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We characterize the fate of the solutions of Hill's type lunar problem usingthe ideas of ground states from PDE. In particular, the relative equilibriumwill be defined as the ground state, which satisfies some crucial energeticvariational properties in our analysis. We study the dynamics of the solutionsbelow, at, and (slightly) above the ground state energy threshold.

Global existence and singularity of the Hill's type lunar problem with strong potential