A new proof of a theorem of J. Moser concerning the restricted problem of three bodies

In a recent paper Barrar (1965)], we have shown that the result ofR. Arenstorf (1963) on the existence of periodic orbits of the second kind for the restricted problem of three bodies can be very readily obtained with the use of Delaunay or Poincaré variables. In the present paper we will show that the results ofJ. Moser (1953) can also be more readily obtained with the use of Poincaré variables.Moser, dealing with the restricted problem of three bodies, demonstrated the existence of periodic solutions that close after many revolutions and are near periodic solutions of the first kind.