Manifold dynamics in the Earth–Moon system via isomorphic mapping with application to spacecraft end-of-life strategies

Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth–Moon system and in alternative multibody environments. With regard to lunar missions, exterior and interior transfers, based on the transit through the regions where the collinear libration points L₁ and L₂ are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is focused on the definition and use of a special isomorphic mapping for low-energy mission analysis. A convenient set of cylindrical coordinates is employed to describe the spacecraft dynamics (i.e. position and velocity), in the context of the circular restricted three-body problem, used to model the spacecraft motion in the Earth–Moon system. This isomorphic mapping of trajectories allows the identification and intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Heteroclinic connections, i.e. the trajectories that belong to both the stable and the unstable manifolds of two distinct periodic orbits, can be easily detected by means of this representation. This paper illustrates the use of isomorphic mapping for finding (a) periodic orbits, (b) heteroclinic connections between trajectories emanating from two Lyapunov orbits, the first at L₁, and the second at L₂, and (c) heteroclinic connections between trajectories emanating from the Lyapunov orbit at L₁ and from a particular unstable lunar orbit. Heteroclinic trajectories are asymptotic trajectories that travels at zero-propellant cost. In practical situations, a modest delta-v budget is required to perform transfers along the manifolds. This circumstance implies the possibility of performing complex missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining suitable, convenient end-of-life strategies for spacecraft orbiting the Earth. Seven distinct options are identified, and lead to placing the spacecraft into the final disposal orbit, which is either (a) a lunar capture orbit, (b) a lunar impact trajectory, (c) a stable lunar periodic orbit, or (d) an outer orbit, never approaching the Earth or the Moon. Two remarkable properties that relate the velocity variations with the spacecraft energy are employed for the purpose of identifying the optimal locations, magnitudes, and directions of the velocity impulses needed to perform the seven transfer trajectories. The overall performance of each end-of-life strategy is evaluated in terms of time of flight and propellant budget.     

探月飞行的调相轨道

早期的探月飞行都采用直接由地球飞到月球的地月转移方式,探测器由运载火箭直接发送到地月转移轨道,这样做的好处是飞行时间比较短,只需3至5天的时间。20世纪90年代开始的新一轮探月活动中采用了一种新的飞行方式,探测器飞离地球前,先在绕地球飞行的调相轨道上运行若干圈,这样做的好处有三：一是可以在运载火箭能力不够的情况下,由探测器来补充;二是可以减小转移轨道中途修正的负担;三是可以扩大发射机会窗口。文章以嫦娥一号探测器及美、日的两个月球探测器为例,详细讨论了这种新的飞行方式,同时还对我国后续探月计划的飞行轨道提出了初步建议。     

Evolution of the out-of-plane amplitude for quasi-periodic trajectories in the Earth–Moon system

The out-of-plane amplitude along quasi-periodic trajectories in the Earth–Moon system is highly sensitive to perturbations in position and/or velocity as underscored recently by the ARTEMIS spacecraft. Controlling the evolution of the out-of-plane amplitude is non-trivial, but can be critical to satisfying mission requirements. The sensitivity of the out-of-plane amplitude evolution to perturbations due to lunar eccentricity, solar gravity, and solar radiation pressure is explored and a strategy for designing low-cost deterministic maneuvers to control the amplitude history is also examined. The method is sufficiently general and is applied to the L₁ quasi-periodic orbit that serves as a baseline for the ARTEMIS P2 trajectory.     

Lunar transportation scenarios utilising the Space Elevator

The Space Elevator (SE) concept has begun to receive an increasing amount of attention within the space community over the past couple of years and is no longer widely dismissed as pure science fiction. In light of the renewed interest in a, possibly sustained, human presence on the Moon and the fact that transportation and logistics form the bottleneck of many conceivable lunar missions, it is interesting to investigate what role the SE could eventually play in implementing an efficient Earth to Moon transportation system. The elevator allows vehicles to ascend from Earth and be injected into a trans-lunar trajectory without the use of chemical thrusters, thus eliminating gravity loss, aerodynamic loss and the need of high thrust multistage launch systems. Such a system therefore promises substantial savings of propellant and structural mass and could greatly increase the efficiency of Earth to Moon transportation. This paper analyzes different elevator-based trans-lunar transportation scenarios and characterizes them in terms of a number of benchmark figures. The transportation scenarios include direct elevator-launched trans-lunar trajectories, elevator launched trajectories via L1 and L2, as well as launch from an Earth-based elevator and subsequent rendezvous with lunar elevators placed either on the near or on the far side of the Moon. The benchmark figures by which the different transfer options are characterized and evaluated include release radius (RR), required delta v, transfer times as well as other factors such as accessibility of different lunar latitudes, frequency of launch opportunities and mission complexity. The performances of the different lunar transfer options are compared with each other as well as with the performance of conventional mission concepts, represented by Apollo.     

On the survivability and detectability of terrestrial meteorites on the moon

Materials blasted into space from the surface of early Earth may preserve a unique record of our planet's early surface environment. Armstrong et al. (2002) pointed out that such materials, in the form of terrestrial meteorites, may exist on the Moon and be of considerable astrobiological interest if biomarkers from early Earth are preserved within them. Here, we report results obtained via the AUTODYN hydrocode to calculate the peak pressures within terrestrial meteorites on the lunar surface to assess their likelihood of surviving the impact. Our results confirm the order-of-magnitude estimates of Armstrong et al. (2002) that substantial survivability is to be expected, especially in the case of relatively low velocity (ca. 2.5 km/s) or oblique (相似文献   

Sсheme of rendezvous mission to lunar orbital station by spacecraft launched from Earth

In recent years, great experience has been accumulated in manned flight astronautics for rendezvous in near-Earth orbit. During flights of Apollo spacecraft with crews that landed on the surface of the Moon, the problem of docking a landing module launched from the Moon’s surface with the Apollo spacecraft’s command module in a circumlunar orbit was successfully solved. A return to the Moon declared by leading space agencies requires a scheme for rendezvous of a spacecraft launched from an earth-based cosmodromee with a lunar orbital station. This paper considers some ballistic schemes making it possible to solve this problem with minimum fuel expenditures.     

Scientific investigations at a lunar base.

Scientific investigations to be carried out at a lunar base can have significant impact on the location, extent, and complexity of lunar surface facilities. Among the potential research activities to be carried out are: (1) Lunar Science: Studies of the origin and history of the Moon and early solar system, based on lunar field investigations, operation of networks of seismic and other instruments, and collection and analysis of materials; (2) Space Plasma Physics: Studies of the time variation of the charged particles of the solar wind, solar flares and cosmic rays that impact the Moon as it moves in and out of the magnetotail of the Earth; (3) Astronomy: Utilizing the lunar environment and stability of the surface to emplace arrays of astronomical instruments across the electromagnetic spectrum to improve spectral and spatial resolution by several orders of magnitude beyond the Hubble Space Telescope and other space observatories; (4) Fundamental physics and chemistry: Research that takes advantage of the lunar environment, such as high vacuum, low magnetic field, and thermal properties to carry out new investigations in chemistry and physics. This includes material sciences and applications; (5) Life Sciences: Experiments, such as those that require extreme isolation, highly sterile conditions, or very low natural background of organic materials may be possible; and (6) Lunar environmental science: Because many of the experiments proposed for the lunar surface depend on the special environment of the Moon, it will be necessary to understand the mechanisms that are active and which determine the major aspects of that environment, particularly the maintenance of high-vacuum conditions. From a large range of experiments, investigations and facilities that have been suggested, three specific classes of investigations are described in greater detail to show how site selection and base complexity may be affected: (1) Extended geological investigation of a complex region up to 250 kilometers from the base requires long range mobility, with transportable life support systems and laboratory facilities for the analysis of rocks and soil. Selection of an optimum base site would depend heavily on an evaluation of the degree to which science objectives could be met. These objectives could include lunar cratering, volcanism, resource surveys or other investigations; (2) An astronomical observatory initially instrumented with a VLF radio telescope, but later expanding to include other instruments, requires site preparation capability, "line shack" life support systems, instrument maintenance and storage facilities, and sortie mode transportation. A site perpetually shielded from Earth is optimum for the advanced stages of a lunar observatory; (3) an experimental physics laboratory conducting studies requiring high vacuum facilities and heavily instrumented experiments, is not highly dependent on lunar location, but will require much more flexibility in experiment operation and EVA capability, and more sophisticated instrument maintenance and fabrication facilities.     

月亮女神探月计划及对我国月球与深空探测的思考

日本月亮女神月球探测器在顺利完成各项探测任务后,于北京时间2009年6月11日受控落月.该探月计划在一箭三星组网探测月球背面重力场、有效载荷创新设计、科研活动组织、成果产出、公众参与和科普宣传等方面有许多亮点,对我国探月工程有重要参考价值.文章综合回顾、分析和评述了月亮女神探月计划的任务、探测器、轨道与飞控、重要事件等...     

地-月系平动点及Halo轨道的应用研究

地-月系统的平动点L1点及L2点的Halo轨道在探月工程中有重要的应用价值，可分别用于地月连续通信覆盖和月球背面的探测。由于在地-月系统中太阳的引力不可忽略，特别是在长时间作用以后，其动力学行为与摄动力较小的日-地系统有明显的不同。本文分析了如何利用太阳引力进入地-月系统的L1点及L2点的Halo轨道、以及由Halo轨道进入近月轨道的问题，两者综合起来构成了一条完整的地月低能转移轨道。研究结果对探月轨道设计有一定的参考价值。     

Determination of the density and percentage of metal oxides in the lunar soil based on radar data

Results of laboratory measurements of the dielectric characteristics of lunar soil samples returned to the Earth by the Luna and Apollo missions have been analyzed. The feasibility of determining the density of the upper cover of the Moon from the permittivity, which is restored as a result of solving the inverse problem of radiolocation, has been discussed. A formula has been proposed for approximating the frequency dependence of the loss tangent for the regolith and bedrock. Relationships have been deduced for estimating the percentage of metal oxides in the lunar soil.     

Rationale and systems architecture for a near-term human lunar return

Early human missions to the Moon have landed on six different sites on the lunar surface. These have all been in the low-latitude regions of the near side of the Moon. Early missions were designed primarily to assure crew safety rather than for scientific value. While the later missions added increasingly more challenging science, they remained restricted to near-side, low-latitude sites. Since the 1970s, we have learned considerably more about lunar planetology and resources. A return within the next five to ten years can greatly stimulate future human space exploration activities. We can learn much more about the distribution of lunar resources, especially about hydrogen, hydrated minerals, and water ice because they appear to be abundant near the lunar poles. The presence of hydrogen opens the possibility of industrial use of lunar resources to provide fuel for space transportation throughout the solar system.This paper discusses the rationale for near-term return of human crews to the Moon, and the advantages to be gained by selecting the Moon as the next target for human missions beyond low-Earth orbit. It describes a systems architecture for early missions, including transportation and habitation aspects. Specifically, we describe a primary transportation architecture that emphasizes existing Earth-to-orbit transportation systems, using expendable launch vehicles for cargo delivery and the Space Shuttle and its derivatives for human transportation. Transfer nodes should be located at the International Space Station (ISS) and at the Earth-Moon L1 (libration point).Each of the major systems is described, and the requisite technology readiness is assessed. These systems include Earth-to-orbit transportation, lunar transfer, lunar descent and landing, surface habitation and mobility, and return to Earth. With optimum reliance on currently existing space systems and a technology readiness assessment, we estimate the minimum development time required and perform order-of-magnitude cost estimates of a near-term human lunar mission.     

Lunar base development missions

On 20 July 1969, humankind first set foot on our Moon. Since then we have developed the Space Shuttle, explored most of the planets, cooperated in the development of the International Space Station, and expanded our knowledge of the universe through use of systems such as the Hubble Space Telescope and the Mars Pathfinder. After just five human follow-on missions to our Moon, we have returned robotically only twice to orbit, to map the surface and explore for resources.

The indication of the presence of hydrogen concentration at the poles of our Moon found by Lunar Prospector has added a new perspective for groups studying and implementing future lunar missions. Plans for nearterm missions such as the European Space Agency (ESA) “Euromoon 2000”, the Japanese Lunar A and Selene, and the Mitsubishi ”Earthrise 2001” Project, along with follow-on phases to the Lunar Prospector, are the beginning of humankind's return to the Moon. Organizations such as the International Academy of Astronautics have long championed the “Case for an International Lunar Base,” and a vision of a commercially-based lunar program has been outlined by several groups. A Lunar Economic Development Authority (LEDA) promoted by the United Society in Space was promulgated by the filing of articles of incorporation in the state of Colorado on 4 August 1997. This non-profit corporation has as its goal the orderly development of the Moon, through issuance of bonds to international private citizens and business entities who care to invest in its long-term development.

This paper draws from the works of the aforementioned, and specifically from the International Academy of Astronautics Lunar Base Committee, to structure a series of architectures leading toward eventual international commercial colonization of the lunar surface. While the prospect of fully reusable transportation systems utilizing fully developed lunar resources to perpetuate the permanent lunar infrastructure is enticing, this is a goal. We must utilize our current and near-term capabilities to re-initiate human lunar presence, and then build on emerging technologies to strengthen our capabilities. Humankind's return to the Moon is a part of our destiny. We can return in the near future, and then proceed to a commercial, permanent settlement in the 21st century.     

Chandrayaan-1 mission to the Moon

Chandrayaan-1 is the first Indian planetary exploration mission that will perform remote sensing observation of the Moon to further our understanding about its origin and evolution. Hyper-spectral studies in the 0.4– region using three different imaging spectrometers, coupled with a low energy X-ray spectrometer, a sub-keV atom analyzer, a 3D terrain mapping camera and a laser ranging instrument will provide data on mineralogical and chemical composition and topography of the lunar surface at high spatial resolution. A low energy gamma ray spectrometer and a miniature imaging radar will investigate volatile transport on lunar surface and possible presence of water ice in the polar region. A radiation dose monitor will provide an estimation of energetic particle flux en route to the Moon as well as in lunar orbit. An impact probe carrying a mass spectrometer will also be a part of the spacecraft. The 1 ton class spacecraft will be launched by using a variant of flight proven indigenous Polar Satellite Launch Vehicle (PSLV-XL). The spacecraft will be finally placed in a 100 km circular polar orbit around the Moon with a planned mission life of two years.     

Does the lunar surface still offer value as a site for astronomical observatories?

Current thinking about the Moon as a destination has revitalized interest in lunar astronomical observatories. Once seen by a large scientific community as a highly enabling site, the dramatic improvement in capabilities for free-space observatories prompts reevaluation of this interest. Whereas the lunar surface offers huge performance advantages for astronomy over terrestrial sites, free-space locales such as Earth orbit or Lagrange points offer performance that is superior to what could be achieved on the Moon. While astronomy from the Moon may be cost-effective once infrastructure is there, it is in many respects no longer clearly enabling compared with free space.     

The ethics of treading on Neil Armstrong''s footprints

The Moon landings of the Apollo programme irrevocably changed the way we see ourselves. Most significantly, this was the first time that humans had set foot on a celestial body other than Earth. The program has left a number of sites on the Moon as well as on Earth. While the management of the sites and artefacts on Earth is fairly straightforward as they are subject to national heritage legislation, it is not so simple with the sites and artefacts on the lunar surface. Moreover, the sites on the Moon differ in one unique aspect from all other heritage sites on Earth: the absence of a lunar atmosphere of any note means that all foot- and track prints of the astronauts are preserved providing a total record of the pioneering phases of human exploration of the Moon. The nascent developments of space tourism, including proposals for lunar heritage tourism, however, threaten the preservation of these traces on the Moon. This paper discusses the terrestrial and in particular the extraterrestrial heritage of the Apollo programme. Set out are the management ethics that need to apply on the lunar surface if this unique heritage is to have a future.     

从月球逃逸探测小行星的发射机会搜索

从月球逃逸探测小行星的发射机会搜索因需考虑日、地、月引力的影响而使问题变得复杂。针对该多体系统的发射机会搜索问题,提出了一种分层渐近的搜索方法。该方法首先通过分析地月系质心与小行星的几何关系,搜索从地月系质心到小行星的发射机会,进而以地月运动为研究对象,推导出了从月球轨道切向逃逸机会的判别条件,并基于此判别条件及等高线图法对逃逸机会进行了搜索。同时,为提高所得发射机会在多体模型下的轨道修正收敛性,给出了基于月心逃逸轨道参数为终端约束的日-地与日-地-月动力学模型的轨道渐近修正方法。最后,以近地小行星(3908)Nyx和(190491)2000 FJ20为例,搜索其从月球逃逸的发射机会,仿真计算表明了该方法的有效性。     

Analytical definition and proposed concept for the manned infrastructure of a lunar outpost

A recent study made by ESA has reviewed the scientific investigations to be only, or best, performed on the Moon (Return to the Moon, ESA SP-1150, June 1992), and has identified the need for a manned lunar outpost to provide support to field geologists in sampling and in-situ observations of the lunar surface, and to allow the refurbishments of surface stations and rovers. Planning and development for a manned outpost on the Moon requires an in-depth understanding and analysis of the functions this outpost is expected to perform. We therefore analyzed the impact of the proposed scientific investigations on the design of a manned lunar outpost. The specific questions raised in our study were: What are the medical, physiological and psychological risks for a crew to stay and to work on the Moon? What transit and lunar surface infrastructures (habitats and vehicles) are needed to minimize those risks?     

Applications of multi-body dynamical environments: The ARTEMIS transfer trajectory design

The application of forces in multi-body dynamical environments to permit the transfer of spacecraft from Earth orbit to Sun–Earth weak stability regions and then return to the Earth–Moon libration (L₁ and L₂) orbits has been successfully accomplished for the first time. This demonstrated that transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecrafts into Earth–Moon libration orbits by means of these applications.     

Orbit determination and control for the European Student Moon Orbiter

This paper presents the preliminary navigation and orbit determination analyses for the European Student Moon Orbiter. The severe constraint on the total mission Δv and the all-day piggy-back launch requirement imposed by the limited available budget, led to the choice of using a low-energy transfer, more specifically a Weak Stability Boundary one, with a capture into an elliptic orbit around the Moon. A particular navigation strategy was devised to ensure capture and fulfil the requirement for the uncontrolled orbit stability at the Moon. This paper presents a simulation of the orbit determination process, based on an extended Kalman filter, and the navigation strategy applied to the baseline transfer of the 2011–2012 window. The navigation strategy optimally allocates multiple Trajectory Correction Manoeuvres to target a so-called capture corridor. The capture corridor is defined, at each point along the transfer, by back-propagating the set of perturbed states at the Moon that provides an acceptable lifetime of the lunar orbit.     

An inversion approach for lunar regolith layer thickness using optical albedo data and microwave emission simulation

An approach to inversion of the lunar regolith layer thickness by using multi-channel brightness temperature observation in passive microwave remote sensing is developed. To first make simulation of brightness temperature from the lunar layered media, the lunar regolith layer thickness (d) is proposed being constructed by available lunar DEM (digital elevation mapping) and on site measurements. The physical temperature distribution (T) over the lunar surface is also empirically assumed as a monotonic function of the latitude. Optical albedo of the lunar nearside from the telescopic observation is employed to construct the spatial distribution of the FeO+TiO₂ content (S) in the lunar regolith layer. A statistic relationship between the DEM and S of the lunar nearside is further extended to construction of S of the lunar farside. Thus, the dielectric permittivity (ε) of global lunar regolith layer can then be determined. Based on all these conditions (d,T,ε), brightness temperature of the lunar regolith layer in passive microwave remote sensing, which is planned for China's Chang-E lunar project, is numerically simulated by a parallel layering model using the strong fluctuation theory of random media.Then, taking these simulations with random noise as observations, an inversion method of the lunar regolith layer thickness is developed by using three- or two-channels brightness temperatures. When the S is low, and the four channels brightness temperatures in China's Chang-E project are well distinguishable, the regolith layer thickness and physical temperature of the underlying lunar rock media can be inverted by the three-channels approach. When the S becomes high that the brightness temperature at high frequency channels such as 19.35, 37 GHz are saturated, the regolith layer thickness is alternatively inverted only by the two-channels approach.Numerical simulation and inversion approach in this paper make an evaluation of the performance for lunar passive microwave remote sensing, and for future data calibration and validation.