Perturbation hollow spheres and planetary perturbation rings pursuant to the gravity assists scattering in the Solar system

Abstract

One of the types of gravitational scattering in the Solar system within the framework of the model of the circular restricted three-body problem (CR3BP) are the gravity assist maneuvers of the "particles of insignificant mass" (spacecraft, asteroids, comets, etc.). For their description, a physical analogy with the beam scattering of charged α-particles in a Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions for the possibility of gravity assists executing related from the restricted size of planet's sphere of influence. At the same time, internal restrictions for the gravity assists performance estimated by the effective radii of planets are known from the literature on CR3BP (including gravitational capture by the planet, falling into it). The limited dynamic possibilities of using gravity maneuvers require their repeated performance. Based on the formalization of the search for the GA- timetables with subsequent adaptive involvement of a large number of options, a high-precision algorithm for synthesizing chains of increasing gravity assists was built. Its use leads to a significant inclination change of the research SC's orbit without significant fuel consumption during a reasonable flight time. They depend from the particle asymptotic velocity relative the planet. For obvious reasons, their influence cuts off the possibility of effective gravity assists performance. In this work the generalized estimates of the sizes of the near-planetary regions (planar rotating "perturbation rings" or "perturbation hollow spheres" in 3D case), falling into which is a necessary condition for the implementation of gravity assists, are presented. The detailed analysis shows that Neptune and Saturn have the characteristic "perturbation rings" and the perturbation hollow spheres of the largest sizes in the Solar system, and Jupiter occupies only the fourth place in this checklist after them and the planet’ Uranus perturbation hollow sphere.