use a frame centered on or on to analyse the dynamics of . Consider a frame centered on . The gravity of is denoted as and will be treated as a perturbation to the dynamics of due to the gravity of body . Due to their gravitational interactions, point is attracted to point with acceleration , this frame is therefore non-inertial. To quantify the effects of the perturbations in this frame, one should consider the ratio of the perturbations to the main body gravity i.e. . The perturbation is also known as the tidal forces due to body . It is possible to construct the perturbation ratio for the frame centered on by interchanging . As gets close to , and , and vice versa. The frame to choose is the one that has the smallest perturbation ratio. The surface for which separates the two regions of influence. In general this region is rather complicated but in the case that one mass dominates the other, say , it is possible to approximate the separating surface. In such a case this surface must be close to the mass , denote as the distance from to the separating surface. The distance to the sphere of influence must thus satisfy and so is the radius of the sphere of influence of body See also Hill sphere Sphere of influence (black hole) References General references External links Project Pluto Astrodynamics Orbits