Figures of Pluto and Charon and their relative motion

The comparative effect of two factors on the translatory motion of the centres of mass of the Pluto-Charon system is investigated. The first important factor is the non-sphericity of the shape and gravitational field of the bodies in the system. The second is the gravitation of the Sun. As a measure of the influence of both factors we use the ratio of the corresponding perturbing acceleration to the main one. The main acceleration is caused by the mutual Newtonian attraction of Pluto and Charon. It has been established that for the first factor this measure is of the order of $10^{-6}$, while for the second factor it is two orders of magnitude smaller. This explains why the Lidov-Kozai effect (despite a large mutual slope of $96^\circ$ between the planes of the satellite's orbit around the planet, and the barycentre of the system around the Sun) does not appear. The situation is similar to the case with the satellites of Uranus. As a result, the Pluto-Charon system remains stable at least on a timescale of millions of years. The tidal effect of the Sun on the surface shape of the bodies under study is also estimated. The ratio of the tidal potential of the Sun at a point on the surface of the body to the gravitational potential of the body itself at this point is taken as a measure of impact. It turned out to be of the order of $3 \cdot 10^{-12}$, which is more than six orders less than the influence of rotation and mutual attraction of Pluto and Charon. In fact, the Sun does not affect the figures of the bodies of the system.