Methods for solving the system of nonlinear oscillation equations that determine the gravitational constant

Methods for solving a system of nonlinear oscillation equations are discussed. The perspective for functional enhancement of existing methods for determining the gravitational constant, $G$, at an aspheric configuration of interacting bodies was demonstrated. A paper that was presented in $DAN SSSR$, 245, N3 (1979) is analyzed. The dependence of the $G$ value on the position of attracting masses may be explained by the paramagnetic effect. Its mass point imitation, which defines its value and position, resulted in the standard $G$ value.