Protoplanetary three-body problem with variable masses and its solutions

Abstract

Two protoplanetary three-body problem is considered in the case when the masses of all three bodies vary isotropically in different rates . It is assumed that the mass of the protoplanets much less than the mass of the proto-Sun . Laws of change masses of bodies are known. The bodies are assumed as material points. On the basis of motion equations in the Jacobi coordinates the problem is described in the analogues of the Poincare second system. The perturbation function is symbolically computed in the system of the analytical calculations Mathematica up to the second degree of small quantities inclusive. It is obtained the equations of secular perturbations and its solutions for the protoplanetary three-body problem with masses changing isotropically in different rates.