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We examine a series of closely related, relatively inert, cyclic aliphatic solutescyclohexane, methylcyclohexane, 1,1-dimethylcyclohexane, 1,4-trans-dimethylcyclohexane, 1,4-cis-dimethylcyclohexane, trans-decalin, and cis-decalinin a nematic solvent and demonstrate that their orientational ordering can be accurately described in terms of purely hard-body interactions with the solvent molecules. These interactions are treated explicitly in the context of a statistical mechanical approximation wherein the orientational correlations among the solvent molecules are not taken into account directly. We test the theory by predicting the observed order parameters of the aliphatic solutes as determined with deuterium nuclear magnetic resonance. The utility and limitations of a description of solute ordering derived exclusively from hard-body interactions is discussed.