A Formulation of the Clohessy-Wiltshire Equations toInclude Dynamic Atmospheric Drag

摘要

The widely known Clohessy-Wiltshire equations are used to represent the relative mo-tion of a chaser satellite about a target satellite about a point mass. These equations can often be limiting because they are derived assuming small deviations from a circular ref-erence orbit and no orbital perturbations. At lower altitudes, atmospheric perturbations become more predominant, specifically for vehicles of different ballistic coefficients. There-fore, incorporating these effects into the equations of relative motion can lead to more accurate mission planning, trajectory analysis, and controller/estimator performance. In this study the equations of relative motion are derived to include the in-plane effects of atmospheric drag of spacecraft in a moving atmosphere. However, this higher fidelity for-mulation still assumes a circular reference orbit, small deviations from the reference state, and no other sources of perturbations in order to produce a set of linear differential equa-tions. The resulting equations of perturbed relative motion are validated, under varied ballistic coefficients and altitudes, against the higher-fidelity non-linear equations of mo-tion. The results of this study demonstrate a significant increase irt the precision of these equations, specifically under the influence of larger ballistic coefficient differences at lower altitudes.