Measurements of the magnetic field induced in the moon while the moon is in the earth's geomagnetic tail lobes have been used to estimate lunar interior magnetic permeability and electrical conductivity and, in particular, to determine constraints on the size of a possible lunar core. We show here that the core size estimates are negligibly affected by currents due to a directed plasma flux toward the moon. Specifically, a theory for the compression of an induced lunar dipole by an incoming sub-Alfv¿nic flus cold plasma is presented for the time independent case where the external magnetic field, induced dipole moment, and plasma velocity vector are all aligned. When the incoming flow travels at 83% of the Alfv¿n speed, the change in the global dipole moment is no more than 5%, while higher order moments increase from zero to 10% of the amplitude of the dipole. Consequently, at very long time periods, effects due to the inertia of an incoming flow of cold plasma can be ignored if care is taken to exclude periods of unusually high plasma density from the data base used for obtaining lunar magnetic permeability and core size estimates. Additionally, we show how a recently derived theory for time dependent fluctuations in a stationary plasma can be modified to include the effects of incoming plasma flux, and we discuss how this theory is related to the approximation that we have used.