The classical problem of three bodies with variable masses is considered in the case when the masses of all three bodies vary isotropically. Solutions to the equation of motion in terms of the...

The three body problem with variable masses with two of the bodies being protoplanets is analyzed. The protoplanetary masses are assumed to be much less than the protosolar mass: m1( t) ≪ m0( t), m2(...

The classical restricted three-body problem for bodies with variable masses is discussed for the case when the masses of two bodies vary isotropically at different rates and their sum varies according to the joint Meshchersky law. Within the perturbation theory in Hills’s approximation, differential equations determining the secular perturbations of the orbital elements are obtained and it is shown that they are integrable under arbitrary laws governing the mass variations satisfying the joint Meshchersky law. The influence of the variations of the body masses on the evolution of the orbital parameters is comparable with the perturbations created by massive bodies. All symbolic computations are performed in Wolfram Mathematica.