Abstract
This article concerns the N-body problem on the existence of non-collinear planar central configurations with three masses on a line. For the case N = 4, the nonexistence can be easily proved with the Perpendicular Bisector Theorem, and thus we study the case N = 5. We prove that with the presence of axial symmetry, such central configurations could exist only in certain shapes. We also give an upper bound for the number of such configurations for any choice of masses.