A limit of nonplanar 5-body central configurations is nonplanar
Moeckel (1990), Moeckel and Simó (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur with 5 bodies. Question 17 in the list Albouy & al (2012) is thus answered negatively.
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