The Langmuir plasma probe model is an important tool in spacecraft current collection and charging calculations. In ideal geometries, such as a sphere or an infinitely long cylinder, the model is well understood. However, the realistic geometries of current collectors, or spacecraft, are nonideal. An empirical formula for a Langmuir probe with a given nonideal geometry would be useful. We derive such a formula for the SCATHA satellite by using the SC10 potential data obtained during electron beam emissions. The satellite rotated perpendicular to sunlight with the SC10 booms in the equatorial plane. We choose one special mode of operation during a quiet space environment. In this mode the beam current increased continuously, while the energy remained constant. We analyzed the variations of the vehicle potential responding to the unique driving factor, the beam current. To provide physical explanation to the behavior of the SC10 potential data, we model the interactions between the beam, photoelectron, and ambient currents. We present an algorithm which successfully yields an empirical Langmuir probe formula for SCATHA, from which we obtain improved estimate of ambient electron temperatures and densities. The results predicted by the improved Langmuir probe model compare favorably with the very few published measurements from the region.