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. Model calculations for density and kinetic temperature at points along the earth-sun axis (solar and antisolar directions) reveal an extensive satellite component, comprising ~ (2)/(3) of the total hydrogen density near 10 earth radii, and a temperature profile suggestive of an isotropic quasi Maxwellian velocity distribution for the bound component. A geotail is also evident as an enhancement of the density at local midnight compared to local noon that increases outward (from ~25% at 10 earth radii to over 60% at 20 earth radii). Additional mechanisms acting upon the geocorona alter the basic evaporative case in notable ways. Solar ionization has been included in a simple fashion; the effect is to partially deplete the density 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.