Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analy...Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.展开更多
Stable or nearly stable orbits do not generally possess well-distinguished manifold structures that assist in designing trajectories for departing from or arriving onto a periodic orbit.For some potential missions,the...Stable or nearly stable orbits do not generally possess well-distinguished manifold structures that assist in designing trajectories for departing from or arriving onto a periodic orbit.For some potential missions,the orbits of interest are selected as nearly stable to reduce the possibility of rapid departure.However,the linearly stable nature of these orbits is also a drawback for their timely insertion into or departure from the orbit.Stable or nearly stable near rectilinear halo orbits(NRHOs),distant retrograde orbits(DROs),and lunar orbits offer potential long-horizon trajectories for exploration missions and demand eficient operations.The current investigation focuses on leveraging stretching directions as a tool for departure and trajectory design applications.The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and,therefore,offers information for efficient departure from the orbit.Similarly,maximum stretching in reverse time enables arrival with a minimal maneuver magnitude.展开更多
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA30010200)。
文摘Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.
文摘Stable or nearly stable orbits do not generally possess well-distinguished manifold structures that assist in designing trajectories for departing from or arriving onto a periodic orbit.For some potential missions,the orbits of interest are selected as nearly stable to reduce the possibility of rapid departure.However,the linearly stable nature of these orbits is also a drawback for their timely insertion into or departure from the orbit.Stable or nearly stable near rectilinear halo orbits(NRHOs),distant retrograde orbits(DROs),and lunar orbits offer potential long-horizon trajectories for exploration missions and demand eficient operations.The current investigation focuses on leveraging stretching directions as a tool for departure and trajectory design applications.The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and,therefore,offers information for efficient departure from the orbit.Similarly,maximum stretching in reverse time enables arrival with a minimal maneuver magnitude.
