This project addresses the exosphere, the outermost fringe of the earth's atmosphere. A preliminary investigation of existing terrestrial exosphere models indicates that errors, in some cases in excess of 2, are likely to have accrued from the use of simplistic approximations of collision processes. The traditional concept of the exobase as a boundary between the thermosphere and a collisionless exosphere appears to have caused major discrepancies. Recent work by the Principal Investigator of this project on the quantum mechanics of H-H+ collisions shows that the common presumption that charge exchange in non- scattering process has led to artificially low abundances of H atoms with satellite velocities. With modern computers, many of the inaccuracies that have resulted from traditional exosphere approximations can be avoided. Works in progress to derive quantum mechanically correct methods for computer simulations of key neutral-ion and neutral-neutral collision process. These tasks are essential precursors to the accomplishment of the main objective of this project: the creation of realistic model exosphere distributions of atomic hydrogen and "hot" oxygen for equinox and solstice conditions over the solar cycle. The exosphere models to be addressed in this project are produced by computer simulation, using Monte Carlo methods that have been developing at UTD since 1973. In an exosphere simulation, the trajectories of a large set of test atoms are traced from their entry into the exosphere to their escape from the planet. Throughout the life of each atom, the computer accounts for kinetic and chemical effects of collisions with atoms, ions, and protons. Statistical data representing the life histories of the test atoms are converted into phenomenological hydrodynamic parameters in a process that is equivalent to Monte Carlo integration of moments of the Boltzmann equation.