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Notes
- 1.
The total angular momentum has both structural and orbital contributions.
- 2.
For a satellite at equilibrium, the ratio of the energy stored in structural rotation to that due to orbital motion scales as \(I\omega _E^2/m''\omega _E^2R_E^2 = a''^2/R_E^2 \ll 1\). Thus, we expect that changes in these energies, due to perturbations, will also scale similarly.
- 3.
We note that except for Lai et al. (1993), other researchers when considering the stability of Roche ellipsoids ignore their orbital stability. This is perfectly adequate for ellipsoids with dimensions smaller than the sizes of their orbit and parent planet.
- 4.
This indicates that the result was obtained from a spectral stability analysis; cf. Sect. 7.2.
- 5.
The polytropic index \(n=0\) corresponds to incompressible fluids.
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Sharma, I. (2017). Satellites. In: Shapes and Dynamics of Granular Minor Planets. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-40490-5_9
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