A mission template for exploration and damage mitigation of potential hazard of Near Earth Asteroids

The Apophis Exploratory and Mitigation Platform (AEMP) concept was developed as a prototype mission to explore and potentially deflect the Near Earth Asteroid (NEA) 99942 Apophis. Deflection of the asteroid from the potential 2036 impact will be achieved using a gravity tractor technique, while a permanent deflection, eliminating future threats, will be imparted using a novel albedo manipulation technique. This mission will serve as an archetypal template for future missions to small NEAs and could be adapted to mitigate the threat of collision with other potential Earth-crossing objects.     

Kinematics of relative motion of two space bodies in close almost circular orbits

The paper is dedicated to a qualitative investigation of relative motion and close convergences of two space bodies located in close almost circular orbits. This problem is topical due to the asteroid hazard originating from the NEA group asteroids located in the orbits close to that of the Earth. P.E. El’yasberg [1] considered similar problems in the 1960s in relation to Earth’s artificial satellites in close almost circular orbits.     

On analysis of close encounters of two cosmic bodies in near almost-circular orbits

This paper is devoted to the study of relative motion and close encounters of two cosmic bodies located in near almost-circular orbits. This problem is topical due to the asteroid hazard proceeding from the NEA group asteroids located in the near-Earth orbits. The (99942) Apophis asteroid, a representative of this group discovered in July 2004 by the Kitt Peak observatory (Arizona), is considered as an example.     

MarcoPolo-R: Near-Earth Asteroid sample return mission selected for the assessment study phase of the ESA program cosmic vision

This paper presents the sample return mission to a primitive Near-Earth Asteroid (NEA) MarcoPolo-R proposed to the European Space Agency in December 2010. MarcoPolo-R was selected in February 2011 with three other missions addressing different science objectives for the two-year Assessment Phase of the Medium-Class mission competition of the Cosmic Vision 2 program for launch in 2022. The baseline target of MarcoPolo-R is the binary NEA (175706) 1996 FG3, which offers an efficient operational and technical mission profile. A binary target also provides enhanced science return. The choice of a binary target allows several scientific investigations to occur more easily than through a single object, in particular regarding the fascinating geology and geophysics of asteroids. MarcoPolo-R will rendezvous with a primitive, organic-rich NEA, scientifically characterize it at multiple scales, and return a bulk sample to Earth for laboratory analyses. The MarcoPolo-R sample will provide a representative sample from the surface of a known asteroid with known geologic context, and will contribute to the inventory of primitive material that is probably missing from the meteorite collection. The MarcoPolo-R samples will thus contribute to the exploration of the origin of planetary materials and initial stages of habitable planet formation, to the identification and characterization of the organics and volatiles in a primitive asteroid and to the understanding of the unique geomorphology, dynamics and evolution of a binary asteroid that belongs to the Potentially Hazardous Asteroid (PHA) population.     

Asteroidal resources for space manufacturing

Earth-approaching asteroids (Apollos and Amors) may be competitive candidates as raw materials for space manufacturing. The total energy per unit mass required to transfer material from some of these bodies to high Earth orbit is comparable to that for lunar material. Recent optical studies suggest ordinary and carbonaceous chondrite compositions for these asteroids, with some containing large quantities of metallic iron and nickel, and others, carbon, hydrogen and nitrogen. Discoveries of several new candidate asteroids over the next few years will allow for a better selection of materials and mission possibilities. Material from one of these asteroids, either in raw or manufactured form, could be returned to the vicinity of the Earth by a solar-powered mass-driver reaction engine. With a requirement of ～60 shuttle flights, and with minimal development costs, an automated mission to a 200-m dia. (10⁷ ton) metal-rich asteroid could be carried out by a mass-driver tug assembled in low Earth orbit using shuttle tankage as reaction mass. Such a tug could, within a few years, move the asteroid into high Earth orbit for the manufacturing of ～ 20 satellite power stations using a portion of the asteroid itself as reaction mass. In the next few years over 100 asteroids in this size range could be discovered, orbits determined and composition types classified using existing earthbased and spaceborne search techniques.     

球形弹丸超高速斜撞击薄板的碎片云和侵彻特征仿真分析

低地球轨道航天器易受到微流星体及空间碎片的超高速撞击。相较于正撞击,斜撞击现象更加普遍、更具研究价值。文章采用Autodyn-3D数值模拟软件,利用光滑粒子流体动力学（smooth particle hydrodynamics, SPH）方法,模拟Al2017-T4球形弹丸超高速斜撞击Al2A12薄板的过程,开展弹丸撞击速度为3～6 km/s、撞击角度为0°～60°时的撞击特征仿真分析。结果表明:撞击角度对碎片云形貌与几何尺寸,以及穿孔大小和形状特征有显著影响;当撞击角度为30°～45°时会发生滑弹反溅现象,造成弹丸侵彻能力下降。研究结果可为超高速撞击防护结构的设计和改进提供支持。     

State propagation in an uncertain asteroid gravity field

Various spacecraft have been and will be sent to asteroids to characterize them. Generally, an asteroid's gravity field is very irregular and not accurately known when compared to the gravity field of a major planet, Earth in particular. It has been well studied that the irregularity significantly affects the trajectory of an orbiting spacecraft, and causes it to impact or to escape from the asteroid. Complementary to that, this paper focuses on the influence of the limited knowledge of this gravity field on the evolution of the spacecraft's orbit. It develops a general method by which this influence can be quantified. This method comprises specific Monte Carlo simulations with a discrete set of low-altitude orbits, taking into account the uncertainties in the gravity-field parameters. For illustration purposes, it is applied to two different asteroids. Already after three revolutions, the gravity-field uncertainties propagate to significant position uncertainties; this specifically holds for prograde orbits, and around the smaller asteroid. Applying this robust and accurate method helps mission designers and planners to assess the risk posed by gravity uncertainties, and take appropriate measures such as choosing the most favorable orbital geometries and/or lowering the orbit more slowly.     

One optimization problem for trajectories of spacecraft rendezvous mission to a group of asteroids

The optimization problem is considered for the trajectory of a spacecraft mission to a group of asteroids. The ratio of the final spacecraft mass to the flight time is maximized. The spacecraft is controlled by changing the value and direction of the jet engine thrust (small thrust). The motion of the Earth, asteroids, and the spacecraft proceeds in the central Newtonian gravitational field of the Sun. The Earth and asteroids are considered as point objects moving in preset elliptical orbits. The spacecraft departure from the Earth is considered in the context of the method of a point-like sphere of action, and the excess of hyperbolic velocity is limited. It is required sequentially to have a rendezvous with asteroids from four various groups, one from each group; it is necessary to be on the first three asteroids for no less than 90 days. The trajectory is finished by arrival at the last asteroid. Constraints on the time of departure from the Earth, flight duration, and final mass are taken into account in this problem.     

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.     

不同密度弹丸对水冰的超高速撞击成坑实验

为了研究冰冻天体表面撞击坑的形成与演化,开展了水冰的超高速撞击成坑实验。使用二级轻气炮发射1.0 mm直径的球形弹丸,以3 km/s、5 km/s和7 km/s速度对圆柱状冰块进行撞击。弹丸材料包括聚碳酸酯和不锈钢两种,冰块温度为253 K。实验观察到了不同弹丸和不同速度条件下,冰块中撞击坑的形貌特征。对撞击坑直径、深度和剖面形状进行了测量,并与文献中铝弹丸对水冰的撞击坑进行了比较分析。获得了水冰撞击坑特征随撞击参数的变化规律,结果表明：撞击坑直径和深度的主导机制不同,坑深主要由弹丸侵彻作用形成,而坑径主要由冰块的剥落所致;坑深比坑径具有更强的对于弹丸密度的依赖性,高密度弹丸撞击坑直径具有比低密度弹丸更强的对于撞击速度的依赖性;撞击坑体积与撞击能量成正比,高密度弹丸形成的撞击坑直径表现出“能量缩比”行为,而低密度弹丸形成的撞击坑直径表现出“动量缩比”行为。     

A plan for worldwide protection against asteroid impacts

Compelling evidence of a catastrophic asteroid impact on Earth 65 million years ago has given rise to international discussions on the likelihood, consequences and prevention of future impacts. An example plan, based on international cooperation and for discussion purposes only, is presented outlining an approach to study the problems of asteroid detection, laboratory experimentation, and defence.     

A method of controlling asteroid collision with the Earth

The planet Earth has endured unwelcome “visitations” of space rocks many times. NASA and agencies of other nations have proposed concepts on how asteroids, in possible collision with planet Earth, can be diverted. These methods range from impulsive techniques using explosives, conventional and nuclear, to the slow nudging action of a spacecraft with powerful thrust. A methods not described elsewhere in any research, as far as the author knows, is presented in this paper. The methods of electrostatics will be employed to show how the new deflection concept can be developed to avoid asteroid collision with Earth.     

Artificial spin-up and fragmentation of sub-kilometre asteroids

The article demonstrates the feasibility of artificially increase the spin rate of asteroids about 200 m in diameter beyond the limit in which they begin to disrupt. In the proposed concept a tethered satellite of less than a few tens of kilometres length anchored to the asteroid surface is employed as a mean to exchange angular momentum with the celestial body and increase its spin rate. Simple calculations based on angular momentum and energy conservation show that a 200 m diameter asteroid can be spun-up to critical rotation speed in less than one year with current technology.The scheme can be utilized as a unique scientific tool to characterize the asteroid internal structure and composition.     

Combining solar science and asteroid science with the space weather observation network (SWON)

The peculiarity of space weather for Earth orbiting satellites, air traffic and power grids on Earth and especially the financial and operational risks posed by damage due to space weather, underline the necessity of space weather observation. The importance of such observations is even more increasing due to the impending solar maximum. In recognition of this importance we propose a mission architecture for solar observation as an alternative to already published mission plans like Solar Probe (NASA) or Solar Orbiter (ESA). Based upon a Concurrent Evaluation session in the Concurrent Engineering Facility of the German Aerospace Center, we suggest using several spacecraft in an observation network. Instead of placing such spacecraft in a solar orbit, we propose landing on several asteroids, which are in opposition to Earth during the course of the mission and thus allow observation of the Sun's far side. Observation of the far side is especially advantageous as it improves the warning time with regard to solar events by about 2 weeks. Landing on Inner Earth Object (IEO) asteroids for observation of the Sun has several benefits over traditional mission architectures. Exploiting shadowing effects of the asteroids reduces thermal stress on the spacecraft, while it is possible to approach the Sun closer than with an orbiter. The closeness to the Sun improves observation quality and solar power generation, which is intended to be achieved with a solar dynamic system. Furthermore landers can execute experiments and measurements with regard to asteroid science, further increasing the scientific output of such a mission. Placing the spacecraft in a network would also benefit the communication contact times of the network and Earth. Concluding we present a first draft of a spacecraft layout, mission objectives and requirements as well as an initial mission analysis calculation.     

An autonomous optical guidance and navigation around asteroids

An impending demand for exploring the small bodies such as the comets and the asteroids envisioned the Japanese MUSES-C mission to the near Earth asteroid Nereus. An autonomous optical guidance and navigation strategy around the asteroid is discussed in this paper. Four major new schemes are dealt with here: They are (1) Aligned intercept guidance, (2) Strategic building of the flight phases, (3) Image processing of line-of-sight shift information instead of characteristic point tracking, and (4) Stability and accuracy analysis associated with the guidance and navigation strategies developed here. Some comprehensive numerical illustrations are also given to support them.     

Tether assisted near earth object diversion

Potential earth impact threats posed by asteroids have motivated researchers to find effective NEO diversion techniques. Several means to perturb the motion of an asteroid have been discussed in the literature. Attaching a long tether and ballast mass to the asteroid can effectively alter its trajectory. In this paper it is shown that by cutting the tether at an appropriate time the diversion can be enhanced. The instant of cutting the tether significantly affects the final orbit of the asteroid and thus the resulting deflection from the original path.     

Analysis of the orbital motion of the asteroid Apophis’ satellite

We have analyzed the orbital disturbed spacecraft motion near an asteroid. The equations of the asteroidocentric spacecraft motion have been used with regard to three perturbations from celestial bodies, the asteroid’s nonsphericity, and solar radiation pressure. It has been shown that the orbital parameters of the main spacecraft and a small satellite with a radio beacon can be selected such that the orbits are rather stable for a fairly long period of time, i.e., a few weeks for the main spacecraft with an orbit initial radius of ~0.5 km and a few years before approaching Apophis with the Earth in 2029, for a small satellite at an orbit initial radius of ~1.5 km. The initial orientation of the spacecraft orbital plane perpendicular to the sunward direction is optimal from the point of view of the stability of the spacecraft flight near an asteroid.     

Comparative investigation of methods for the numerical prediction of motion of asteroids that approach the Earth: Example of the 99942 Apophis asteroid

Using the 99942 Apophis asteroid (currently known as one of the most dangerous asteroids that is approaching the Earth) as an example, we estimate the error of predicting its motion with the use of several integrators over the time interval from 2012 to 2029. The minimum distance (and its error) between the Earth’s center and Apophis was estimated for the rendezvous moment on April 13, 2029. It is shown that this error for various integrators is comparable in the order of magnitude with the influence of certain components of the dynamic model of motion, such as, for example, the influence of harmonics of the Earth’s gravitational filed, solar-light pressure, the Jarkowski effect, etc.     

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。