  The three-body problem has been studied for more than three centuries [1,2],
and has received much attention in recent years [3-5]. It shows complex
dynamical phenomena due to the mutual gravitational interaction of the three
bodies. Triple systems are common in astronomy, but all observed periodic
triple systems are hierarchical up till now [6-8]. It is traditionally believed
that bound non-hierarchical triple systems are almost unstable and disintegrate
into a stable binary system and a single star [5], and thus stable periodic
orbits of non-hierarchical triple systems are rather scarce. Here we report one
family of 13315 stable periodic orbits of the non-hierarchical triple system
with unequal mass. Compared with the narrow mass region (only 10E-5) of the
stable figure-eight solution [9], our newly-found stable periodic orbits can
have fairly large mass region. It is found that many of these newly-found
stable periodic orbits have the mass ratios close to those of the hierarchical
triple systems that have been measured by the astronomical observation. It
implies that these stable periodic orbits of the non-hierarchical triple system
with distinctly unequal masses can be quite possibly observed in practice. Our
investigation also suggests that there should exist an infinite number of
stable periodic orbits of non-hierarchical triple systems with distinctly
unequal masses. Obviously, these stable periodic orbits of the non-hierarchical
unequal-mass triple system have broad impact for the astrophysical scenario:
they could inspire the theoretical and observational study of the
non-hierarchical triple system, the formation of triple stars [6], the
gravitational waves pattern [10] and the gravitational waves observation [11]
of the non-hierarchical triple system.
