共查询到20条相似文献，搜索用时 140 毫秒
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《天文学进展》2018,(4)
针对限制性三体问题,分别选取以中心天体和摄动体质心为坐标原点的惯性系,及以中心天体为坐标原点的非惯性系,讨论了不同坐标系下天体运动轨道描述的异同。利用运动天体轨道能量E的大小,可以确定受摄运动方程采用椭圆轨道根数还是采用双曲线轨道根数进行描述。为此,推导出一个关于轨道半长径和偏心率满足的临界关系判别式。结果表明,在摄动天体质量较大的情况下,非惯性系中存在大量轨道,这些轨道在原惯性坐标系中是稳定的椭圆轨道,转换到非惯性系中后却无法用椭圆轨道根数进行描述。只能引入双曲线轨道根数来描述轨道,由此将产生非惯性系下摄动运动方程轨道根数类型选择问题。最后,指出选择雅可比坐标系可以避免上述问题,并推导出适用于任意运动区域的具有统一形式的摄动函数展开式。 相似文献
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HUANG Yong HU Xiaogong HUANG Cheng 《中国科学院上海天文台年刊》2005,(1):14-21
从解析形式出发,利用月球重力场模型JGL165P1,分析了月球重力场(带谐项)对绕月低轨卫星的长期影响。为了减少计算误差,保证计算精度,在分析解中使用循环公式来计算倾角函数。结果指出对于一个高度为100km的极月轨道卫星,冻结轨道存在的可能性不大,但是当轨道倾角在i=90°附近或者高度再高一些,则有可能存在冻结轨道;对于100km高的初始圆轨道,卫星在无控的情况下半年内将会坠落到月球表面,如果高度增加到200km,则不进行轨道控制也不会坠落到月面上。利用仿真软件GEODYN解算出来的结果证实了上述结论。 相似文献
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月球卫星轨道力学综述 总被引：5，自引：0，他引：5
月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。 相似文献
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借助光压将探测器推向月球 总被引：2，自引：0，他引：2
若采用圆型限制性三体问题模型，从近地停泊轨道上发射一个月球探测器，其最小初始速度必须使相应的Jacobi常数C小于某一临界值C2。但这仅仅是探测器可能飞向月球的必要条件，而且这样飞向月球耗时过长。若采用Hohmann转移轨道，则需要获得较大的变轨冲量，能量消耗较大。如果需要仔细探测地月空间环境，而又不必很快地飞往月球，那么采用较大的太阳帆板，并使其法向有一特殊指向，可借助太阳光压加速引导探测器在不长的时间内飞向月球。利用相应的分析和计算，证实上述考虑是有效的，而且若使太阳帆板截面积大到一定程度（如果技术上能实现），则无需任何动力，也可借助光压将探测器推向月球，就像一条太空帆船（简称太空帆）。 相似文献
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在间接法求解小推力轨道计算中,通过先选取合适的性能指标,并对小推力最优控制问题转化为两点边值问题的方程在开普勒轨道附近线性展开,有效增强了协态变量初值收敛性,使得该方法无需对协态变量初值进行反复的随机猜测,迭代过程也不需要人工干预,提高了轨道搜索应用中的计算效率.之后再对性能指标进行迭代优化,可获得逼近于Bang-bang控制的控制方案. 相似文献
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讨论满足约束条件的月球卫星飞行轨道的设计问题，将约束条件分类为只与太阳，月球，地球，飞行器和观测站之间的相对位置有关的运行学约束条件以及涉及到飞行器轨道运行的动力学约束条件，在考虑月球卫星轨道的受力情况后，给出一种准确快速地计算和设计满足约束条件的标准飞行轨道的方法，并应用于不同约束条件下月球卫星的轨道预设计，初步讨论了轨道设计的误差分析，轨道跟踪及实时精密定轨等正在进行的其它相关工作。 相似文献
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Asymptotic solution for the two-body problem with constant tangential thrust acceleration 总被引：1，自引：0，他引：1
Claudio Bombardelli Giulio Baù Jesus Peláez 《Celestial Mechanics and Dynamical Astronomy》2011,110(3):239-256
An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of
perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the
instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical
method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space
with negligible error. 相似文献
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Hideki Asada 《Celestial Mechanics and Dynamical Astronomy》2007,97(3):151-164
We present an exact solution of the equations for orbit determination of a two body system in a hyperbolic or parabolic motion.
In solving this problem, we extend the method employed by Asada, Akasaka and Kasai (AAK) for a binary system in an elliptic
orbit. The solutions applicable to each of elliptic, hyperbolic and parabolic orbits are obtained by the new approach, and
they are all expressed in an explicit form, remarkably, only in terms of elementary functions. We show also that the solutions
for an open orbit are recovered by making a suitable transformation of the AAK solution for an elliptic case. 相似文献
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Two fully regular and universal solutions to the problem of spacecraft relative motion are derived from the Sperling–Burdet (SB) and the Kustaanheimo–Stiefel (KS) regularizations. There are no singularities in the resulting solutions, and their form is not affected by the type of reference orbit (circular, elliptic, parabolic, or hyperbolic). In addition, the solutions to the problem are given in compact tensorial expressions and directly referred to the initial state vector of the leader spacecraft. The SB and KS formulations introduce a fictitious time by means of the Sundman transformation. Because of using an alternative independent variable, the solutions are built based on the theory of asynchronous relative motion. This technique simplifies the required derivations. Closed-form expressions of the partial derivatives of orbital motion with respect to the initial state are provided explicitly. Numerical experiments show that the performance of a given representation of the dynamics depends strongly on the time transformation, whereas it is virtually independent from the choice of variables to parameterize orbital motion. In the circular and elliptic cases, the linear solutions coincide exactly with the results obtained with the Clohessy–Wiltshire and Yamanaka–Ankersen state-transition matrices. Examples of relative orbits about parabolic and hyperbolic reference orbits are also presented. Finally, the theory of asynchronous relative motion provides a simple mechanism to introduce nonlinearities in the solution, improving its accuracy. 相似文献
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Preliminary orbit determination is a multipoint boundary value problem which may be solved by the generalized Newton-Raphson iteration. When applied formally the method suffers from extensive computer storage requirements, fairly long execution times and in some cases, insufficient accuracy. In this work we seek to remove these practical difficulties via modification of the computational algorithm in such a way that solution storage is eliminated for the most part and computational speed and tolerance to imprecise integration algorithms is improved. The modified methods are applied to nine typical preliminary orbit determination problems to demonstrate fast convergence and short computation times, even with very poor starting values for the iteration. Excellent precision of the resulting solution is also demonstrated as well as the algorithm's ability to handle circular, elliptic, parabolic and hyperbolic orbits. 相似文献
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In this paper, a method to capture near-Earth objects (NEOs) incorporating low-thrust propulsion into the invariant manifolds technique is investigated. Assuming that a tugboat-spacecraft is in a rendez-vous condition with the candidate asteroid, the aim is to take the joint spacecraft-asteroid system to a selected periodic orbit of the Sun–Earth restricted three-body system: the orbit can be either a libration point periodic orbit (LPO) or a distant prograde periodic orbit (DPO) around the Earth. In detail, low-thrust propulsion is used to bring the joint spacecraft-asteroid system from the initial condition to a point belonging to the stable manifold associated to the final periodic orbit: from here onward, thanks to the intrinsic dynamics of the physical model adopted, the flight is purely ballistic. Dedicated guided and capture sets are introduced to exploit the combined use of low-thrust propulsion with stable manifolds trajectories, aiming at defining feasible first guess solutions. Then, an optimal control problem is formulated to refine and improve them. This approach enables a new class of missions, whose solutions are not obtainable neither through the patched-conics method nor through the classic invariant manifolds technique. 相似文献
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In this paper, we make use of the Stumpff's functions to solve the problem of determining the orbit of a visual binary star in universal variables. The method is thus valid for all types of orbits: hyperbolic, parabolic and elliptic. 相似文献
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We study two and three-dimensional resonant periodic orbits, usingthe model of the restricted three-body problem with the Sun andNeptune as primaries. The position and the stability character ofthe periodic orbits determine the structure of the phase space andthis will provide useful information on the stability and longterm evolution of trans-Neptunian objects. The circular planarmodel is used as the starting point. Families of periodic orbitsare computed at the exterior resonances 1/2, 2/3 and 3/4 withNeptune and these are used as a guide to select the energy levelsfor the computation of the Poincaré maps, so that all basicresonances are included in the study. Using the circular planarmodel as the basic model, we extend our study to more realisticmodels by considering an elliptic orbit of Neptune and introducingthe inclination of the orbit. Families of symmetric periodicorbits of the planar elliptic restricted three-body problem andthe three-dimensional problem are found. All these orbitsbifurcate from the families of periodic orbits of the planarcircular problem. The stability of all orbits is studied. Althoughthe resonant structure in the circular problem is similar for allresonances, the situation changes if the eccentricity of Neptuneor the inclination of the orbit is taken into account. All theseresults are combined to explain why in some resonances there aremany bodies and other resonances are empty. 相似文献
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Ming Xu Jiamin Zhu Tian Tan Shijie Xu 《Celestial Mechanics and Dynamical Astronomy》2012,113(4):403-433
The bounded quasi-periodic relative trajectories are investigated in this paper for on-orbit surveillance, inspection or repair, which requires rapid changes in formation configuration for full three-dimensional imaging and unpredictable evolutions of relative trajectories for non-allied spacecraft. A linearized differential equation for modeling J 2 perturbed relative dynamics is derived without any simplified treatment of full short-period effects. The equation serves as a nominal reference model for stationkeeping controller to generate the quasi-periodic trajectories near the equilibrium, i.e., the location of the chief. The developed model exhibits good numerical accuracy and is applicable to an elliptic orbit with small eccentricity inheriting from the osculating conversion of orbital elements. A Hamiltonian structure-preserving controller is derived for the three-dimensional time-periodic system that models the J 2-perturbed relative dynamics on a mean circular orbit. The equilibrium of the system has time-varying topological types and no fixed-dimensional unstable/stable/center manifolds, which are quite different from the two-dimensional time-independent system with a permanent pair of hyperbolic eigenvalues and fixed-dimensions of unstable/stable/ center manifolds. The unstable and stable manifolds are employed to change the hyperbolic equilibrium to elliptic one with the poles assigned on the imaginary axis. The detailed investigations are conducted on the critical controller gain for Floquet stability and the optimal gain for the fuel cost, respectively. Any initial relative position and velocity leads to a bounded trajectory around the controlled elliptic equilibrium. The numerical simulation indicates that the controller effectively stabilizes motions relative to the perturbed elliptic orbit with small eccentricity and unperturbed elliptic orbit with arbitrary eccentricity. The developed controller stabilizes the quasi-periodic relative trajectories involved in six foundational motions with different frequencies generated by the eigenvectors of the Floquet multipliers, rather than to track a reference relative configuration. Only the relative positions are employed for the feedback without the information from the direct measurement or the filter estimation of relative velocity. So the current controller has potential applications in formation flying for its less computation overload for on-board computer, less constraint on the measurements, and easily-achievable quasi-periodic relative trajectories. 相似文献
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Transition from elliptic to hyperbolic orbits in the two-body problem with slowly decreasing mass is investigated by means of asymptotic approximations.Analytical results by Verhulst and Eckhaus are extended to construct approximate solutions for the true anomaly and the eccentricity of the osculating orbit if the initial conditions are nearly-parabolic. It becomes clear that the eccentricity will monotonously increase with time for all mass functions satisfying a Jeans-Eddington relation and even for a larger set of functions. To illustrate these results quantitatively we calculate the eccentricity as a function of time for Jeans-Eddington functionsn=0(1) 5 and 18 nearly-parabolic initial conditions to find that 93 out of 108 elliptic orbits become hyperbolic. 相似文献