A Limit of Nonplanar 5-Body Central Configurations is Nonplanar

Moeckel (Math Z 205:499-517, 1990), Moeckel and Simó (SIAM J Math Anal 26:978-998, 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 et al. in Celest Mech Dyn Astr 113:369-375, 2012) is thus answered negatively.