Central configurations of four gravitational masses with an axis of symmetry

Daniel Lazard (1)

1 SPACES - Solving problems through algebraic computation and efficient software

A central configuration of n masses under gravitational potential is a configuration such that all accelerations are oriented toward the center of masses and are proportional to the distance to this center. It follows that the plane central configurations are those that remain homothetic to themselves, with convenient initial velocities. For three masses these configurations are well known as those of Lagrange. A well known conjecture is that the number of central configurations of n bodies is always finite when the masses are fixed. In this talk, we describe the number of central configurations of four masses in the plane, which have an axis of symmetry. In this case symmetric masses are equal. In the case where none of the masses are on the axis (trapezoidal configuration), it is rather easy to show that for any value of the two masses, there is exactly one central configuration.

Mots clés: real solutions; configuration centrale; central configurations; celestial mechanics; polynomial system; mécanique céleste; systeme polynomial; paramètres; solutions réelles

Domaines: Autre [cs.OH]

Daniel Lazard. Central configurations of four gravitational masses with an axis of symmetry. 8th International Conference on Applications of Computer Algebra - ACA 2002, 2002, Volos, Grèce. ⟨inria-00107621⟩