The Galileo Ultravilet Spectrometer Experiment (UVS) obtained a partial celestial sphere map of interplanetary Lyman-alpha (IP L alpha) on 13-14 December 1990 during the first Earth encounter. The Galileo spacecraft was near the downwind axis of the local interstellar medium flow. These UVS measurements sampled the downwind, anti-sunward hemisphere. The data were modeled using a hot model of the interplanetary hydrogen density distribution with the goal of studying multiple scattering effects in the inner solar system. The derived ratio in the downwind direction of the observed brightness and a single scattering model brightness, both normalized to unity in the upwind direction, is 1.82 +/- 0.2. This brightness ratio requires a multiple scattering correction which is 36% larger than can be accounted for by theoretical calculations. The hot model may require: (1) a temperature perturbation of the interstellar wind velocity distribution or (2) an additional downstream source of interplanetary hydrogen. However, a more likely exlanation which affects the hot model is the latitude dependence of the radiation pressure. This dependence, based on the known solar L alpha flux latitude variation at solar maximum, causes a downwind brightness enhancement by preferential focusing of H-atoms with trajectory planes containing the solar poles. This result implies that radiation pressure near the solar poles is nearly independent of solar cycle and is insufficient to lead to a net repulsion of hydrogen atoms by the sun, as can occur near the ecliptic plane during the solar maximum. In addition, the UVS performed 13 observations of IP L alpha while in cruise between Venus and the Earth in 3 directions fixed in ecliptic coordinates.