  The famous three-body problem can be traced back to Newton in 1687, but quite
few families of periodic orbits were found in 300 years thereafter. In this
paper, we propose an effective approach and roadmap to numerically gain planar
periodic orbits of three-body systems with arbitrary masses by means of machine
learning based on an artificial neural network (ANN) model. Given any a known
periodic orbit as a starting point, this approach can provide more and more
periodic orbits (of the same family name) with variable masses, while the mass
domain having periodic orbits becomes larger and larger, and the ANN model
becomes wiser and wiser. Finally we have an ANN model trained by means of all
obtained periodic orbits of the same family, which provides a convenient way to
give accurate enough predictions of periodic orbits with arbitrary masses for
physicists and astronomers. It suggests that the high-performance computer and
artificial intelligence (including machine learning) should be the key to gain
periodic orbits of the famous three-body problem.
