The theory of planetary exospheres is extended to incorporate solar radiation pressure in a rigorous manner, and an evaporative geocoronal prototype (classical, motionless exobase) is constructed using Liouville's theorem. Calculations for density and kinetic temperature at points along the Earth-Sun axis (solar and anti-solar directions) reveal an extensive satellite component, comprising (TURN)2/3 of the total hydrogen density near 10 Earth radii, and a temperature profile suggestive of a near-isotropic quasi-Maxwellian kinetic distribution for the bound component. A geotail is also evident in this model as an enhancement of the local midnight density compared to local noon that increases radially outward from roughly 25% at 10 Earth radii to over 60% at 20 Earth radii. Additional mechanisms acting upon the geocorona alter this evaporative case in notable ways. Solar ionization has been included in a simple fashion; the effect is to deplete the density somewhat without otherwise altering the structure. Interaction with a simple plasmasphere via the Boltzmann equation results in heating the geocorona and enhancing the escape flux at the expense of the density of the bound component, an effect not appreciated in earlier studies; the geotail survives this interaction.