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This potential is commonly used to model fluid motions in celestial bodies. First, we demonstrate that the system admits only steady-state solutions of the form $\\left(\\rho,\\mathbf{V},p\\right)=\\left(\\rho_{0},\\mathbf{0},P_{0}\\right)$, where $P_0$ and $\\rho_0$ satisfy the hydrostatic balance condition $\\nabla P_{0}=-\\rho_{0}\\nabla f$. 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