On the asteroid hazard

The concept of “space patrol” is considered, aimed at discovering and cataloging the majority of celestial bodies that constitute a menace for the Earth [1, 2]. The scheme of “optical barrier” formed by telescopes of the space patrol is analyzed, requirements to the observation system are formulated, and some schemes of sighting the optical barrier region are suggested (for reliable detection of the celestial bodies approaching the Earth and for determination of their orbits). A comparison is made of capabilities of electro-jet engines and traditional chemical engines for arrangement of patrol spacecraft constellation in the Earth’s orbit.     

A model for the evolution of the on-orbit man-made debris environment

A model for the evolution of the low Earth orbit man-made debris population is presented and the results of several test cases discussed. Debris sources include normal operations in space, explosions occurring on spacecraft in orbit, and collisions between objects in orbit; the stochastic occurrence of these deposition events is modeled using Monte Carlo techniques. A technique for discriminating between objects populating long-life vs rapid-decay orbits is discussed and applied to the analysis of debris contributions from collisions of comparable sized objects. In varying degrees, each of the cases presented indicate there is cause for concern for spacecraft and space operations from the 1990s onward-man-made debris will play a role which may vary from presenting a considerable hazard to certain operations or certain spacecraft to effectively prohibiting the use of certain spaceccraft or space operations.     

Pressing Issues of the Day in Studying Deep Space

Two problems in studying deep space are discussed that are, in the author's opinion, the most important. The first is soil sampling from the smaller bodies of the Solar System, such as the Martian satellite Phobos and asteroids of groups C and S of the Main Asteroid Belt. This soil (so-called primordial substance) can help to elucidate some problems of the Solar System's formation; in particular, to construct a reliable model of the internal structure of the Earth. The second problem is to reveal all sufficiently large asteroids penetrating inside the Earth's orbit and to catalog those asteroids that are hazardous from the viewpoint of collision with the Earth. To this end, it is suggested to launch five or six Earth-orbiting spacecraft with telescopes capable of recording objects down to a brightness of 22– 25 ^m . It is pointed out that both problems can be solved in the near future using comparatively cheap standardized space vehicles launched into near-Earth orbits by the Soyuz carrier rocket and boosted further by electro-jet engines of small thrust.     

嫦娥五号平动点拓展任务轨道方案研究

中国嫦娥五号探测器成功实现月球采样返回任务,为最大限度利用任务资源,研究了利用嫦娥五号轨道器的平动点拓展任务轨道方案,设计了平动点轨道及其转移轨道.首先,给出了任务轨道设计的轨道动力学模型,包括圆型限制性三体问题模型和精确力模型.其次,基于嫦娥二号和嫦娥5T1平动点拓展任务设计经验,介绍了平动点轨道直接转移与入轨等轨道...     

A space based radar on a micro-satellite for in-situ detection of small orbital debris

The increase in the number of satellites in the Near Earth Orbit is exponential. The consequent increase in pollution of the orbital environment is of growing concern to the international community. There are currently only two observation systems available for measurement of orbital debris. Ground based radar and telescopes can detect objects larger than about 7 cm. Passive space based systems provide an accurate statistical estimation of flux for debris smaller than about 0.1 mm in size. Consequently, there is no way of obtaining information about debris in the millimeter-size range. Considering that the relative speed between objects in space is commonly in the km/s range, millimeter sized debris carry enough energy to be deadly to astronauts or to totally destroy the functioning of any satellite. Then National space agencies have recommended launching orbital spacecraft carrying debris detection experiments for gaining a better understanding of small debris.CNES (the French Space Agency) is developing a new family of micro-satellites, that will make possible to put into orbit a totally new system of radar that could measure in-situ flux of debris. We present results of this system analysis, which would cumulate the advantages of both ground-based radar and in orbit passive experiments.The proposed method for detection is quite original and allows the radar to act like a band-pass filter with respect to the debris diameter. The optimum frequency is shown to be in the Ka-band. Two points are critical in the definition of the radar: the average power available and the false alarm probability in the detection criterion. Therefore, we present a special receiver chain in order to optimize the signal-to-noise ratio. The estimate of the radial velocity through Doppler frequency measurement may be used to discriminate orbital debris from meteoroids. This system could be built today using an existing Continuous Wave amplifier. Several hundreds of objects per year could be detected yielding an accurate statistical estimation.The orbital debris radar would be a major contribution to our knowledge of millimeter sized debris. This experiment would contribute to making the current models more accurate at all inclinations. The micro-satellite concept would make the orbital debris radar mission cheap enough for considering a constellation of such satellites.     

航天器碰撞分析方法研究

作为航天器碰撞与规避控制方法研究课题的一部分,为此分别建立了航天器及其它空间目标的轨道确定方法;并在此基础上,提出了可能与航天器碰撞的其它空间编目目标的初选准则和碰撞预报算法。实测数据计算表明,该方法对于航天器轨道设计以及飞行安全性分析等均是实用可行的。     

Trajectory correction of the Spektr-R spacecraft motion

The results of refining the parameters of the Spektr-R spacecraft (RadioAstron project) motion after it was launched into the orbit of the Earth’s artificial satellite in July 2011 showed that, at the beginning of 2013, the condition of staying in the Earth’s shadow was violated. The duration of shading of the spacecraft exceeds the acceptable value (about 2 h). At the end of 2013 to the beginning of 2014, the ballistic lifetime of the spacecraft completed. Therefore, the question arose of how to correct the trajectory of the motion of the Spektr-R satellite using its onboard propulsion system. In this paper, the ballistic parameters that define the operation of onboard propulsion system when implementing the correction, and the ballistic characteristics of the orbital spacecraft motion before and after correction are presented.     

Optimal flights to near-Earth asteroid

The spacecraft flights to the Near-Earth asteroid in order to give an impact influence on the asteroid, correct its orbit and prevent the asteroid’s collision with the Earth are analyzed.In the first part, the impulse flights are analyzed in the Lambert approach. There are determined the optimal trajectories maximizing the asteroid deviation from the Earth.In the second part, the flights with the chemical and electric-jet engines are analyzed. The high thrust is used to launch the spacecraft from the geocentric orbit, and the low thrust is applied for the heliocentric motion. On the base of optimal impulse transfer, the optimal low thrust trajectories are determined using Pontryagin maximum principle.The numerical results are given for the flight to the asteroid Toutatis. Parameters of the spacecraft impact on the asteroid are determined. The asteroid deviation from the Earth caused by the spacecraft influence is presented.     

Space System for Detecting Hazardous Celestial Bodies Approaching Earth from the Daytime Sky (<Emphasis Type="Italic">SODA</Emphasis>)

The concept of the System for the Observation of Daytime Asteroids (SODA system) has been developed, the purpose of which is to detect at least 95% of hazardous celestial bodies larger than 10 m in size that fly towards Earth from the Sun side. Spacecraft, equipped with the optimum version, which has three wide-angle optical telescopes of small aperture (20–30 cm) will be placed in a halo orbit around the L₁ libration point of the Sun–Earth system. This will provide a warning on the hazardous object, approaching from the Sun side, and will allow one to determine the orbit and the point of body entering Earth atmosphere to a sufficient accuracy, at least a few hours before the body collides with Earth. The requirements to the system are considered, the results of a preliminary design of the set of instruments have been described, the areas of visibility are calculated, and the versions of data transmission modes have been proposed. It has been shown that, in cooperation with other (particularly ground-based) projects aimed to observing objects flying from the night sky side, it is possible to detect in advance all hazardous bodies in the near-Earth space larger than 10 m in size that approach Earth from almost any direction.     

Application of periodic solutions of three-dimensional three-body problem to designing the orbit of a space telescope

A method of constructing three-dimensional orbits with a necessary evolution in the system the Sun — (Earth + Moon) is described. The orbit (promising from the viewpoint of solving formulated research problems) of the Millimetron spacecraft is suggested. Feasibility of such an orbit is demonstrated, as well as a possibility to observe with its help the majority of objects on the celestial sphere and to transmit the data to the Earth.     

太阳电池阵表面充电反向电位梯度的地面模拟

太阳电池阵等部件由于其表面介质的高二次电子发射及光电子发射特性,使得其在轨表面充电典型表现为反向电位梯度（inverted potential gradient, IPG）。为了评估航天器部组件在轨的表面充电风险,需要研究IPG的特点及在地面模拟IPG的方法。文章通过分析地球中高轨道与低轨道空间等离子体环境中表面充电的特点,提出了地面模拟IPG表面充电的方法,并给出典型试验结果。推荐中高轨道利用电子枪或紫外源、低轨道利用冷稠等离子体源模拟表面充电IPG;模拟过程中为了建立IPG,试样基底导电部位需要悬浮且有直流负偏压电源驱动;模拟IPG时需要针对试样尺度进行缩比补偿;文章给出的方法可用于一般太阳电池阵或其他在轨充电会产生IPG的试样开展地面模拟及静电放电防护性能评价试验。     

Halo orbits in the vicinity of the L 2 libration point in the Sun-Earth system

Methods are proposed for constructing the orbits of spacecraft remaining for long periods of time in the vicinity of the L ₂ libration point in the Sun-Earth system (so-called halo orbits), and the trajectories of uncontrolled flights from low near-Earth orbits to halo orbits. Halo orbits and flight trajectories are constructed in two stages: A suitable solution to a circular restricted three-body problem is first constructed and then transformed into the solution for a restricted four-body problem in view of the real motions of the Sun, Earth, and Moon. For a halo orbit, its prototype in the first stage is a combination of a periodic Lyapunov solution in the vicinity of the L ₂ point and lying in the plane of large-body motion, with the solution for the linear second-order system describing small deviations of the spacecraft from this plane along the periodic solution. The desired orbit is found as the solution to the three-body problem best approximating the prototype in the mean square. The constructed orbit serves as a similar prototype in the second stage. In both stages, the approximating solution is constructed by continuation along a parameter that is the length of the approximation interval. Flight trajectories are constructed in a similar manner. The prototype orbit in the first stage is a combination of a solution lying in the plane of large-body motion and a solution for a linear second-order system describing small deviations of the spacecraft from this plane. The planar solution begins near the Earth and over time tends toward the Lyapunov solution existing in the vicinity of the L ₂ point. The initial conditions of both prototypes and the approximating solutions correspond to the spacecraft’s departure from a low near-Earth orbit at a given distance, perigee, and inclination.     

Protecting the GEO environment: policies and practices

The geosynchronous orbital regime has long been recognized as a unique space resource, dictating special measures to ensure its continuing use for future generations. During the past 20 yr a variety of national and international policies have been developed to preserve this environment. A review of current practices involving the deployment and disposal of geosynchronous spacecraft, associated upper stages and apogee kick motors, and geosynchronous orbit transfer objects indicates both positive and negative trends. Most spacecraft operators are indeed performing end-of-mission maneuvers, but the boost altitudes normally fall short of policy guidelines. Russia, a major operator in geosynchronous orbit, maneuvers only 1 in 3 spacecraft out of the region, while China has never retired a spacecraft above GEO. The viability of voluntary protection measures for this regime depends upon the responsible actions of the aerospace community as a whole.     

木星探测器轨道计算中的动力学

针对木星探测任务中轨道计算所面临的轨道动力学问题进行研究。首先，对木星探测轨道计算中涉及的时空参考系进行概述，比较了木星动力学时(TDJ)与质心动力学时(TDB)的差异；其次，对木星的定向参数模型及转换关系进行描述，给出了木星天球参考系与固联参考系的转换关系；再次，对木星探测器定轨计算中所需考虑的动力学模型进行讨论，提供了各类摄动加速度计算所需的公式；最后，对木星探测器JUNO的星历数据进行动力学拟合，检验了动力学模型的正确性。     

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.     

On the planar inertial motion of a system of three coupled bodies

Numerous papers are devoted to studying the motion of a system (coupling) of two bodies in the Earth’s satellite orbit ([1–4] and others). The problem on the planar inertial motion of three bodies, coupled by a non-extensible weightless string having the form of an unfastened chain, is considered in the paper. Such a configuration can be represented, for example, by a system of two coupled spacecraft rotating around their common center of mass (in order to simulate the gravity force) in long-term space missions, when the third body (the lift) is located on a connecting cable. The bodies are considered to be the material points (particles).     

Design of optimal earth pole-sitter transfers using low-thrust propulsion

Recent studies have shown the feasibility of an Earth pole-sitter mission using low-thrust propulsion. This mission concept involves a spacecraft following the Earth's polar axis to have a continuous, hemispherical view of one of the Earth's poles. Such a view will enhance future Earth observation and telecommunications for high latitude and polar regions. To assess the accessibility of the pole-sitter orbit, this paper investigates optimum Earth pole-sitter transfers employing low-thrust propulsion. A launch from low Earth orbit (LEO) by a Soyuz Fregat upper stage is assumed after which solar electric propulsion is used to transfer the spacecraft to the pole-sitter orbit. The objective is to minimize the mass in LEO for a given spacecraft mass to be inserted into the pole-sitter orbit. The results are compared with a ballistic transfer that exploits manifold-like trajectories that wind onto the pole-sitter orbit. It is shown that, with respect to the ballistic case, low-thrust propulsion can achieve significant mass savings in excess of 200 kg for a pole-sitter spacecraft of 1000 kg upon insertion. To finally obtain a full low-thrust transfer from LEO up to the pole-sitter orbit, the Fregat launch is replaced by a low-thrust, minimum time spiral, which provides further mass savings, but at the cost of an increased time of flight.     

Magnetobraking for Mars return vehicles

It is proposed that magnetobraking may be used to dissipate hyperbolic excess velocity from a spacecraft returning from Mars to Earth orbit. In magnetobraking, an electrodynamic tether is deployed from the spacecraft. The Earth's magnetic field produces a force on electrical current in the tether, which can be used to either brake or accelerate the spacecraft without expenditure of reaction mass. The peak acceleration on the Mars return is 0.007 m/s², and the amount of braking possible is dependent on the density and current-carrying capacity of the tether, but is independent of length. Since energy is produced as the spacecraft velocity decreases, no on-board power source is required. As the spacecraft approaches the Earth, the magnetic field increases and the power produced by the tether increases, reaching a maximum of about 800 W per kg of spacecraft mass at closest approach.     

Optimization of transfer trajectories to the Apophis asteroid for spacecraft with high and low thrust

The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid’s satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft’s hyperbolic velocity “at infinity” during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft’s final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.     

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.