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.     

The effect of climber transit on the space elevator dynamics

The space elevator offers an alternate and efficient method for space travel. It will have two main components. The first component is the tether (or the ribbon), which extends from the Earth to an equatorial satellite at an altitude beyond the geostationary orbit, and is fixed to a base on the surface of the Earth at its lower end. The second component is the climber, which scales the ribbon, transporting payloads to space. An important issue for effective operation of the space elevator will be to understand its dynamics. This paper attempts to develop a realistic and yet simple planar model for this purpose. The basic response of the ribbon to climber transit is determined. Both analytical and numerical results are presented. Specific climbing procedures are devised based on these results so as to minimize the adverse effects of climber transit on the ribbon.     

Stability and bifurcations of relative equilibria of a pendulum suspended on the equator

The problem of equilibria of a pendulum suspended at an equatorial point relative to the rotating Earth is considered. An altitude is determined at which the degree of instability of the inverted pendulum changes from two to unity. Relative equilibria are investigated that bifurcate from the radial one when its degree of instability changes. Their stability properties are studied.     

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).     

Observations in the thermal IR and visible of a retired satellite in the graveyard orbit,and comparisons to active satellites in GEO

There exists a population of defunct satellites in the geo-stationary arc that potentially pose a hazard to current and future operational satellites. These drifting, non-station-kept objects have a variety of ages and sizes, and many are trapped in libration orbits around the Earth?s two gravitational potential wells (the non-spherical nature of the Earth gives rise to two geo-potential wells or “stable points” that affect objects in geostationary and geosynchronous orbits), whereas others were boosted to higher altitudes into so-called “graveyard” orbits.     

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。     

Two-craft tether formation relative equilibria about circular orbits and libration points

The relative equilibria of a two spacecraft tether formation connected by line-of-sight elastic forces moving in the context of a restricted two-body system and a circularly restricted three-body system are investigated. For a two spacecraft formation moving in a central gravitational field, a common assumption is that the center of the circular orbit is located at the primary mass and the center of mass of the formation orbits around the primary in a great-circle orbit. The relative equilibrium is called great-circle if the center of mass of the formation moves on the plane with the center of the gravitational field residing on it; otherwise, it is called a nongreat-circle orbit. Previous research shows that nongreat-circle equilibria in low Earth orbits exhibit a deflection of about a degree from the great-circle equilibria when spacecraft with unequal masses are separated by 350 km. This paper studies these equilibria (radial, along-track and orbit-normal in circular Earth orbit and Earth–Moon Libration points) for a range of inter-craft distances and semi-major axes of the formation center of mass. In the context of a two-spacecraft Coulomb formation with separation distances on the order of dozens of meters, this paper shows that the equilibria deflections are negligible (less than 10^?6°) even for very heterogeneous mass distributions. Furthermore, the nongreat-circle equilibria conditions for a two spacecraft tether structure at the Lagrangian libration points are developed.     

用于对地观测定位的编队飞行卫星群轨道构形设计

编队飞行卫星群是一组小卫星,它们具有短的相对距离、相等的轨道半长轴和微小差别的其它轨道要素,它们形成相互伴随运动,并且具有一定的构形。提出将编队飞行卫星群的轨道设计技术应用于对地观测定位卫星系统中。根据设想的要求,针对由四颗伴随卫星围绕基准卫星(或一个虚拟的中心)飞行的轨道设计案例,初步分析了编队飞行卫星群的构形保持,地球引力和大气阻力的摄动影响等问题。     

Developing a Low-Velocity Collision Model Based on the Nasa Standard Breakup Model

We have conducted a series of low-velocity impact experiments to understand the dispersion properties of fragments newly created by low-velocity impacts possible in space, especially in geostationary Earth orbit. The test results are utilized to establish a mathematical prediction model to be used in debris generation and propagation codes. Since the expected collision velocity between catalogued objects in geostationary Earth orbit shows a peak at a few hundreds meters per second, these impact experiments were conducted at a velocity range lower than 300m/s. As a typical structure of satellites in geostationary Earth orbit, thin aluminum honeycomb sandwich panels with carbon fiber reinforced plastics face sheets were prepared, while the projectile was a stainless steel ball of 9mm diameter. The data collected through these impact experiments have been re-analyzed based on the method used in the National Aeronautics and Space Administration (NASA) standard breakup model 1998 revision. The results indicate that the NASA standard breakup model derived from hypervelocity impacts could be applied to low-velocity collision possible in geostationary Earth orbit with some modifications.     

新一代无源微波遥感器及其在地球同步卫星上的应用研究

星载无源微波遥感已发展成为观测大气与地球表面的重要手段，地球同步气象卫星上使用的微波遥感仪器必须是新一代先进的遥感器；它应兼备传统的无源微波大气探测仪及微波成像仪的双重功能。本文叙述了国际上新一代星载无源微波遥感器的研究现状和发展趋势，讨论了在地球同步气象卫星上装载无源微波遥感仪器的可行性及其关键技术，并研究了其频率的选择问题。     

Equilibrium attitude and stability of a spacecraft on a stationary orbit around an asteroid

The stationary orbits around an asteroid, if exist, can be used for communication and navigation purposes just as around the Earth. The equilibrium attitude and stability of a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid are studied. The linearized equations of attitude motion are obtained under the small motion assumption. Then, the equilibrium attitude is determined in both cases of a general and a symmetrical spacecraft. Due to the higher-order inertia integrals of the spacecraft, the equilibrium attitude is slightly away from zero Euler angles. Then necessary conditions of stability of this conservative system are analyzed based on the linearized equations of motion. The effects of different parameters, including the harmonic coefficients C₂₀ and C₂₂ of the asteroid and higher-order inertia integrals of the spacecraft, on the stability are assessed and compared. Due to the significantly non-spherical shape and rapid rotation of the asteroid, the effects of the harmonic coefficients C₂₀ and C₂₂ are very significant, while effects of the third- and fourth-order inertia integrals of the spacecraft can be neglected. Considering a spacecraft on a stationary orbit around an example asteroid, we show that the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field is modified due to the non-spherical mass distribution of the asteroid. Our results are confirmed by a numerical simulation.     

Ground assisted rendezvous with geosynchronous satellites for the disposal of space debris by means of Earth-oriented tethers

Previous studies have shown that extended length Earth-oriented tethers in the geosynchronous (GEO) region can be used to re-orbit satellites to disposal orbits. One such approach involves the extension of a GEO based tether, collection of a debris object, and retraction of the tether, which transfers the retracted configuration to a higher energy orbit for debris disposal. The re-extension of the tether after debris disposal returns the configuration to the near-GEO altitude. The practical feasibility of such a system depends on the ability to collect GEO debris objects, attach them to a deployed tether system, and retract the tethers for transfer to the disposal orbits.This study addresses the collection and delivery of debris objects to the deployed tether system in GEO. The investigation considers the number, type and the characteristics of the debris objects as well as the collection tug that can be ground controlled to detect, rendezvous and dock with the debris objects for their delivery to the tethers system.A total of more than 400 objects are in drift orbits crossing all longitudes either below or above the geostationary radius. More than 130 objects are also known to librate around the stable points in GEO with periods of libration up to five or more years. A characterization of the position and velocity of the debris objects relative to the collection tug is investigated. Typical rendezvous performance requirements for uncooperative GEO satellites are examined, and the similarities with other approaches such as the ESA's CX-OLEV commercial mission proposal to extend the life of geostationary telecommunication satellites are noted.     

Orbital transfer: Some links between the low-thrust and the impulse cases

Here, we investigate an orbital transfer from a low Earth orbit to the geostationary one where the considered criterion to maximize is the final mass. We seek to observe numerically the connections between the impulse transfer and the low-thrust one after giving two computational methods in each cases. We see that the links are very strong and that the impulse transfer can be viewed as the limit of the low-thrust transfer when its number of revolutions increases.     

导弹敏捷转弯段的新型非奇异终端滑模控制

针对具有快时变性、不确定性、强非线性和系统初始状态远离平衡点等特点的敏捷导弹的直接力/气动力复合控制律设计问题,提出了一种新型非奇异终端滑模控制方法。为缩短到达平衡态的时间,设计了一种组合非奇异终端滑模面,提高了系统状态在滑模面上的收敛速度,设计了改进的变系数双幂次趋近律,提高了系统状态到达滑模面的速度,并利用扩张状态观测器实时估计系统内外扰动,消除了观测误差对系统造成的干扰,抑制了抖振。最后,证明了所提方法的有限时间收敛特性,通过仿真对比校验了所提方法的有效性。     

Near-optimal geostationary transfer maneuvers with cooperative en-route inspection using hybrid optimal control

This research investigates the performance of bi-level hybrid optimal control algorithms in the solution of minimum delta-velocity geostationary transfer maneuvers with cooperative en-route inspection. The maneuvers, introduced here for the first time, are designed to populate a geostationary constellation of space situational awareness satellites while providing additional characterization of objects in lower-altitude orbit regimes. The maneuvering satellite, called the chaser, performs a transfer from low Earth orbit to geostationary orbit, during which it performs an inspection of one of several orbiting targets in conjunction with a ground site for the duration of the target?s line-of-site contact with that site. A three-target scenario is used to test the performance of multiple bi-level hybrid optimal control algorithms. A bi-level hybrid algorithm is then utilized to solve fifteen-, and thirty-target scenarios and shown to have increasing benefit to complete enumeration as the number of targets is increased. Results indicate that the en-route inspection can be accomplished for a small increase in the delta-velocity required for a simple transfer to geostationary orbit given the same initial conditions.     

Novel mission concepts for polar coverage: An overview of recent developments and possible future applications

The paper provides a survey of novel mission concepts for continuous, hemispheric polar observation and direct-link polar telecommunications. It is well known that these services cannot be provided by traditional platforms: geostationary satellites do not cover high-latitude regions, while low- and medium-orbit Sun-synchronous spacecraft only cover a narrow swath of the Earth at each passage. Concepts that are proposed in the literature are described, including the pole-sitter concept (in which a spacecraft is stationary above the pole), spacecraft in artificial equilibrium points in the Sun–Earth system and non-Keplerian polar Molniya orbits. Additionally, novel displaced eight-shaped orbits at Lagrangian points are presented. For many of these concepts, a continuous acceleration is required and propulsion systems include solar electric propulsion, solar sail and a hybridisation of the two. Advantages and drawbacks of each mission concept are assessed, and a comparison in terms of high-latitude coverage and distance, spacecraft mass, payload and lifetime is presented. Finally, the paper will describe a number of potential applications enabled by these concepts, focusing on polar Earth observation and telecommunications.     

太阳帆绕地球周期轨道研究

  地球同步和太阳同步卫星在各个领域有着广泛的应用。静止轨道是一种特殊的地球同步轨道,轨道资源有限。利用化学推进或电推进可以实现轨道高度不同的同步轨道,如悬挂轨道,但需要消耗较多的燃料,工程上无法承受。本文考虑利用太阳帆实现地球同步和太阳同步轨道。太阳光压力在轨道平面内沿拱线方向,选择光压力与平面的夹角使得轨道平面的旋转速率与太阳光同步。研究表明,设计合适的半长轴和偏心率可以使得轨道旋转速率与地球自转速率一致。假设太阳光与赤道平面平行,可以得到准静止轨道,太阳帆将在传统静止轨道的附近运动,星下点的经度将在一个固定值附近振动。实际上太阳光是与黄道面平行,黄道面与赤道面之间存在夹角。考虑黄赤交角的情况下,太阳帆将在一定纬度和经度范围内运动。适合于对某个区域进行长期观测任务。     

Spectral signatures of photosynthesis. II. Coevolution with other stars and the atmosphere on extrasolar worlds

As photosynthesis on Earth produces the primary signatures of life that can be detected astronomically at the global scale, a strong focus of the search for extrasolar life will be photosynthesis, particularly photosynthesis that has evolved with a different parent star. We take previously simulated planetary atmospheric compositions for Earth-like planets around observed F2V and K2V, modeled M1V and M5V stars, and around the active M4.5V star AD Leo; our scenarios use Earth's atmospheric composition as well as very low O2 content in case anoxygenic photosynthesis dominates. With a line-by-line radiative transfer model, we calculate the incident spectral photon flux densities at the surface of the planet and under water. We identify bands of available photosynthetically relevant radiation and find that photosynthetic pigments on planets around F2V stars may peak in absorbance in the blue, K2V in the red-orange, and M stars in the near-infrared, in bands at 0.93-1.1 microm, 1.1-1.4 microm, 1.5-1.8 microm, and 1.8-2.5 microm. However, underwater organisms will be restricted to wavelengths shorter than 1.4 microm and more likely below 1.1 microm. M star planets without oxygenic photosynthesis will have photon fluxes above 1.6 microm curtailed by methane. Longer-wavelength, multi-photo-system series would reduce the quantum yield but could allow for oxygenic photosystems at longer wavelengths. A wavelength of 1.1 microm is a possible upper cutoff for electronic transitions versus only vibrational energy; however, this cutoff is not strict, since such energetics depend on molecular configuration. M star planets could be a half to a tenth as productive as Earth in the visible, but exceed Earth if useful photons extend to 1.1 microm for anoxygenic photosynthesis. Under water, organisms would still be able to survive ultraviolet flares from young M stars and acquire adequate light for growth.     

The data compression problem for the “GAIA” astrometric satellite of ESA

Space-based astrometry has a great tradition at ESA. The first space-based astrometric satellite in history, “Hipparcos”, was launched by ESA in 1989 and, in spite of orbital problems, was able to accomplish almost all of its tasks until it was finally shut down in 1993. The results of the Hipparcos mission were published by ESA in 1997 in the form of six CD-ROMs: the Hipparcos Catalogue contains 118,218 entries with median astrometric precision of around 1 milliarcsec, and specific results for double and multiple systems. In practice, Hipparcos drew for the first time the three-dimensional “map” of the spherical region of the Galaxy surrounding the Sun and having a radius of roughly 1,000 light years.

Then, in 1995, ESA launched the study of a new astrometric satellite, named “GAIA” and about a hundred times more powerful than Hipparcos, i.e. with median astrometric precision of around 10 microarcsec. This new satellite is intended to measure the parallaxes of over 50 million stars in the Galaxy, at least for the brightest stars, and this would mean to “draw” the three-dimensional map of the whole Galaxy, reaching out even to the Magellanic Clouds, 180,000 light years away.

The team of European scientists and engineers now designing GAIA, however, is facing hard technological difficulties. One of these is the design and coding of radically new and ultra-powerful mathematical algorithms for the on-board compression of the 50-million-stars data that GAIA will send to Earth from its intended geostationary orbit. Preliminary estimates of the raw data rates from the GAIA focal plane, in fact, are of the order of a few Gigabits per second. To reduce the data stream to the envisaged telemetry link of 1 Megabit per second, on-board data compression with a 1 to 1,000 ratio is the target. Clearly, this is far beyond the capabilities of any lossless compression technique (enabling compression ratios of 1 to some tens), and so some “wise” lossy compression mathematical procedure must be adopted.

In this paper a GAIA-adapted lossy data compression technique is presented, based on the Karhunen-Loève Transform (KLT). The essence of this method was already used by NASA for the Galileo mission when the large antenna got stuck and the mission was rescued by re-programming the on-board computer in terms of the KLT. That transform was officially named ICT — “Integer Cosine Transform” — by the NASA-JPL team led by Dr. Kahr-Ming Cheung. But the KLT here described for GAIA will of course differ from the JPL one in many regards, owing to the advances in computer technology.

Finally, estimates are also given about the possibility of using the KLT for onboard data compression in case GAIA is going to be put into orbit around the Lagrangian point L2 of the Earth-Sun system, and, above all, in case the number of stars to be observed is actually raised from 50 millions to one billion, as ESA currently appears to be likely to pursue.     

Dynamics of the orbital cable system

The Orbital Cable System (OCS) consists of a vehicle with an engine, a long connecting cable (string) and a satellite probe for low altitude geophysical explorations. The vehicle orbits the Earth at an altitude of 200–250 km and tows a probe at an altitude of 100–150 km. The air drag is compensated by the vehicle engine thrust. In the OCS dynamics study the cable weight, elasticity and air drag are taken into account. The OCS stationary motions are found, and stability of these motions is investigated. The OCS periodical motions that are close to the stationary motions are found. Simple ways of the OCS deployment in orbit are described.