On the absence of the generating function and its implications for the convergence region of the interior spherical Bessel gravity field

Abstract It is a well known fact that the conventional exterior gravity field only converges outside the Brillouin (circumscribing) sphere. The counterpart of this gravity model is the interior spherical Bessel gravity field that converges within the Bril-louin sphere. These two gravity fields allow for global modeling of the gravity by alternating at the Brillouin sphere. The divergence of the exterior gravity field within the Brillouin sphere is understood by expanding the potential definition with the generating function for the Legendre polynomial. We note that there is no equivalent expression with the generating function that leads us to the interior spherical Bessel harmonics. We believe that the lack of the generating function for the interior spherical Bessel gravity field, which confers the convergence region of the gravity model, can be leveraged to our advantage. We show that the convergence region of the interior spherical Bessel harmonics can be arbitrarily made larger than the physical Brillouin radius, thereby increasing the convergence region beyond the Brillouin sphere. This allows us to avoid alternating between the two gravity models and simply use the interior spherical Bessel gravity field at all times for global gravity modeling.