The two-body problem associated with a force field described by a potential of the form U = n k=1 a k /r k (r = distance between particles, a k = real parameters) is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in

more »

... 's coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure.