Pioneer 10 Lyman-alpha data obtained beyond the heliocentric distance of 30 AU are used here to determine the local ISM hydrogen density and downwind Galactic glow. The resulting asymptotic interstellar hydrogen density obtained using a conventional interplanetary model is 0.06/cu cm, and the Galactic Lyman-alpha glow is found to be negligible in the downwind direction. Discrepancies are found between observations and the conventional theoretical predictions of the glow dependence on radial distance. Based solely on data obtained between 30 and 39 AU, a better fit is obtained with a constant density distribution beyond 30 AU. In this case, a density of 0.05/cu cm and Galactic glow of 1.5 R is obtained. These results suggest that a complex density distribution may be more appropriate than either the conventional exponential distribution or the constant distribution. 43 references.