Modeling Relative Position Relative Velocity and Range Rate for Formation Flying

The relative position, relative velocity, and range rate evolution is examined for various formations of satellites. A simple analytical model including Earth oblateness effects for the equations of relative motion is presented. This model provides physical insight into the Earth oblateness effects that are neglected by using Hill's equations. The accuracy of the relative position, relative velocity, and range rate predictions for the analytical model are compared to realistic force modeling obtained using the Draper Semianalytical Satellite Theory for Formations of varying size, inclination, and altitude.