Motions of the perihelions of Neptune and Pluto

Five outer planets are numerically integrated over five million years in the Newtonian frame. The argument of Pluto's perihelion librates about 90 degrees with an amplitude of about 23 degrees. The period of the libration depends on the mass of Pluto: 4.0×10⁶ years forM_pluto=2.78×10^–6M_sun and 3.8×10⁶ years forM_pluto=7.69×10^–9M_sun, which is the newly determined mass. The motion of Neptune's perihelion is more sensitive to the mass of Pluto. ForM_pluto=7.69×10^–9M_sun, the perihelion of Neptune does circulate counter-clockwise and forM_pluto=2.78×10^–6M_sun, it does not circulate and the Neptune's eccentricity does not have a minimum. With the initial conditions which do not lie in the resonance region between Neptune and Pluto, a close approach between them takes place frequently and the orbit of Pluto becomes unstable and irregular.