Gravity assists near Venus for reaching positions over ecliptic. Resonant asymptotic velocity

Venus, the closest neighbor of the Earth in the Solar system, is primarily suitable for the spacecraft gravity assists maneuvers in order to low-cost orbit inclination changing relative to the Ecliptic. The 'resonance' values of the spacecraft asymptotic velocity relative to the planet are calculated. Their implementation allows the increasing of the inclination of the spacecraft orbit by means of gravity assists without jumping between neighboring synchronisms along the invariant lines of the main resonances on the $V_\infty$-sphere up until to the pole of the maximum inclination. The Venusian cometary invariant is calculated, which not changes with the gravity assists near Venus. An adaptive semi-analytical and geometrically distinct technique for the synthesis of chains of gravity assists near Venus for low-cost changes of the spacecraft's orbit inclination is presented.