Study On Dynamics And Control Of Orbits Around Mercury

Mercury is the innermost major planet in the Solar system. The explorationof Mercury can not only investigate the nature of Mercury itself, but also hasgreat significant in the evolution of the solar system and origin of life. Mercuryhas the smallest distance from the Sun, and the eccentricity is non-ignorable. Soorbits around Mercury are influence by the strong periodic time-varying gravityfrom the Sun. To deal with this problem, the orbital dynamics and stationkeeping methods around Mercury are studied in this paper.When the motion of the spacecraft is in the sphere of influence of Mercury,the perturbation of elliptic third-body gravity from the Sun and the second andthird zonal harmonics have been considered. To learn about the long-termbehaviors of the orbital elements, Lie transform is applied as an average methodto put two types of the periodic terms to higher order terms. The averagedsystem is reduced to a single degree of freedom system, and the equilibrium ofthis system is a frozen orbit in common sense. According to the properties ofequilibriums (frozen orbits) and trajectories around them, method of orbitalcorrection to the frozen orbits is investigated. First, the orbital correction isdesigned in the two-body model for different ephase point in the sameinitial orbit, the feasibility and fuel consumption of different phase points arestudied. Then the transfer orbit is corrected in the perturbed model.The averaged eccentricity of the frozen orbit is constant, so it caneffectively keep the periapsis altitude of high eccentricity orbit unchanged andtherefore avoid the spacecraft avoid crashing into Mercury. However, theforming conditions are too harsh to meet practical needs. In this paper, acontinuous control method that combines analytical theory and parameteroptimization is proposed to build an artificial frozen orbit. Coefficients ofperturbations which satisfy the conditions of frozen orbits are involved ascontrol parameters, and the relevant artificial perturbations are compensated bythe control strategy. So probes around Mercury can be kept on frozen orbitunder the influence of continuous control force. After deriving the forming condition of each type of artificial frozen orbits and their constraints, complexmethod of optimization is used to search for the energy optimized artificialfrozen orbits. Evolution of optimal control parameters are given in large rangesof semi-major axis and eccentricity, and the feasibility of artificial frozen orbitsare evaluated.At last, distant quasi-periodic orbits around Mercury are studied. All ofthese orbits have relatively large sizes, with their altitudes near or above theMercury sphere of influence. The research is carried out in the framework of theelliptic restricted three-body problem (ER3BP) to account for the planet’snon-negligible orbital eccentricity. In this paper, Quasi-periodic orbits aroundMercury are defined according to de need of Mercury missions. Retrograde andprograde quasi-periodic trajectories in the planar ER3BP are generalized fromperiodic orbits in the CR3BP by the homotopy algorithm, and the shapeevolution of such quasi-periodic trajectories around Mercury is investigated.Then, the numerical stability of these quasi-periodic orbits around Mercury isinvestigated.