An equation of oscillations for the arrangement of attracting solids on the equilibrium line of a balance with account for nonlinearity of up to the seventh power

The accuracy of calculating the gravitational constant, G , using a method based on the numerical integration of an equation of oscillations and a method based on the nonlinear oscillation theory is analyzed. Taking account of a higher (the seventh) power at an amplitude of 80 mrad reduces the error of calculating the moment of attraction forces by 47 times. This reduces the error of calculating G from 15 to 0.3 ppm.