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.     

线性相对运动的正切拦截和正切交会轨道研究

针对冲量方向与追踪器速度方向相同的正切轨道问题,用线性相对运动方程研究了正切于初始轨道和正切于目标轨道的共面轨道拦截和轨道交会问题。得到初始和终端时刻的相对速度向量的解析表达式,定义了两个关于目标真近点角的单变量函数,于是正切拦截和正切交会问题等价于这两个函数分别等于零,最后用割线法求解这两个函数的数值解。根据能量最优要求,考虑初始漂移段,分析了一个周期内的最佳初始正切冲量点。仿真结果校验了本文提出的方法。     

Estimation of the determination accuracy of orbit parameters of the apophis asteroid from measurement results

An analysis of the existing astrometric and radar observations of the Apophis asteroid is performed. On the basis of this analysis, characteristics of future measurements of the asteroid orbit and limitation on their conduction are accepted. A proposed launching of a spacecraft to the asteroid in order to obtain high-accuracy measurements of its distance and radial velocity is also considered. Trajectories of the flight to the asteroid in 2012–2022 are studied. Estimates of the accuracy of the Apophis position determination at various sets of both available and planned measurements at various numbers of determined parameters are obtained. The method of estimating accuracy is similar to that used in [1] for the Vega project.     

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.     

Reachable domain of spacecraft with a single tangent impulse considering trajectory safety

The reachable domain of the two-body transfer orbit with a single upper-bounded tangent impulse is studied. Three cases are analyzed for either the magnitude of the tangent impulse or the initial impulse point being free, or both being free. For a fixed impulse magnitude and a free initial impulse point, the initial orbit is proved to be one of the envelopes of the reachable domain. Moreover, the trajectory safety for the transfer orbit requires a lower bound on the perigee altitude and an upper bound on the apogee altitude. Then the ranges of the impulse magnitude and the initial true anomaly can be obtained by solving quadratic and cubic inequalities, respectively. If both constraints are required for an arbitrary impulse point, the range of the impulse magnitude is obtained with impulses at the perigee and the apogee. Several numerical examples with different eccentricities are provided to show the geometry of the reachable domain and to verify the proposed method.     

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.     

Rosetta visits asteroid (21)Lutetia

The International Rosetta Mission, cornerstone of the European Space Agency Scientific Programme, was launched on 2nd March 2004 to its 10 years journey to comet Churyumov–Gerasimenko. Rosetta will reach the comet in summer 2014, orbit it for about 1.5 years down to distances of a few Kilometres and deliver the Lander Philae onto its surface. After its successful asteroid fly-by in September 2008, Rosetta came back to Earth, for the final gravity acceleration towards its longest heliocentric orbit, up to a distance of 5.3 AU. It is during this phase that Rosetta crossed for the second time the main asteroids belt and performed a close encounter with asteroid (21)Lutetia on the 10th of July 2010 at a distance of ca. 3160 km and a relative velocity of 15 km/s. The payload complement of the spacecraft was activated to perform highly valuable scientific observations. The approach phase to the celestial body required a careful and accurate optical navigation campaign that will prove to be useful also for the comet approach phase. The experience gained with first asteroid flyby in 2008 was fed back into the operations definition and preparation for this highly critical phase; this concerns in particular the operations of the navigation camera for the close-loop autonomous asteroid tracking and of the main scientific camera for high resolution imaging. It was shortly after the flyby that Rosetta became the solar-powered spacecraft to have flown furthest from the Sun (>2.72 AU). This paper presents the activities carried out and planned for the definition, preparation and implementation of the asteroid flyby mission operations, including the test campaign conducted to improve the performance of the spacecraft and payload compared to the previous flyby. The results of the flyby itself are presented, with the operations implemented, the achieved performance and the lessons learned.     

High-resolution simulations of the final assembly of Earth-like planets. 2. Water delivery and planetary habitability

The water content and habitability of terrestrial planets are determined during their final assembly, from perhaps 100 1,000-km "planetary embryos " and a swarm of billions of 1-10-km "planetesimals. " During this process, we assume that water-rich material is accreted by terrestrial planets via impacts of water-rich bodies that originate in the outer asteroid region. We present analysis of water delivery and planetary habitability in five high-resolution simulations containing about 10 times more particles than in previous simulations. These simulations formed 15 terrestrial planets from 0.4 to 2.6 Earth masses, including five planets in the habitable zone. Every planet from each simulation accreted at least the Earth's current water budget; most accreted several times that amount (assuming no impact depletion). Each planet accreted at least five water-rich embryos and planetesimals from the past 2.5 astronomical units; most accreted 10-20 water-rich bodies. We present a new model for water delivery to terrestrial planets in dynamically calm systems, with low-eccentricity or low-mass giant planets-such systems may be very common in the Galaxy. We suggest that water is accreted in comparable amounts from a few planetary embryos in a " hit or miss " way and from millions of planetesimals in a statistically robust process. Variations in water content are likely to be caused by fluctuations in the number of water-rich embryos accreted, as well as from systematic effects, such as planetary mass and location, and giant planet properties.     

Neutralization of negative electric charge of a satellite by ionospheric plasma ions

The dynamics of the process of neutralization of a satellites negative electric charge by the charge of a layer of positive ions of ionospheric plasma is investigated. The changes in the electric field strength, as well as in the velocity and density of plasma ions, are obtained depending on the initial position of a particle and the distance to the satellites surface. It is found that under the conditions of accepted approximations, as the time grows unlimitedly, the satellites charge tends to zero but does not reach this value. The time during which the satellites electric charge decreases in magnitude as many times as specified is determined. It is shown that the negative charge of a satellite and the charge of a layer of plasma ions can form a structure of a double charged layer type whose lifetime is much longer than the time of its formation.Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 1, 2005, pp. 9–18.Original Russian Text Copyright © 2005 by Fedorov.     

远程导引脉冲变轨方案的有限推力修正

对远程导引脉冲变轨方案的有限推力修正进行了研究。将多脉冲变轨方案设计结果转换为有限推力式并进行修正,以消除转换误差和摄动模型误差。分析了由转换算法和摄动模型产生的初值误差,比较了不同工况下的修正效果。算例表明:将初始多脉冲变轨方案转换为有限推力后进行修正,所得结果能实现真实飞行环境中追踪航天器对目标航天器的拦截或交会。     

变深度水下发射系统内弹道实验研究

利用变深度水下发射模拟实验装置开展了变发射深度和发射速度条件下导弹发射系统内弹道研究。建立了描述缩比模型弹在发射筒内运动规律的简化模型,并提出了基于实验结果的运动方程求解方法。通过实验结果分析获得了模型弹的运动摩擦系数和发射速度,并利用高速摄影测量结果对获得的发射速度进行了验证。建立了运动摩擦系数和发射速度的数值拟合关系。结果表明,运动摩擦系数与发射速度呈反向变化规律,并且存在影响运动摩擦系数变化速率的临界发射速度,当发射速度小于临界值时运动摩擦系数变化剧烈,发射速度临界值为18～20 m/s。     

Optimization of the Flight of a Spacecraft with a Solar Sail from the Earth to Mars with a Perturbation Maneuver near Venus

The trajectories of the fastest flight of a spacecraft (SC) with a solar sail from the Earth's sphere of activity to the Martian sphere of activity including the section of a perturbation maneuver near Venus are investigated. The planetary spheres of activity are assumed to be point-like; i.e., the maneuver section and the initial and final positions of the SC coincide with the corresponding positions of the planets. The initial velocity of the SC is assumed to be equal to the Earth's velocity, so that no leveling of the velocities of the SC and Mars in the final point of the flight is required. The perturbation maneuver is considered as a jump of the heliocentric velocity of the SC at the point of its contact with Venus, which does not change the magnitude of its Venus-centric velocity. The orbits of planets are assumed to be circular and coplanar; the SC trajectory lies at the plane of these orbits. The sail is planar with a specularly reflecting surface. The trajectories of optimum flights are determined as a result of solving the boundary value problem of the Pontryagin maximum principle. The families of solutions to this problem depending on the initial angular positions of Venus and Mars are constructed by the method of continuation over a parameter.     

拉格朗日点附近编队的离散控制方法

由于拉格朗日点的独特空间位置，它附近的编队研究对深空探测有着很重要的意义。讨论了日地系统拉格朗日点附近编队的脉冲控制方法，给出了一种简单的实现编队的迭代算法。基于该算法，讨论了两种不同控制策略。根据编队任务的特点，定义了几个与编队误差和能量消耗相关的性能指标。通过仿真圆形编队算例，对两种策略进行了比较分析。结果表明策略二无论在消耗能量方面还是在误差控制方面都优于策略一。对于策略二，当脉冲间隔一定时，能量消耗随编队半径的增加线性增加。当编队半径一定时，误差随脉冲间隔的减小呈指数减小，而能量消耗随脉冲的变化很小。     

航天器环绕小行星Ivar的运动分析

将小行星Ivar近似为三轴椭球体，给出了非球形引力势函数，建立了航天器环绕小行星Ivar的轨道动力学方程。利用Jacobi积分常数绘制了航天器在Ivar周围的零速度曲线，并分析了航天器的可能运动区域，给出了航天器不碰撞小行星Ivar的边界条件及不同偏心率下的近拱点半径。分析了小行星Ivar扁率和椭率对环绕轨道的影响，数学仿真结果表明：在一个轨道周期内，顺行轨道的开普勒能量、轨道角动量、偏心率和近拱点半径变化较大，而逆行轨道的相应参数变化较小。     

Fast solar sail rendezvous mission to near Earth asteroids

The concept of fast solar sail rendezvous missions to near Earth asteroids is presented by considering the hyperbolic launch excess velocity as a design parameter. After introducing an initial constraint on the hyperbolic excess velocity, a time optimal control framework is derived and solved by using an indirect method. The coplanar circular orbit rendezvous scenario is investigated first to evaluate the variational trend of the transfer time with respect to different hyperbolic excess velocities and solar sail characteristic accelerations. The influence of the asteroid orbital inclination and eccentricity on the transfer time is studied in a parametric way. The optimal direction and magnitude of the hyperbolic excess velocity are identified via numerical simulations. The found results for coplanar circular scenarios are compared in terms of fuel consumption to the corresponding bi-impulsive transfer of the same flight time, but without using a solar sail. The fuel consumption tradeoff between the required hyperbolic excess velocity and the achievable flight time is discussed. The required total launch mass for a particular solar sail is derived in analytical form. A practical mission application is proposed to rendezvous with the asteroid 99942 Apophis by using a solar sail in combination with the provided hyperbolic excess velocity.     

Optimal nodal flyby with near-Earth asteroids using electric sail

The aim of this paper is to quantify the performance of an Electric Solar Wind Sail for accomplishing flyby missions toward one of the two orbital nodes of a near-Earth asteroid. Assuming a simplified, two-dimensional mission scenario, a preliminary mission analysis has been conducted involving the whole known population of those asteroids at the beginning of the 2013 year. The analysis of each mission scenario has been performed within an optimal framework, by calculating the minimum-time trajectory required to reach each orbital node of the target asteroid. A considerable amount of simulation data have been collected, using the spacecraft characteristic acceleration as a parameter to quantify the Electric Solar Wind Sail propulsive performance. The minimum time trajectory exhibits a different structure, which may or may not include a solar wind assist maneuver, depending both on the Sun-node distance and the value of the spacecraft characteristic acceleration. Simulations show that over 60% of near-Earth asteroids can be reached with a total mission time less than 100 days, whereas the entire population can be reached in less than 10 months with a spacecraft characteristic acceleration of 1 mm/s².     

有限推力椭圆轨道近距离拦截方法

针对椭圆轨道近距离飞行器确定时间最小能量拦截问题,研究了有限推力一次机动作     

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.     

Endurance testing of a pulsed plasma thruster for nanosatellites

The mission complexity of Nanosatellites has increased tremendously in recent years, but their mission range is limited due to the lack of an active orbit control or ∆v capability. Pulsed Plasma Thrusters (PPT), featuring structural simplicity and very low power consumption are a prime candidate for such applications. However, the required miniaturization of standard PPTs and the adaption to the low power consumption is not straightforward. Most investigated systems have failed to show the required lifetime. The present coaxial design has shown a lifetime of up to 1 million discharges at discharge energies of 1.8 J in previous studies. The present paper focuses on performance characterizations of this design. For this purpose direct thrust measurements with a µN thrust balance were conducted. Thrust measurements in conjunction with mass bit determination allowed a comprehensive assessment. Based on those measurements the present µPPT has a total impulses capability of approximately I≈1.7 Ns, an average mass bit of 0.37 µg s⁻¹ and an average specific impulse of I_sp≈904 s. All tests have shown very good EM compatibility of the PPT with the electronics of the flight-like printed circuit board. Consequently, a complete µPPT unit can provide a ∆v change of 5.1 m/s or 2.6 m/s to a standard 1-unit or 2-unit CubeSat respectively.