Rutherford's extended formula and optimization of the gravity assists beam modeling in the Solar system

The extended Rutherford formula for the gravitational scattering is obtained. Semi-analytical guaranteeing estimates are presented for a sufficient number of a spacecraft’ virtual trajectories in a beam when simulating gravity assist maneuvers around the Solar system massive bodies which are forming the unceasing procedure for searching for the interplanetary ballistic scenarios. A special importance here is assured by the guaranteed synthesis of the bang-bang gravity assist maneuvers chains if it is necessary to change the asymptotic velocity of the spacecraft relative to the planet.