Perturbation Function

an auxiliary function in the theory of perturbations of celestial bodies. It depends on the coordinates of the given perturbed celestial body and on the coordinates and masses of the bodies attracting that body. The partial derivatives of the perturbation function with respect to the coordinates of the perturbed body are equal to the components of the acceleration imparted to the body in its relative motion about a central body as a result of the attraction of other celestial bodies. The concept of perturbation function was first introduced in 1776 by J. L. C. de Lagrange. In the series integration of the differential equations of the perturbed motion of celestial bodies, important problems are the expansion of the perturbation function in series, the investigation of the series’ convergence, and the estimation of the remainder terms.