Approximate solution of two-body problem using weighted combination of linear and inversely cubic gravity models

An approximate solution of two-body problem is proposed using weighted combination of linear and inversely cubic gravity models. First, two approximations are introduced for the weight coefficients. To enhance the accuracy of the solution, a modified weight coefficient is suggested by a linear combination of the two primary weight coefficients. The accuracy and computational burden of the combined method are compared to those of power series solution, including the Lagrangian coefficients and the recursive formulation introduced by Turner et al. The comparison is made with the same computational burden by setting an appropriate number of terms of power series solution. The advantage among the methods depends on the computational burden of square, trigonometric, and logarithmic functions. In the case that the computational burden of these functions is less than 10 floating point operations, the proposed method has the potential to give a better accuracy, especially for a specific application.