F</b></font><sub>s</sub> is based on the balance of currents between escaping photoelectrons and incoming plasma electrons. A three-dimensional model of the potential structure surrounding Interball-2, including a realistic geometry and neglecting the space-charge densities, is used to find, through particle simulations, current-voltage relations of impacting plasma electrons I<sub>e</sub> (<font face="Symbol"><b>F</b></font><sub>s</sub> ) and escaping photoelectrons I<sub>ph</sub> (<font face="Symbol"><b>F</b></font><sub>s</sub> ). The inferred relations are compared to analytic relationships in order to quantify the effects of the spacecraft geometry, the ambient magnetic field <b><i>B<sub>0</sub></i></b> and the electron temperature T<sub>e</sub> . We found that the complex geometry has a weak effect on the inferred currents, while the presence of <b><i>B<sub>0</sub></i></b> tends to decrease their values. Providing that the photoemission saturation current density J<sub>ph0</sub> is known, a relation between <font face="Symbol"><b>F</b></font><sub>s</sub> and the plasma density N<sub>e </sub>can be derived by using the current balance. Since J<sub>ph0</sub> is critical to this process, simultaneous measurements of N<sub>e</sub> from Z-mode observations in the plasmapause, and data on the potential difference <font face="Symbol"><b>F</b></font><sub>s</sub> - <font face="Symbol"><b>F</b></font><sub>p</sub> between the spacecraft and an electric probe (p) are used in order to reverse the process. A value J<sub>ph0</sub> ~ = 32 µAm<sup>-2</sup> is estimated, close to laboratory tests, but less than typical measurements in space. Using this value, N<sub>e</sub> and <font face="Symbol"><b>F</b></font><sub>s</sub> can be derived systematically from electric field measurements without any additional calculation. These values are needed for correcting the distributions of low-energy ions measured by the Hyperboloid experiment on Interball-2. The effects of the potential structure on ion trajectories reaching Hyperboloid are discussed quantitatively in a companion paper.<br><br><b>Key words. </b>Space plasma physics (charged particle motion and acceleration; numerical simulation studies; spacecraft sheaths, wakes, charging)