A family of retrograde orbits around the triangular equilibrium points

A new family of periodic orbits in the restricted problem of three bodies is described. This family is based on periodic orbits found by F. R. Moulton in 1920 which are examined in view of the controversies regarding their existence. It is shown by numerical integration that these retrograde orbits, of large amplitude en- closing one or the other of the triangular libration points, indeed exist, and that Moulton's originally estab- lished initial conditions require only slight modifications in order to satisfy the conditions of periodicity. Using Moulton's improved orbits a complete family is developed, terminated by two asymptotic-periodic orbits. These limiting orbits which show symmetry only to the axis perpendicular to the axis of syzygies and which spiral into the triangular liberation points, were approximately established by E. in 1930. Their initimate relation to the family of orbits being presented for the first time in this paper was conjectured in 1965.