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Non-convergence of the spherical harmonic expansion of gravitational potential below the Brillouin sphere: The continuous case
C. Ogle, O. Costin, M. Bevis
Source abstract
For a singleton planet, P, with gravitational potential, V, we show that for each ɛ > 0, there exists a planet P′ with gravitational potential V′, with (P′, V′) “ɛ-close” to (P, V) (in an appropriate C0-sense), for which the spherical harmonic expansion of V′ does not extend more than a distance ɛ below the Brillouin sphere of P′.
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