Solar System Research

, Volume 53, Issue 4, pp 245–253 | Cite as

Gravity Assist Maneuvers Near Venus for Exit to Non-Ecliptic Positions: Resonance Asymptotic Velocity

  • Yu. F. GolubevEmail author
  • A. V. GrushevskiiEmail author
  • V. V. KoryanovEmail author
  • A. G. TuchinEmail author
  • D. A. TuchinEmail author


Venus, the closest planetary neighbor of the Earth in the Solar System, is eminently suitable for performing gravity assist maneuvers by a spacecraft for a low-cost change of its orbit inclination relative to the ecliptic. We calculate the resonance values of the spacecraft asymptotic velocity relative to the planet, such that each orbital period of the spacecraft after each gravity assist maneuver are commensurate with the few orbital period of Venus, providing a new encounter with it. This enables an increase in the orbital inclination of the spacecraft using gravity-assist maneuvers without transitions to adjacent resonances along the invariant line of the main resonance on \({{\operatorname{V} }_{\infty }}\)-sphere, reaching a maximum inclination. A Venusian invariant has been obtained that does not vary after performing gravity assist maneuvers near Venus. An adaptive semianalytic method and its geometric interpretation for creating a sequence of sequences of gravitational maneuvers near Venus for a low-cost changes in the orbital inclination of the spacecraft have been presented.


gravity assist maneuver generalized cometary variant inclination pole resonance asymptotic velocity invariant resonance lines 



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© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Keldysh Institute of Applied Mathematics, Russian Academy of SciencesMoscowRussia

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