The interaction of the solar wind with the very local interstellar medium depends strongly on charge exchange between the neutral and ionized hydrogen outside of the heliopause. While the protons are diverted by the heliosphere obstacle, the neutral atomic hydrogen sees no immediate change in environment and continues its free streaming. The ensuing difference in flow velocities results in resonant charge exchange that tends to divert the neutral flow around the heliosphere as well. Large mean free paths strictly require a kinetic approach, yet some idea of the interaction can be gleaned from a much less computationally complex fluid treatment. We show that the momentum- and energy-exchange operators between the charge and neutral fluids can be evaluated in a near-exact fashion for the charge-exchange cross section. This new formulation can be used both to provide a better fluid description and to test how robust the fluid picture is. ¿ 1999 American Geophysical Union