Perturbation effect of the Coulomb drag on the orbital elements of the earth satellite moving in the ionosphere

The perturbation effects of the Coulomb drag on the orbital elements of the earth satellite moving in the ionosphere are studied. The theoretical results show that the Coulomb drag results in both the secular and periodic variation in the semi-major axis and eccentricity. However, the argument of the perigee exhibits no secular variation, but only periodic variation. The inclination and the ascending node remain no variation. As an example, the secular effects of the Coulomb drag on the semi-major axis and the eccentricity of an ionosphere satellite Alouette (S-27) are calculated in the ionosphere with the mean height 1000 km. It can be shown that the semi-major axis contracts and the eccentricity decreases for the case of the Coulomb drag under the interaction of the ions with the electric field of an earth satellite.     

Broad-search algorithms for the spacecraft trajectory design of Callisto–Ganymede–Io triple flyby sequences from 2024 to 2040, Part II: Lambert pathfinding and trajectory solutions

Triple-satellite-aided capture employs gravity-assist flybys of three of the Galilean moons of Jupiter in order to decrease the amount of ΔV$\mathrm{\Delta }V$ required to capture a spacecraft into Jupiter orbit. Similarly, triple flybys can be used within a Jupiter satellite tour to rapidly modify the orbital parameters of a Jovicentric orbit, or to increase the number of science flybys. In order to provide a nearly comprehensive search of the solution space of Callisto–Ganymede–Io triple flybys from 2024 to 2040, a third-order, Chebyshev's method variant of the p-iteration solution to Lambert's problem is paired with a second-order, Newton–Raphson method, time of flight iteration solution to the _V∞$V_{\infty }$-matching problem. The iterative solutions of these problems provide the orbital parameters of the Callisto–Ganymede transfer, the Ganymede flyby, and the Ganymede–Io transfer, but the characteristics of the Callisto and Io flybys are unconstrained, so they are permitted to vary in order to produce an even larger number of trajectory solutions. The vast amount of solution data is searched to find the best triple-satellite-aided capture window between 2024 and 2040.     

Internet access for everybody: The satellite solution

The use of the Internet has been grown tremendously within the last decade to more than one billion subscribers. The other five billion people on Earth cannot enjoy the possibilities offered by the Internet.The digital divide is everywhere: in the developing as well as in the developed part of the world.In the developing countries basic communication needs (voice, IP access) need to be provided to a large population not living in cities.In the developed part of the world people residing outside the large cities, on the nice country side, have still difficulties to get broadband access. The reason being, that the investment to install the network infrastructure to this minority part of the population is a major part of the total investment for the network. The benefit for the telecom operators is marginal to get these customers on board.In this paper an analysis of the Internet and satellite development is being presented and based on these historical data a prediction of a possible evolution of satellite communications and broadband access is performed.One result is that the capacity of the GEO ring at the ${\mathrm{K}}_{\mathrm{a}}$-band alone would allow to provide to each individual on Earth in 2050 (assumed to be 10 billion people) a monthly capacity of about 1 Gbyte for a charge of 1$ per month.     

Nonlinear H∞ based underactuated attitude control for small satellites with two reaction wheels

Underactuated attitude control is supposed to be used on spacecraft when failure happens with onboard actuators. One main problem with existing underactuated attitude control designs is their limited capabilities against disturbances. In order to solve this problem, an approach based on the theory of H∞$H\infty$ is proposed in this paper. Two propositions are derived from the H∞$H\infty$ theory to improve the robustness of one popular underactuated attitude control design, which was presented by Tsiotras et al. It is proved mathematically that the controller satisfying these two propositions respectively can stabilize the underactuated attitude system locally or globally. The numerical simulations show that the improved controllers based on the H∞$H\infty$ theory could provide higher pointing accuracy for small satellites against disturbances. This validates the effectiveness of the proposed H∞$H\infty$ based approach to improve existing underactuated attitude control designs.     

分布式卫星轨道构形的大气摄动分析及修正方法

在低轨道运行的分布式卫星受大气摄动的影响,其轨道构形很快遭到破坏,环绕卫星的相对运动轨迹中心不断发生漂移。本研究的目的在于建立一种降低大气摄动对分布式卫星轨道构形影响的补偿方法,以使分布式卫星的轨道构形能够更好地自然维持。研究基于考虑高度变化和太阳周日变化的大气密度模型,得出分布式卫星不同初始相位环绕卫星的长半轴摄动方程。并提出一种补偿大气摄动影响的长半轴修正方法。仿真结果显示,采用此大气摄动补偿方法能够在给定时间内大大降低大气摄动的影响,从而显著提高分布式卫星轨道构形的自然维持能力。     

Design of transfer trajectories between resonant orbits in the Earth–Moon restricted problem

The application of dynamical systems techniques to mission design has demonstrated that employing invariant manifolds and resonant flybys enables previously unknown trajectory options and potentially reduces the ΔV$\mathrm{\Delta }V$ requirements. In this investigation, planar and three-dimensional resonant orbits are analyzed and cataloged in the Earth–Moon system and the associated invariant manifold structures are computed and visualized with the aid of higher-dimensional Poincaré maps. The relationship between the manifold trajectories associated with multiple resonant orbits is explored through the maps with the objective of constructing resonant transfer arcs. As a result, planar and three-dimensional homoclinic- and heteroclinic-type trajectories between unstable periodic resonant orbits are identified in the Earth–Moon system. To further illustrate the applicability of 2D and 3D resonant orbits in preliminary trajectory design, planar transfers to the vicinity of L₅ and an out-of-plane transfer to a 3D periodic orbit, one that tours the entire Earth–Moon system, are constructed. The design process exploits the invariant manifolds associated with orbits in resonance with the Moon as transfer mechanisms.     

地磁扰动期间低轨目标轨道预报的误差修正

针对地磁扰动期间大气密度变化造成的低轨目标较大的轨道预报误差,提出一种根据POES卫星观测的极光能量注入数据改进短期轨道预报的方法。分析表明CHAMP卫星的沿迹大气密度及轨道衰减与极光能量注入具有较好的相关性。通过线性回归方法,建立轨道半长轴衰减及阻力调制系数的修正公式,并使用修正后的阻力调制系数取代两行元(TLE)中的该系数带入SGP4模型进行位置预报。该方案考虑了外推过程中地磁扰动引起的大气密度响应,能更准确地反映外推过程中大气阻力对轨道的影响。将其应用到2008年CHAMP卫星和国际空间站的轨道预报中,结果表明,半长轴和位置的预报误差可分别降低50%和30%左右。进一步对不同年份、不同轨道高度的目标进行了预报误差修正的分析,验证了该方法的普适性。     

星钟和星历误差分离的广域差分新方法

针对WAAS等传统的广域差分方法存在DOP值太大和要求基准站时 间严格同步等问题,提出了星钟和星历误差相对分离的广域差分新方法。提出的相对分离理 论包括以所有卫星的广播星历为基准的星钟误差的相对分离,以各卫星星钟误差相对分离结 果为基准的相对星历误差分离和固定偏差的星钟二次修正三部分,其可简单归纳为星钟-星 历-星钟的修正思路。这种方法除无需基准站同步外,用户定位比WAAS准。理论论证和算例 仿真证明这种理论是科学的,对建设各种卫星导航系统的差分增强系统均是适用的。     

Effects of stand-off bursts on rubble-pile targets: Evaluation of a hazardous asteroid mitigation strategy

We explore the aftereffects of stand-off burst mitigation on kilometer-scale rubble pile asteroids. We use a simple model of X-ray energy deposition to calculate the impulse transferred to the target, in particular to burst-facing blocks on the target surface. The impulse allows us to estimate an initial velocity field for the blocks on the outer side of the target facing the burst. We model the dynamics using an N-body polyhedron program built on the Open Dynamics Engine, a “physics engine” that integrates the dynamical equations for objects of general shapes and includes collision detection, friction, and dissipation.We tested several different models for target objects: rubble piles with different mass distributions, a “brick-pile” made of closely fitting blocks and zero void space, and a non-spherical “contact binary” rubble pile. Objects were bound together by self-gravity and friction/inelastic restitution with no other cohesive forces. Our fiducial cases involved objects of m=3.5×10¹² kg (corresponding to a radius of 0.7 km for the bulk object), an X-ray yield of 1 megaton, and stand-off burst distances of R=0.8–2.5 km from the target center of mass.Kilometer-scale rubble piles are robust to stand-off bursts of a yield ($Y\sim 1$ megaton) that would be sufficient to provide an effective velocity change ($\mathrm{\Delta }v\sim 0.05\mathrm{m}{\mathrm{s}}^{-1}$). Disaggregation involving some tens of percent of the target mass happens immediately after the impulse; the bulk of the object re-accretes on a few gravitational timescales, and the final deflected target contains over 95% (typically, 98–99%) of the original mass. Off-center components of the mitigation impulse and the target mass distribution cause a small amount of induced spin and off-axis components of velocity change. The off-axis velocity component amounts to an angular deviation of $\sim$ 0.05–0.1 radians from the nominal impulse vector, which may be important for mitigation planning.     

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。     

Polyhedron tracking and gravity tractor asteroid deflection

In the wake of the Chelyabinsk airburst, the defense against hazardous asteroids is becoming a topic of high interest. This work improves the gravity tractor asteroid deflection approach by tracking realistic small body shapes with tilted ion engines. An algorithm for polyhedron tracking was evaluated in a fictitious impact scenario. The simulations suggest a capability increase up to 38.2% with such improved tilting strategies. The long- and short-term effects within polyhedron tracking are illustrated. In particular, the orbital reorientation effect is influential when realistic asteroid shapes and rotations are accounted for. Also analyzed is the subject of altitude profiles, a way to tailor the gravity tractor performance, and to achieve a steering ability within the B-plane. A novel analytical solution for the classic gravity tractor is derived. It removes the simulation need for classic tractor designs to obtain comparable two body model Δv$\mathrm{\Delta }v$ figures. This paper corroborates that the asteroid shape can be exploited for maximum performance. Even a single engine tilt adjustment at the beginning of deflection operations yields more deflection than a fixed preset tilt.     

动量轮卸载在改进GEO卫星东西轨道保持中的应用

空间外干扰力矩会使在轨GEO三轴卫星动量轮转速发生周期性变化,因此需要进行动量轮卸载。通过对卸载前后卫星轨道根数的比较,发现动量轮卸载可以延长卫星实际的东西轨道保持周期。以动量轮卸载有利卫星轨道保持为研究目的,通过计算和分析,推导出动量轮卸载时转速变化与卫星半长轴变化关系的数学模型,并以实际测量数据为基础,对模型进行了仿真验证,证明了动量轮卸载对改进GEO卫星东西轨道保持的可行性,提出了一种利用动量轮卸载改进GEO卫星东西轨道保持策略的新方法。     

Satellite orbit perturbations in a dusty Martian atmosphere

In this paper we calculate the effect of atmospheric dust on the orbital elements of a satellite. Dust storms that originate in the Martian surface may evolve into global storms in the atmosphere that can last for months can affect low orbiter and lander missions. We model the dust as a velocity-square depended drag force acting on a satellite and we derive an appropriate disturbing function that accounts for the effect of dust on the orbit, using a Lagrangean formulation. A first-order perturbation solution of Lagrange's planetary equations of motion indicates that for a local dust storm cloud that has a possible density of 8.323×10⁻¹⁰ kg m⁻³ at an altitude of 100 km affects the orbital semimajor axis of a 1000 kg satellite up −0.142 m day⁻¹. Regional dust storms of the same density may affect the semimajor axis up to of −0.418 m day⁻¹. Other orbital elements are also affected but to a lesser extent.     

Families of Periodic Solutions to the Beletsky Equation

A review of achievements in the investigation of the planar periodic oscillations and rotations of a satellite around its center of mass, which moves along an elliptic orbit in the central gravitational field, is presented. These oscillations and rotations of the satellite are described by an ordinary differential equation (Beletsky equation) of the second order with periodic coefficients and two parameters. The equation is equivalent to a periodic Hamiltonian system with a single degree of freedom and has a singularity. It turned out that two-parameter families of the generalized periodic solutions to this simple equation form complicated structures of a new type. A comparison of numerous separate results made it possible to outline a sufficiently unified and complete picture of the location and structure of the families of generalized 2-periodic solutions with an integer number of rotation. These families are compared with known data related to the resonance rotations of the natural satellites in the solar system.