Optimal spacecraft asymptotic velocity for the high inclined orbits formation using gravity assists in the planetary systems

The inclination changing of the celestial bodies' orbits is one of the most energy-consuming procedures. Nevertheless, for a number of promising space projects, leaving the main plane of the planetary or satellite system is fundamentally necessary and demanded. In this case only the possibility of realizing the formation of maximally inclined spacecraft (SC) orbits using gravity assist maneuvers (GM) is remained. However, the dynamic possibilities of GM using are also limited. The maximum possible value of the SC orbital inclination (which gives the extreme point inclination pole – IncPole) depends on the modulus V _inf of the SC asymptotic velocity on the flyby hyperbola and is directly proportional to it (GM geometric limitation). However, the magnitude of the change in inclination at one GM is inversely proportional to V _inf (GM dynamic limitation). As a result, a compromise value of V _inf is existing, which varies for each specific case of the flyby planet. Since in order to achieve a significant inclination a whole series of GMs may be required, in addition, each GM must ensure the "resonance" of the orbital periods of the planet and SC after the GM in order to guarantee their new meeting. According the Jacobi integral in the restricted three body problem the V _inf is an invariant during in all interplanetary flights using GMs. It's possible to construct the series of increasing GM in form of "jumps" along the $$V_{inf}^{res}$$ resonance levels from the initial inclination to the maximum possible point IncPole. This point may not belong to any isoline of one of the main resonances itself in the general case. This reduces the GMs effectiveness and necessarily increases the mission time of flight. A heuristic consideration consists in choosing (in the "resonant tuning") the such value of the design V _inf, which ensures the localization of the inclination pole in the vicinity of some resonance curves between the orbital periods of the spacecraft and the planet (resonant $$V_{inf}^{res}$$). Thus it is possible to get to the IncPole by jumping along the resonance curve thru the minimum amount of GM. The paper describes the $$V_{inf}^{res}$$ formulas and gives its estimates for the Solar system and for the planets satellite systems. (paper)