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.     

Characterizing the near-earth object hazard and its mitigation

Within observational constraints and analytic orbit determinations, potential NEO hazards and mitigations are characterized in terms of orbit displacements to establish (arbitrary) “safe” closest approach distances and corresponding energies that must be externally applied to achieve appropriate orbit displacements from the Earth. Required orbital velocity changes depend on projected closest Earth approach distances and time to (near) impact. Energy to achieve orbital displacement depends on NEO mass, required orbital velocity change, and the energy–momentum coupling coefficient. Errors in these parameters introduce uncertainties into hazard index and mitigation procedures. Hazard avoidance levels and mitigation indices for nine near-Earth asteroids, including 1997 XF₁₁ and 1999 AN₁₀, with non-zero Earth-impact probabilities are computed as examples of the proposed methodology, generating insight into the dilemma of predicting near impacts. This zeroth order approximation should not be construed as solving an orbital mechanics problem, nor establishing a particular set of criteria for mitigation action, but rather as a “survival index”.     

Horseshoe orbits in the Earth–Moon system

Horseshoe orbits in the restricted three-body problem have been mostly considered in the Sun–Jupiter system and, in recent years, in the Sun–Earth system. Here, these orbits have been used to find asteroids that have orbits of this kind. We have built a planar family of horseshoe orbits in the Earth–Moon system and determined the points of planar and 1/1 vertical resonances on this family. We have presented examples of orbits generated by these spatial families.     

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。     

Low cost planetary exploration: surrey lunar minisatellite and interplanetary platform missions

In order to meet the growing global requirement for affordable missions beyond Low Earth Orbit, two types of platform are under design at the Surrey Space Centre. The first platform is a derivative of Surrey's UoSAT-12 minisatellite, launched in April 1999 and operating successfully in-orbit. The minisatellite has been modified to accommodate a propulsion system capable of delivering up to 1700 m/s delta-V, enabling it to support a wide range of very low cost missions to LaGrange points, Near-Earth Objects, and the Moon. A mission to the Moon - dubbed “MoonShine” - is proposed as the first demonstration of the modified minisatellite beyond LEO. The second platform - Surrey's Interplanetary Platform - has been designed to support missions with delta-V requirements up to 3200 m/s, making it ideal for low cost missions to Mars and Venus, as well as Near Earth Objects (NEOs) and other interplanetary trajectories. Analysis has proved mission feasibility, identifying key challenges in both missions for developing cost-effective techniques for: spacecraft propulsion; navigation; autonomous operations; and a reliable safe mode strategy. To reduce mission risk, inherently failure resistant lunar and interplanetary trajectories are under study. In order to significantly reduce cost and increase reliability, both platforms can communicate with low-cost ground stations and exploit Surrey's experience in autonomous operations. The lunar minisatellite can provide up to 70 kg payload margin in lunar orbit for a total mission cost US$16–25 M. The interplanetary platform can deliver 20 kg of scientific payload to Mars or Venus orbit for a mission cost US$25–50 M. Together, the platforms will enable regular flight of payloads to the Moon and interplanetary space at unprecedented low cost. This paper outlines key systems engineering issues for the proposed Lunar Minisatellite and interplanetary Platform Missions, and describes the accommodation and performance offered to planetary payloads.     

On plane oscillations of a pendulum with variable length suspended on the surface of a planet’s satellite

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We discuss how the change in length of a pendulum can be used to compensate its oscillations. We wrote equations of motion, indicated a rule for the change in length of a pendulum, at which it has equilibrium positions relative to the coordinate system rotating together with the Moon and Earth. We study the necessary conditions for the stability of these motions. Chaotic dynamics of the pendulum is studied numerically and analytically.     

Innovations for competitiveness: European views on “better-faster-cheaper”

The paper elaborates on “ lessons learned” from two recent ESA workshops, one focussing on the role of Innovation in the competitiveness of the space sector and the second on technology and engineering aspects conducive to better, faster and cheaper space programmes. The paper focuses primarily on four major aspects, namely:

1. a) the adaptations of industrial and public organisations to the global market needs;

2. b) the understanding of the bottleneck factors limiting competitiveness;

3. c) the trends toward new system architectures and new engineering and production methods;

4. d) the understanding of the role of new technology in the future applications.

Under the pressure of market forces and the influence of many global and regional players, applications of space systems and technology are becoming more and more competitive. It is well recognised that without major effort for innovation in industrial practices, organisations, R&D, marketing and financial approaches the European space sector will stagnate and loose its competence as well as its competitiveness. It is also recognised that a programme run according to the “better, faster, cheaper” philosophy relies on much closer integration of system design, development and verification, and draws heavily on a robust and comprehensive programme of technology development, which must run in parallel and off-line with respect to flight programmes.

A company's innovation capabilities will determine its future competitive advantage (in time, cost, performance or value) and overall growth potential. Innovation must be a process that can be counted on to provide repetitive, sustainable, long-term performance improvements. As such, it needs not depend on great breakthroughs in technology and concepts (which are accidental and rare). Rather, it could be based on bold evolution through the establishment of know-how, application of best practices, process effectiveness and high standards, performance measurement, and attention to customers and professional marketing. Having a technological lead allows industry to gain a competitive advantage in performance, cost and opportunities. Instrumental to better competitiveness is an R&D effort based on the adaptation of high technology products, capable of capturing new users, increasing production, decreasing the cost and delivery time and integrating high level of intelligence, information and autonomy. New systems will have to take in to account from the start what types of technologies are being developed or are already available in other areas outside space, and design their system accordingly. The future challenge for “faster, better, cheaper” appears to concern primarily “cost-effective”, performant autonomous spacecraft, “cost-effective”, reliable launching means and intelligent data fusion technologies and robust software serving mass- market real time services, distributed via EHF bands and Internet.

In conclusion, it can be noticed that in the past few years new approaches have considerably enlarged the ways in which space missions can be implemented. They are supported by true innovations in mission concepts, system architecture, development and technologies, in particular for the development of initiatives based on multi-mission mini-satellites platforms for communication and Earth observation missions. There are also definite limits to cost cutting (such as lowering heads counts and increasing efficiency), and therefore the strategic perspective must be shifted from the present emphasis on cost-driven enhancement to revenue-driven improvements for growth. And since the product life-cycle is continuously shortening, competitiveness is linked very strongly with the capability to generate new technology products which enhance cost/benefit performance.     

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...     

The use of three-impulse transfer to insert the spacecraft into the high Moon Artificial Satellite orbits

The problem of the optimal spacecraft’s insertion from the Earth into the high circular polar Moon Artificial Satellite’s orbit (MAS) with a radius of 4000–8000 km has been investigated. A comparison of single- and three-impulse insertion schemes has been performed. The analysis was made taking into account the disturbances from the lunar gravity field harmonics and the gravity fields of the Earth and the Sun, as well as the engine’s limited thrust. It has been shown that the three-impulse transfer from the initial selenocentric hyperbola of the approach into the considered final high MAS orbit is noticeably better with respect to the final mass than the ordinary single-impulse deceleration. The control parameters that implement this maneuver and provide nearly the same energy expenses as in the Keplerian case have been presented. It was found that, in contrast to the Keplerian case, in the considered case of the real gravity field, there is the optimal maximum distance of the maneuver. Recently, the Moon exploration problem became actual again.     

Potential evolution of an international moon base programme

The Moon is a major target in expanding human activity in Space. President Bush has called for a Space Exploration Initiative. European participation may depend on achieving an affordable programme and identifying distinct elements for non-U.S. participation. Affordability requires that all participants can influence the “cost to user” of Base operations. If lunar activity is to evolve towards resource exploitation, there will need to be a progressive reduction in operating costs. European interest would prefer participation that allowed longer-term independent interests. The paper addresses how non-U.S. agencies could contribute valuable elements to an International Moon Base while meeting three criteria:

• — Keep a core infrastructure under U.S. control.

• — Avoid a total reliance by the partner on U.S. services.

• — Allow the partner to evolve towards an eventual, semi-autonomous or autonomous capability.

The paper illustrates possible implications of meeting these constraints through “mini infrastructures” combining several elements to form a working architecture. It is concluded that any European participation in an International Moon Base Programme should contain both Space transport and surface elements.     

On the strategy of space station injection in the point of Earth — Moon Libration / way of making the asteroid patrol/

One of the most important problem in the ecological area that stay for humanity is the problem of prevention Earth and asteroids collision. The danger of such collision isn't realized of the general public. But we know that on average twice in the every century the Earth comes into collision with the large celestial bodies (for example Tungussky or Arizonsky meteorites). The incidence of such meteorite in density population region of the Earth will simulate the ecumenical catastrophe. Much more seldom the Earth experiences collision with the particularly large celestial bodies. In accordance with one of the hypotheses namely the collision Earth with such body 65,000,000 years ago leads to the global change of Earth biosphere (in particular to the extinction of dinosaurs).Now we are able to stave off or at least to forewarn of this danger. One of the way for that is making the specific space station - asteroid patrol. Such the station will be able to track the approaching celestial bodies and perhaps (on second stage) to attempt altering its trajectory (for example with directional thermonuclear explosions)Some of the expedient points in the Space for the asteroid patrol's placing are the librations' points of the Earth - Moon system. In the report the preliminary results of analysis the problem of space station's taking into the libration's point are presented. For this taking it is suggested the electric jet propulsion to use.     

Autonomous optical navigation for orbits around Earth–Moon collinear libration points

The analysis of optical navigation in an Earth–Moon libration point orbit is examined. Missions to libration points have been winning momentum during the last decades. Its unique characteristics make it suitable for a number of operational and scientific goals. Literature aimed to study dynamics, guidance and control of unstable orbits around collinear libration points is vast. In particular, several papers deal with the optimisation of the Δv budget associated to the station-keeping of these orbits. One of the results obtained in literature establishes the critical character of the Moon–Earth system in this aspect. The reason for this behaviour is twofold: high Δv cost and short optimal manoeuvre spacing. Optical autonomous navigation can address the issue of allowing a more flexible manoeuvre design. This technology has been selected to overcome similar difficulties in other critical scenarios. This paper analyses in detail this solution. A whole GNC system is defined to meet the requirements imposed by the unstable dynamic environment. Finally, a real simulation of a spacecraft following a halo orbit of the L2 Moon–Earth system is carried out to assess the actual capabilities of the optical navigation in this scenario.     

Research and development of On-Board Processor for advanced mobile satellite communications

This paper describes the research and development of an On-Board Processor (OBP) for a mobile satellite communications system using a geostationaly satellite. The system, which based on Multi-Carrier Time Division Multiple Access, can realize high performance and facilitate the use of miniature hand-held mobile Earth terminals.

Our research and development results indicate as follows.

1. 1) The simultaneous-slot switching method will be the most suitable for an on-board base-band switching with consideration of traffic capacity, time delay, and hardware scale.

2. 2) The OBP performs channel exchange with regeneration that contributes to a reduction in the size of mobile terminals because of the coding gain.

3. 3) Many kinds of Application Specific Integrated Circuits are designed to realize large channel capacity and reduce the size and power consumption of the OBP. These OBP design can increase the channel capacity, which is equivalent to in 5.6kbps voice channel, up to over 500 channels within 5MHz frequency band

Some results are applied to the OBP being developed for the Japanese Engineering Test Satellite VII (ETS-VB).     

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.     

Transfer orbits to/from the Lagrangian points in the restricted four-body problem

The well-known Lagrangian points that appear in the planar restricted three-body problem are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L₁, L₂ and L₃) are always unstable and the triangular points (L₄ and L₅) are stable in the present case studied (Earth–Sun system). They are all very good points to locate a space-station, since they require a small amount of ΔV (and fuel), the control to be used, for station-keeping. The triangular points are especially good for this purpose, since they are stable equilibrium points.In this paper, the planar restricted four-body problem applied to the Sun–Earth–Moon–Spacecraft is combined with numerical integration and gradient methods to solve the two-point boundary value problem. This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Earth–Sun system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth.The dynamics given by the restricted four-body problem is used to obtain the trajectory of the spacecraft, but not the position of the equilibrium points. Their position is taken from the restricted three-body model. The goal to use this model is to evaluate the perturbation of the Sun in those important trajectories, in terms of fuel consumption and time of flight. The solutions will also show how to apply the impulses to accomplish the transfers under this force model.The results showed a large collection of transfers, and that there are initial conditions (position of the Sun with respect to the other bodies) where the force of the Sun can be used to reduce the cost of the transfers.     

Rosetta: The ESA comet rendezvous mission

Rosetta was selected in November 1993 for the ESA Cornerstone 3 mission, to be launched in 2003, dedicated to the exploration of the small bodies of the solar system (asteroids and comets). Following this selection, the Rosetta mission and its spacecraft have been completely reviewed: this paper presents the studies performed the proposed mission and the resulting spacecraft design.

Three mission opportunities have been identified in 2003–2004, allowing rendezvous with a comet. From a single Ariane 5 launch, the transfer to the comet orbit will be supported by planetary gravity assists (two from Earth, one from Venus or Mars); during the transfer sequence, two asteroid fly-bys will occur, allowing first mission science phases. The comet rendezvous will occur 8–9 years after launch; Rosetta will orbit around the comet and the main science mission phase will take place up to the comet perihelion (1–2 years duration).

The spacecraft design is driven (i) by the communication scenario with the Earth and its equipment, (ii) by the autonomy requirements for the long cruise phases which are not supported by the ground stations, (iii) by the solar cells solar array for the electrical power supply and (iv) by the navigation scenario and sensors for cruise, target approach and rendezvous phases. These requirements will be developed and the satellite design will be presented.     

Planetary resources and astroecology. Planetary microcosm models of asteroid and meteorite interiors: electrolyte solutions and microbial growth--implications for space populations and panspermia

Planetary microcosms were constructed using extracts from meteorites that simulate solutions in the pores of carbonaceous chondrites. The microcosms were found to support the growth of complex algal and microbial populations. Such astroecology experiments demonstrate how a diverse ecosystem could exist in fluids within asteroids, and in meteorites that land on aqueous planets. The microcosm solutions were obtained by extracting nutrient electrolytes under natural conditions from powders of the Allende (CV3) and Murchison (CM2) meteorites at low (0.02 g/ml) and high (10.0 g/ml) solid/solution ratios. The latter solutions contain > 3 mol/L electrolytes and about 10 g/L organics, that simulate natural fluids in asteroids during aqueous alteration and in the pores of meteorites, which can help prebiotic synthesis and the survival of early microorganisms. These solutions and wet solids were in fact found to support complex self-sustaining microbial communities with populations of 4 x 10(5) algae and 6 x 10(6) bacteria and fungi for long periods (> 8 months). The results show that planetary microcosms based on meteorites can: assay the fertilities of planetary materials; identify space bioresources; target astrobiology exploration; and model past and future space-based ecosystems. The results show that bioresources in the carbonaceous asteroids can sustain a biomass of 10(18) kg, comprising 10(32) microorganisms and a human population of 10(14). The results also suggest that protoplanetary nebulae can support and disperse microorganisms and can be therefore effective environments for natural and directed panspermia.     

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.     

Human roles in future space operations.

Mankind has evolved in the biosphere from essentially another animal to the level that his industries and societies are powerful components of the life-cycles of Earth. Terrestrial industrial experience can be extended to the use of matter from the Moon and other non-terrestrial sources to create permanent habitats and industry in space. Space stations in low Earth orbit and small bases on the Moon can be the foci of early space industries for learning how to grow in space with local resources. Several near term and long range research topics appropriate to permanent human occupancy of space are reviewed.     

Optimal ballistically captured Earth–Moon transfers

The optimality of a low-energy Earth–Moon transfer terminating in ballistic capture is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the problem is then modified to fix the time of transfer, allowing for optimal multi-impulse transfers. The tradeoff between transfer time and fuel cost is shown for Earth–Moon ballistic lunar capture transfers.