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– When alpha > 0, the minimum energy configuration is obtained when the dumbell lies parallel to the z-axis (theta = 0).
– When alpha < 0, the minimum energy configuration is the one where the dumbell lies perpendicular to the z-axis (alpha = 90).
– When alpha = 0, there is no quadrupole term in the gravitational potential energy expansion, so the energy of the dumbell will be independent of theta and only depend on the monopole energy.
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