Exploration of the molecular geometry in rotating powder solids on the basis of magnetization exchange between spins with identical isotropic chemical shifts but differing chemical shielding tensor orientations is demonstrated experimentally. For this we take advantage of the potential of the ODESSA (one-dimensional exchange spectroscopy by sidebands alternation) experiment for the accurate measurement of spin exchange rate constants. We also report the observation of oscillatory behavior of the rotor-driven magnetization exchange at this so-called n=0 rotational-resonance condition which, in contrast to n=1,2,3,... rotational-resonance conditions, takes place at nearly arbitrary magic-angle spinning frequencies. The sensitivity of the longitudinal exchange decays to the relevant physical parameters of the spin system under conditions of rotor-driven and proton-driven magnetization exchange is discussed theoretically and demonstrated experimentally. Several C-13 and P-31 spin-exchange measurements have been performed on a series of model compounds covering a broad range of internuclear distances between carboxyl carbon atoms, and on a series of phosphorylated amino acids with different internuclear distances between phosphorus sites. The capacity of the ODESSA experiment for an unambiguous recognition of distinct internuclear distances is demonstrated. Potential applications of such measurements involve the exploration of intermolecular distances and the determination of the mutual orientation of neighboring molecular fragments in polycrystalline and noncrystalline solids.