Planetary Defense From Space: Part 1-Keplerian Theory

A system of two space bases housing missiles is proposed to achieve the Planetary Defense of the Earth against dangerous asteroids and comets. We show that the layout of the Earth–Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth).

We show that placing bases of missiles at L1 and L3 would cause those missiles to deflect the trajectory of asteroids by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that the confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement.

An additional remark is that the theory developed in this paper is just a beginning of a larger set of future research work. In fact, while in this paper we only develop the Keplerian analytical theory of the Optimal Planetary Defense achievable from the Earth–Moon Lagrangian points L1 and L3, much more sophisticated analytical refinements would be needed to:

1. Take into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3;

2. add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L4 and L5 of the Earth–Moon system or from the surface of the Moon itself;

3. encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see “which asteroids could be diverted by which missiles”, even in the very simplified scheme outlined here.

Outlined for the first time in February 2002, our Confocal Planetary Defense concept is a Keplerian Theory that proved simple enough to catch the attention of scholars, representatives of the US Military and popular writers. These developments could possibly mark the beginning of an “all embracing” mathematical vision of Planetary Defense beyond all learned activities, dramatic movies and unknown military plans covered by secret.     

地月平动点拟周期轨道探测器自主导航方法研究

地月L2点的拟周期轨道可以用于实现与月球背面的持续通信,具有重要的科学研究价值和广阔的应用前景。针对地月L2点探测器所处的弱稳定拟周期轨道,论证了基于日地月信息的自主导航方法的可行性,并进行了深入分析。首先,推导了会合坐标系下带有星历的精确导航动力学方程;其次,针对弱稳定轨道不同于近地强稳定轨道的特性,在基于日地月方位信息导航的基础上,提出了三种敏感器组合方案。使用迭代最小二乘方法给出导航仿真结果,并结合非线性可辨识性理论对这三种情况下历元状态的可辨识性及可辨识度进行分析。最后,仿真结果表明,使用日地月敏感器以及对地多普勒雷达可以满足历元状态的可辨识性、导航的收敛性以及系统经济性的要求。     

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.     

Space and the fate of humanity

Current growth and consumption rates on Earth cannot be sustained into the future. Space technology is already a vital tool in the management of the planet and we should look at it to mitigate some of the problems we face. However, this should not include colonization of interstellar space. Rather we should focus on using solar energy from space and on mining asteroids, both of which would be feasible if the Moon was developed as a space base and power station. The most difficult and expensive part of getting into space is escaping Earth's gravity - something that could be avoided once a presence was established on the Moon. A lunar base would also provide the obvious site from which to reach GEO, travel to Mars or back to Earth and, ultimately, to explore the further reaches of the Solar System.     

星历模型下地月自由返回全飞行过程轨道设计

面向载人登月任务需要,针对星历模型下具备自由返回能力的地月转移轨道设计问题进行了研究。在三体模型下对地月三维自由返回轨道进行了求解,得到了地月空间内的自由返回轨道分布情况。在二体模型假设下对近月段的三脉冲变轨进行了求解,给出了变平面机动的计算方法。进一步提出了两轮逐次优化修正策略,分别以高度和再入走廊为主要约束,采用内点法和SQP算法在高精度星历模型下对自由返回轨道初值进行逐次优化修正。之后,采用SQP算法在星历模型下对近月三脉冲变轨进行优化修正,得到了星历模型下的自由返回+近月三脉冲变轨地月转移策略。仿真校验结果表明本文提出的方法能够在给定约束下有效求解星历模型下具备自由返回能力的地月转移轨道,为载人登月任务的转移轨道设计提供参考。     

Assessment on the feasibility of future shepherding of asteroid resources

Most plausible futures for space exploration and exploitation require a large mass in Earth orbit. Delivering this mass requires overcoming the Earth's natural gravity well, which imposes a distinct obstacle to any future space venture. An alternative solution is to search for more accessible resources elsewhere. In particular, this paper examines the possibility of future utilisation of near Earth asteroid resources. The accessibility of asteroid material can be estimated by analysing the volume of Keplerian orbital element space from which Earth can be reached under a certain energy threshold and then by mapping this analysis onto an existing statistical near Earth objects (NEO) model. Earth is reached through orbital transfers defined by a series of impulsive manoeuvres and computed using the patched-conic approximation. The NEO model allows an estimation of the probability of finding an object that could be transferred with a given Δv budget. For the first time, a resource map provides a realistic assessment of the mass of material resources in near Earth space as a function of energy investment. The results show that there is a considerable mass of resources that can be accessed and exploited at relatively low levels of energy. More importantly, asteroid resources can be accessed with an entire spectrum of levels of energy, unlike other more massive bodies such as the Earth or Moon, which require a minimum energy threshold implicit in their gravity well. With this resource map, the total change of velocity required to capture an asteroid, or transfer its resources to Earth, can be estimated as a function of object size. Thus, realistic examples of asteroid resource utilisation can be provided.     

An exploration of the effectiveness of artificial mini-magnetospheres as a potential solar storm shelter for long term human space missions

If mankind is to explore the solar system beyond the confines of our Earth and Moon the problem of radiation protection must be addressed. Galactic cosmic rays and highly variable energetic solar particles are an ever-present hazard in interplanetary space.     

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.     

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。     

Monitoring of the space system

We have performed monitoring of the space system that includes the Earth, the Moon, the Sun, and the GPS satellite group. We have discovered semi-diurnal and diurnal periodicities in the number of satellites detected as well as in the altitude, latitude and longitude by a GPS receiver. We have revealed tidal deformations related to changes in the Earth?s orientation with respect to the Moon and the Sun.     

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   

Extraterrestrial environmental impact assessments – A foreseeable prerequisite for wise decisions regarding outer space exploration,research and development

Although existing international instruments such as the Outer Space Treaty and Moon Agreement generally express sentiments for minimizing missions' extraterrestrial environmental impacts, they tend to be limited in scope, vague and generally unenforceable. There is no formal structure for assessing how and to what extent we affect those environments, no opportunity for public participation, no uniform protocol for documenting and registering the effects of our actions and no requirement to mitigate adverse impacts or take them into consideration in the decision-making process. Except for precautions limiting forward biological contamination and issues related to Earth satellites, environmental impact analysis, when done at all, remains focused on how missions affect the Earth and near-Earth environments, not how our actions affect the Moon, Mars, Europa, comets and other potential destinations. Extraterrestrial environmental impacts are potentially counterproductive to future space exploration, exploitation and scientific investigations. Clear, consistent and effective international protocols guiding a process for assessing such impacts are warranted. While instruments such as the US National Environmental Policy Act provide legally tested and efficient regulatory models that can guide impact assessment here on Earth, statutory legal frameworks may not work as well in the international environment of outer space. A proposal for industry-driven standards and an environmental code of conduct based, in part, on best management practices are offered for consideration.     

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.     

Planetary Defense From Space: Part 2 (Simple) Asteroid Deflection Law

A system of two space bases housing missiles for an efficient Planetary Defense of the Earth from asteroids and comets was firstly proposed by this author in 2002. It was then shown that the five Lagrangian points of the Earth–Moon system lead naturally to only two unmistakable locations of these two space bases within the sphere of influence of the Earth. These locations are the two Lagrangian points L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth). In fact, placing missiles based at L1 and L3 would enable the missiles to deflect the trajectory of incoming asteroids by hitting them orthogonally to their impact trajectory toward the Earth, thus maximizing the deflection at best. It was also shown that confocal conics are the only class of missile trajectories fulfilling this “best orthogonal deflection” requirement.The mathematical theory developed by the author in the years 2002–2004 was just the beginning of a more expanded research program about the Planetary Defense. In fact, while those papers developed the formal Keplerian theory of the Optimal Planetary Defense achievable from the Earth–Moon Lagrangian points L1 and L3, this paper is devoted to the proof of a simple “(small) asteroid deflection law” relating directly the following variables to each other:

(1) the speed of the arriving asteroid with respect to the Earth (known from the astrometric observations);

(2) the asteroid's size and density (also supposed to be known from astronomical observations of various types);

(3) the “security radius” of the Earth, that is, the minimal sphere around the Earth outside which we must force the asteroid to fly if we want to be safe on Earth. Typically, we assume the security radius to equal about 10,000 km from the Earth center, but this number might be changed by more refined analyses, especially in the case of “rubble pile” asteroids;

(4) the distance from the Earth of the two Lagrangian points L1 and L3 where the defense missiles are to be housed;

(5) the deflecting missile's data, namely its mass and especially its “extra-boost”, that is, the extra-energy by which the missile must hit the asteroid to achieve the requested minimal deflection outside the security radius around the Earth.

This discovery of the simple “asteroid deflection law” presented in this paper was possible because:

(1) In the vicinity of the Earth, the hyperbola of the arriving asteroid is nearly the same as its own asymptote, namely, the asteroid's hyperbola is very much like a straight line. We call this approximation the line/circle approximation. Although “rough” compared to the ordinary Keplerian theory, this approximation simplifies the mathematical problem to such an extent that two simple, final equations can be derived.

(2) The confocal missile trajectory, orthogonal to this straight line, ceases then to be an ellipse to become just a circle centered at the Earth. This fact also simplifies things greatly. Our results are thus to be regarded as a good engineering approximation, valid for a preliminary astronautical design of the missiles and bases at L1 and L3.

Still, many more sophisticated refinements would be needed for a complete Planetary Defense System:

(1) taking into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3;

(2) adding more (non-optimal) trajectories of missiles shot from either the Lagrangian points L4 and L5 of the Earth–Moon system or from the surface of the Moon itself;

(3) encompassing the full range of missiles currently available to the USA (and possibly other countries) so as to really see “which missiles could divert which asteroids”, even just within the very simplified scheme proposed in this paper.

In summary: outlined for the first time in February 2002, our Confocal Planetary Defense concept is a simplified Keplerian Theory that already proved simple enough to catch the attention of scholars, popular writers, and representatives of the US Military. These developments would hopefully mark the beginning of a general mathematical vision for building an efficient Planetary Defense System in space and in the vicinity of the Earth, although not on the surface of the Earth itself!We must make a real progress beyond academic papers, Hollywood movies and secret military plans, before asteroids like 99942 Apophis get close enough to destroy us in 2029 or a little later.     

On halo orbits spacecraft stabilization

The paper deals with the application of recent non-linear control techniques to the problem of tracking and maintaining a given satellite on prescribed orbits around the so-called translunar libration point L₂. Such orbits, known in literature as Halo Orbits, have the property of ensuring visibility both from the dark side of the Moon and from Earth at any time. Their importance is strictly related to the placement of a base situated on the dark side of the Moon for advanced space missions as deep space observation, solar system exploration and scientific researches in a low gravity enviroment.

Because of the instability of the equilibrium L₂, such orbits cannot be maintained without an active control. In this paper we investigate the application of nonlinear control techniques to solve the problem. A comparison between linear and nonlinear methods is developed and simulation results are discussed.     

地月高能共振循环轨道的快速计算及最优选择

针对现有高能共振循环轨道计算方法存在计算量大、有可能改变轨道共振特性和不能构造共振比大于2.3的地月循环轨道等缺点,本文提出了一种地月圆型限制性三体问题下高能共振循环轨道的快速计算方法。首先根据轨道在月球附近的组成弧段对高能共振循环轨道进行分类;然后根据轨道类型构建二体开普勒椭圆轨道;再进一步计算圆型限制性三体问题下的地月高能共振循环轨道;最后根据能量、稳定性、时间周期、近地点高度和近月点高度对所计算出的地月高能共振循环轨道进行最优选择。仿真结果表明,本文所提出的方法简单有效,能够计算出共振比为5:2的地月高能共振循环轨道。     

Spherical harmonic series for derivatives of all orders of the gravitational potential of a planet and their application in satellite geodesy and space navigation

Series of spherical harmonics are constructed for derivatives of all orders of the gravitational potential of an arbitrary three-dimensional body, including the Earth, Moon and other planets. These series have a common structure, as simple as the potential itself. They differ from each other and from the series for the potential only by numerical coefficients of the spherical functions, by the degree of a numerical multiplier of the sum of double series, and by the limits of summation. The constructed series can be applied in solving many problems of celestial mechanics, satellite geodesy, and space navigation.     

Human Mission from Planet Earth: finding a rationale for exploration of the Moon and Mars

This paper advances scenarios for an evolutionary approach to the establishment of a Human Mission from Planet Earth involving exploration and utilization of the Moon and Mars. Of critical importance are the concepts of robotic–human and Moon–Mars synergies. The paper discusses the rationale variables that have an influence on types of space activities pursued and thus the policy that leads to particular scenarios. In this regard, the technological, scientific, and sociopolitical/socioeconomic impacts and consequences related to a Human Mission from Planet Earth are examined.     

嫦娥五号探测器多圈调相地月转移应急轨道设计与分析

针对嫦娥五号任务上升段末期火箭二级发动机可能出现的提前关机故障造成入轨半长轴偏差较大和中途修正速度增量超限问题,提出了多圈调相地月转移轨道应急控制策略.首先,分析了不同入轨半长轴偏差、中途修正时刻与中途修正速度增量消耗之间的关系;其次,针对半长轴偏差较大问题,基于微分改正算法与B平面参数,设计了解析窗口搜索与多圈调相地...     

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.