The following study investigates the effects of radiation pressure on H-atoms in the earth's exosphere. The exosphere is regarded as collisionless, permitting the atoms to be treated as particles in orbit about the earth obeying the laws of celestial mechanics. Attention is restricted to a class of atoms called satellites, whose initial orbital parameters place them in Keplerian satellite orbits, as distinguished from captive atoms whose orbits intersect the exobase (ballistic particles) and those which escape on hyperbolic trajectories. The evolution of these satellite orbits under the perturbing force of radiation pressure is determined by numerically integrating the classical perturbation equations for the orbital elements. These equations express the rates of change of the standard orbital elements in terms of the other elements and the vector components of a perturbing force. Results are presented graphically and compared with analytical results from a paper by Chamberlain (1979).