On some necessary conditions for double pyramidal central configurations with concave heptagon for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with concave heptagon base for nine-body problems is proved in this paper, and the range of the ratio σ of the circularity radius of the heptagon to the half-height of the double pyramidal central configuration involved in this class configurations is obtained, which is in the interval ( 3 /3,1.099 600 679) , and the configuration involved in the bodies with any σ ∈ ( 3 /3, 1.099 600 679) can form a central configuration which is a uniquely central configuration is proved.
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