Earlier analyses of Lunar Prospector (LP) data found that the shadowed lunar surface charges negative. The potential difference between the surface and LP has unexplained dependences on solar zenith angle and tip angle. The dependence on tip angle may arise because electrons with pitch angles close to the loss cone angle on field lines with higher tip angles encounter a smaller average potential before reflecting (the technique used to infer potentials relies upon loss cone angle measurements). The correlation may therefore be due to a systematic measurement error. However, since this measurement error depends upon the ratio of gyroradius to double layer scale height, it allows us to estimate the scale height. By comparing data with the results of particle tracing simulations, we estimate an average nightside scale height of a few km. This is somewhat larger than the electron Debye length, but much smaller than recent theoretical estimates.