on the evolution of the ‘f ’ family in the restricted three-body problem

poincaré surface of section technique is used to study the evolution of a family ῾f᾿ of simply symmetric retrograde periodic orbits around the smaller primary in the framework of restricted three-body problem for a number of systems, actual and hypothetical, with mass ratio varying from 10⁻⁷ to 0.015. it is found that as the mass ratio decreases the region of phase space containing the two separatrices shrinks in size and moves closer to the smaller primary. also the corresponding value of jacobi constant tends towards 3.