In this paper we investigated the translational-rotational motion of a triaxial body of constant dynamic shape and variable mass and size in a non-stationary Newtonian central gravitational field. Differential equations of the translationalrotational motion of the triaxial non-stationary body in the relative coordinate system with the origin at the center of a non-stationary spherical body are derived. The axes of the own coordinate system of the non-stationary triaxial body are directed along the principle axes of inertia of the body and we assumed that in the course of evolution their relative orientation remains unchanged. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is given. In the presence of reactive forces and moments the equations of translational-rotational motion of a triaxial non-stationary body in osculating elements are obtained in the presence of reactive forces and moments.