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Rutherford’s extended formula and optimization of the gravity assists beam modelling in the Solar system

Rutherford’s formula for the scattering of charged α-particles in the Coulomb field can be easily generalized to the case of gravitational scattering. The extended Rutherford formula for the gravitational scattering is presented. One of the types of the gravitational scattering in the Solar system is the gravity assist maneuvers. In this paper, an effective gravitational scattering cross-section is introduced by analogy for them and the generalized Rutherford formula for gravitational scattering is presented out when performing gravity assists. Modern methods of the ballistic design of the interplanetary space flights using gravity assist maneuvers around planets [1-3] are associated with the need to calculate a lot of trajectories (i.e. of the phase beams). For their effective use it is necessary to study the structure of non-linear flyby gravitational scattering using the Rutherford’ formula and to construct the corresponding effective modelling using according regularized phase beams. It is shown that with using of such approach, it is possible to significantly increase the efficiency of the recurrent procedure for the gravity assists chains searching for ballistic scenarios of the modern interplanetary flights.