Further analysis of the region of permissible motion in the problem of three bodies

In this paper we investigate the range of variation of the orbital inclination I between two bodies in the problem of three bodies. We give the conditions to determine whether the two bodies move in the same or opposite senses and give the maximum and minimum values of I when the three bodies are in collinear positions. We prove that the range of variation of I must attain maximum and minimum values when the bodies are collinear.