Transfer Trajectory Design And Lorentz Force Formation Flying In Earth-Moon System

The libration points in the Earth-Moon system are the equilibrium points of the gravitational forces between the Earth and the Moon,which are the passage of both unmanned and manned explorations to the Moon,the Mars and the space beyond.If a space station is deployed close to the Earth-Moon collinear libration point,it can serve as the staging launch platform of deep space exploration,as the relay station of the lunar landers,as the repair centre of the moonbase,as the space-borne telescope plat,and as the space base beyond the Earth's radiation belt.With the destination for the human space exploration activities becomes further and further,the ground-based observatory and near Earth satellites can no longer meet the ever increasing requirement of the observation and communication in space.A visual mission is considered in the paper such that a formation observation plat-form on lunar orbits are constructed by spacecrafts launched from an Earth-Moon L₁space station.As an applying basic research,the paper aims at solving some representa-tively key problems arising from the mission,which include the transfer from the space base to a lunar orbit and the relative dynamics of the space formation flying.In order to obtain general conclusions,nonlinear dynamical system theory is applied to explore thoroughly the dynamics in the transfer trajectory design and the formation flying model.The paper considers firstly the design of a general transfer procedure from a libration point orbit?LPO?to a lunar orbit,to solve the problem of launching satellite from libra-tion point space station to the Moon.To solve the key issue of the limited propellent for long term observation missions in the construction of space-borne formation observatory,a new dynamical scenario of propellentless formation flying is proposed using lorentz froce produced by an artificial magnetic filed.Fortran packages are developed,along with im-provements on the classical methods for the computation of periodic and quasi-periodic orbits.In the studies of the transfer from a LPO to a lunar orbit,a general transfer pro-cedure based on invariant manifold has been designed.An analytical solution of a two-manoeuvre transfer based on two-body assumption has been obtained,which provides a fast initial guess for the transfer problem in the three-body problem.The transfer procedure analysed has two legs:the first one is an orbit of the unstable manifold of the LPO and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit.There are only two manoeuvres involved in the method and they are performed at the beginning and at the end of the second leg.In the numerical simulation,the Earth-Moon system has been chosen as an example,together with the L₁Halo orbit as the departing orbit and the lunar polar orbits with altitude of 100?500km as the target orbit.Possible parameters that may affect the total transfer cost and their influences have been analysed qualitatively.As general conclusions we can say that,to have low transfer cost:the departure manoeuvre should be done at the first apolune of the unstable invariant manifold of the LPO,and the inclination to be achieved by the first manoeuvre must be set equal to the target final inclination.The general procedure we develop can be applied to any kind of lunar orbits,libration orbits around the L₁or L₂points of the Earth-Moon system,or to other similar cases with different values of the mass ratio.Concerning the Lorentz force formation flying,the paper focuses on the relative dy-namics analysis of the charged follower moving in the artificial magnetic field of the leader using dynamical system theory as the tool.Three kinds of motion and the orbital be-haviour nearby have been studied:equilibrium points,periodic orbits and quasi-periodic orbits?2D invariant tori?,to obtain a detailed and accurate dynamical description.To explore the potential of this model in formation flying,different kinds of formation con-figurations have been designed using the numerical results of these three kinds of motion as the nominal orbits.Firstly,we deduce the system equations of motion along with its symmetry analysis,the dynamical characteristics of the system are studied as a function of its parameters,with special attention to the ratio of the leader's mean motion around the Earth to the rotating rate of the dipole.For the equilibrium points,nine kinds of critical points of the model are computed,and their linear stabilities analysed.Moreover,the configuration space is explored using zero velocity surfaces,the admissible and forbidden regions of motion of the deputy are classified,and the topological evolution behaviour of the surfaces is demonstrated around the energy of the equilibrium point.Considering the equilibrium points with non-empty centre manifolds,18 families of periodic orbits emanating from equilibria and embedded in the centre manifold are computed,as well as 8 bifurcated families of periodic orbits.According to the topology structure of the characteristic multiplier,the stability and topological classification of all the families of the periodic orbits are explored.To extend the solution space of this model,we pay special attention to the periodic orbits of elliptic type in the normal case and to the families of 2D tori surrounding them.Three families of 2D quasi-periodic orbits are computed by means of a parameterisation method and numerical continuation up to the resonances 15:64,1:64 and 2:27,respectively.Last but not the least,as an illustration of application,several fixed or loose formation configurations are designed using the equilibrium points,symmetric periodic orbits and quasi-periodic orbits as the nominal orbits.The result is a fine catalog of orbits together with an accurate dynamical description suitable to researchers interested in potential applications of satellite formation flight using this kind of technology.The general transfer procedure proposed in the paper can be applied to the transfer from LPO to the vicinity of the smaller primary in any three-body problem,and the methodology and results achieved in the study of the Lorentz force formation flying under artificial magnetic field are promising technologies for the relevant requirements and applications in the propellentless formation flying in space.The researches conducted in this paper can serve as the theoretical and technical basis for the mission analysis and design of the construction of formation observation platform by spacecrafts launched from LPO space base,which extend the application of dynamical system theory in the space mission design.