  We numerically discovered around 100 distinct nonrelativistic collisionless
periodic three-body orbits in the Coulomb potential in vacuo, with vanishing
angular momentum, for equal-mass ions with equal absolute values of charges.
These orbits are classified according to their symmetry and topology, and a
linear relation is established between the periods, at equal energy, and the
topologies of orbits. Coulombic three-body orbits can be formed in ion traps,
such as the Paul, or the Penning one, where one can test the period vs topology
prediction.
