Theoretical studies are made on the free oscillation of a homogeneous self-gravitating elastic sphere. Numerical results for torsional and spheroidal oscillations are shown in Tables 1 and 3, respectively. In these tables, are shown also the free periods of a model moon, for which density ρ = 3.33 g/cm and shear wave velocity V8 = 4.7 km/sec. For the model moon, the effect of gravity on the periods of oscillations is shown to be negligible. From Table 3, we can make an estimation of the effect of curvature on the phase velocity dispersion.
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Takeuchi et al. (1961) studied this question.
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