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1.
This paper presents a generalized problem of the restricted three body studied in Abdul Raheem and Singh with the inclusion that the third body is an oblate spheroidal test particle of infinitesimally mass. The positions and stability of the equilibrium point of this problem is studied for a model in which the primaries is the binary system Struve 2398 (Gliese 725) in the constellation Draco; which consist of a pair of radiating oblate stars. It is seen that additional equilibrium points exist on the line collinear with the primaries, for some combined parameters of the problem. Hence, there can be up to five collinear equilibrium points. Two triangular points exist and depends on the oblateness of the participating bodies, radiation pressure of the primaries and a small perturbation in the centrifugal force. The stability analysis ensures that, the collinear equilibrium points are unstable in the linear sense while the triangular points are stable under certain conditions. Illustrative numerical exploration is given to indicate significant improvement of the problem in Abdul Raheem and Singh. 相似文献
2.
We analyse stability and equilibrium of a unipolar large-scale magnetic field pervading a plane horizontal subphotospheric layer with the possible implications for sunspots in mind. Eddy diffusivity is applied to account for the effects of the small-scale convective turbulence. Diffusivity quenching by magnetic field results in a secondary large-scale instability. A linear stability analysis is performed to define the marginal stability boundary in parametric space and the unstable mode structure. The nonlinear dynamics of the unstable modes are followed numerically. The original state of a uniform vertical magnetic field is transformed via the instability into the nonlinear dynamical equilibrium with a highly intermittant distribution of the magnetic field. Magnetic flux is concentrated in a relatively small area surrounded by an almost field-free region. The role of the fluid motion in the hydromagnetic equilibrium is emphasized. Although the relevance of the instability to the process of sunspot formation is rather questionable, the resulting equilibrium structures are similar to mature spots in their thermal and magnetic properties. Also, the simulated flow structure agrees with helioseismic tomography results. 相似文献
3.
The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations. 相似文献
4.
The paper deals with the effect of solar pressure on the motion and stability of two satellites connected by an inextensible string in a central gravitational field of force. A system of nonlinear, nonhomogeneous, and non-autonomous equations under the rotating frame of reference in Nechvíle's coordinate system have been obtained. The general solution of the above system of equations is beyond our reach. The particular solutions have been obtained.The particular solution in which the system lies, wholly along the radius vector joining the attracting centre and the centre of mass of the system under the central attracting force along was found to be stable (Singh, 1973). Naturally we got interested in examining the effect of solar radiation pressure on the stability of this particular solution. 相似文献
5.
J.K. MillerA.S. Konopliv P.G. AntreasianJ.J. Bordi S. ChesleyC.E. Helfrich W.M. OwenT.C. Wang B.G. WilliamsD.K. Yeomans D.J. Scheeres 《Icarus》2002,155(1):3-17
Prior to the Near Earth Asteroid Rendezvous (NEAR) mission, little was known about Eros except for its orbit, spin rate, and pole orientation, which could be determined from ground-based telescope observations. Radar bounce data provided a rough estimate of the shape of Eros. On December 23, 1998, after an engine misfire, the NEAR-Shoemaker spacecraft flew by Eros on a high-velocity trajectory that provided a brief glimpse of Eros and allowed for an estimate of the asteroid's pole, prime meridian, and mass. This new information, when combined with the ground-based observations, provided good a priori estimates for processing data in the orbit phase.After a one-year delay, NEAR orbit operations began when the spacecraft was successfully inserted into a 320×360 km orbit about Eros on February 14, 2000. Since that time, the NEAR spacecraft was in many different types of orbits where radiometric tracking data, optical images, and NEAR laser rangefinder (NLR) data allowed a determination of the shape, gravity, and rotational state of Eros. The NLR data, collected predominantly from the 50-km orbit, together with landmark tracking from the optical data, have been processed to determine a 24th degree and order shape model. Radiometric tracking data and optical landmark data were used in a separate orbit determination process. As part of this latter process, the spherical harmonic gravity field of Eros was primarily determined from the 10 days in the 35-km orbit. Estimates for the gravity field of Eros were made as high as degree and order 15, but the coefficients are determined relative to their uncertainty only up to degree and order 10. The differences between the measured gravity field and one determined from a constant density shape model are detected relative to their uncertainty only to degree and order 6. The offset between the center of figure and the center of mass is only about 30 m, indicating that Eros has a very uniform density (1% variation) on a large scale (35 km). Variations to degree and order 6 (about 6 km) may be partly explained by the existence of a 100-m, regolith or by small internal density variations. The best estimates for the J2000 right ascension and declination of the pole of Eros are α=11.3692±0.003° and δ=17.2273±0.006°. The rotation rate of Eros is 1639.38922±0.00015°/day, which gives a rotation period of 5.27025547 h. No wobble greater than 0.02° has been detected. Solar gravity gradient torques would introduce a wobble of at most 0.001°. 相似文献
6.
The strongly perturbed dynamical environment near asteroids has been a great challenge for the mission design. Besides the non-spherical gravity, solar radiation pressure, and solar tide, the orbital motion actually suffers from another perturbation caused by the gravitational orbit–attitude coupling of the spacecraft. This gravitational orbit–attitude coupling perturbation (GOACP) has its origin in the fact that the gravity acting on a non-spherical extended body, the real case of the spacecraft, is actually different from that acting on a point mass, the approximation of the spacecraft in the orbital dynamics. We intend to take into account GOACP besides the non-spherical gravity to improve the previous close-proximity orbital dynamics. GOACP depends on the spacecraft attitude, which is assumed to be controlled ideally with respect to the asteroid in this study. Then, we focus on the orbital motion perturbed by the non-spherical gravity and GOACP with the given attitude. This new orbital model can be called the attitude-restricted orbital dynamics, where restricted means that the orbital motion is studied as a restricted problem at a given attitude. In the present paper, equilibrium points of the attitude-restricted orbital dynamics in the second degree and order gravity field of a uniformly rotating asteroid are investigated. Two kinds of equilibria are obtained: on and off the asteroid equatorial principal axis. These equilibria are different from and more diverse than those in the classical orbital dynamics without GOACP. In the case of a large spacecraft, the off-axis equilibrium points can exist at an arbitrary longitude in the equatorial plane. These results are useful for close-proximity operations, such as the asteroid body-fixed hovering. 相似文献
7.
Attitude stability of spacecraft subjected to the gravity gradient torque in a central gravity field has been one of the most fundamental problems in space engineering since the beginning of the space age. Over the last two decades, the interest in asteroid missions for scientific exploration and near-Earth object hazard mitigation is increasing. In this paper, the problem of attitude stability is generalized to a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied via the linearized equations of motion, in which the harmonic coefficients $C_{20}$ and $C_{22}$ of the gravity field of the asteroid are considered. The necessary conditions of stability of this conservative system are investigated in detail with respect to three important parameters of the asteroid, which include the harmonic coefficients $C_{20}$ and $C_{22}$ , as well as the ratio of the mean radius to the radius of the stationary orbit. We find that, due to the significantly non-spherical shape and the rapid rotation of the asteroid, the attitude stability domain is modified significantly in comparison with the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field. Especially, when the spacecraft is located on the intermediate-moment principal axis of the asteroid, the stability domain can be totally different from the classical stability domain. Our results are useful for the design of attitude control system in the future asteroid missions. 相似文献
8.
Hanlun Lei Christian Circi Emiliano Ortore Bo Xu 《Celestial Mechanics and Dynamical Astronomy》2018,130(8):53
In this work, periodic attitudes and bifurcations of periodic families are investigated for a rigid spacecraft moving on a stationary orbit around a uniformly rotating asteroid. Under the second degree and order gravity field of an asteroid, the dynamical model of attitude motion is formulated by truncating the integrals of inertia of the spacecraft at the second order. In this dynamical system, the equilibrium attitude has zero Euler angles. The linearised equations of attitude motion are utilised to study the stability of equilibrium attitude. It is found that there are three fundamental types of periodic attitude motions around a stable equilibrium attitude point. We explicitly present the linear solutions around a stable equilibrium attitude, which can be used to provide the initial guesses for computing the true periodic attitudes in the complete model. By means of a numerical approach, three fundamental families of periodic attitudes are studied, and their characteristic curves, distribution of eigenvalues, stability curves and stability distributions are determined. Interestingly, along the characteristic curves of the fundamental families, some critical points are found to exist, and these points correspond to tangent and period-doubling bifurcations. By means of a numerical approach, the bifurcated families of periodic attitudes are identified. The natural and bifurcated families constitute networks of periodic attitude families. 相似文献
9.
We study the stability of charged dust grains orbiting a planet and subject to gravity and the electromagnetic force. Our numerical models cover a broad range of launch distances from the planetary surface to beyond synchronous orbit, and the full range of charge-to-mass ratios from ions to rocks. Treating the spinning planetary magnetic field as an aligned dipole, we map regions of radial and vertical instability where dust grains are driven to escape or crash into the planet. We derive the boundaries between stable and unstable trajectories analytically, and apply our models to Jupiter, Saturn and the Earth, whose magnetic fields are reasonably well represented by aligned dipoles. 相似文献
10.
11.
We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and the stable conditions of the equilibrium points are derived and discussed. First, a new metric is presented to link the orbit and the geodesic of the smooth manifold. Then, using the eigenvalues of the characteristic equation, the equilibrium points are classified into 8 cases. A theorem is presented and proved to describe the structure of the submanifold as well as the stable and unstable behaviours of a massless test particle near the equilibrium points. The linearly stable, the non-resonant unstable, and the resonant equilibrium points are discussed. There are three families of periodic orbits and four families of quasi-periodic orbits near the linearly stable equilibrium point. For the non-resonant unstable equilibrium points, there are four relevant cases; for the periodic orbit and the quasi-periodic orbit, the structures of the submanifold and the subspace near the equilibrium points are studied for each case. For the resonant equilibrium points, the dimension of the resonant manifold is greater than 4, and we find at least one family of periodic orbits near the resonant equilibrium points. As an application of the theory developed here, we study relevant orbits for the asteroids 216 Kleopatra, 1620 Geographos, 4769 Castalia and 6489 Golevka. 相似文献
12.
We consider the mechanical equilibrium of a cylinder of plasma suspended horizontally by magnetic fields in uniform gravity. This configuration is what may be expected if a quiescent prominence were to condense in a region initially filled with a uniform magnetic field. A set of exact solutions describing the equilibrium situation is presented. Although the plasma distribution is assumed to be cylindrically symmetric to obtain tractibility of the problem, exact force balance between plasma pressure, the Lorentz force and gravity is achieved everywhere in space. The set of solutions covers a particular case of a uniform temperature as well as cases where the temperature rises from zero at the center of the plasma cylinder to rapidly reach a constant asymptotic value outside the cylinder. The physical properties of these solutions are described. A suggestion is made for future development, based on the present work, to construct a prominence model in which the requirements of both mechanical and radiative equilibrium are satisfied. 相似文献
13.
Giacomo Giampieri 《Icarus》2004,167(1):228-230
A planetary body moving on an eccentric orbit around the primary is subject to a periodic perturbing potential, affecting its internal mass distribution. In a previous paper (Rappaport et al., 1997, Icarus 126, 313), we have calculated the periodic modulation of the gravity coefficients of degree 2, for a body on a synchronous orbit. Here, the previous analysis is extended by considering also non-synchronous orbits, and by properly accounting for the apparent motion of the primary due to the non uniform motion along the elliptical orbit. The cases of Titan and Mercury are briefly discussed. 相似文献
14.
After GRACE and GOCE there will still be need and room for improvement of the knowledge (1) of the static gravity field at
spatial scales between 40 km and 100 km, and (2) of the time varying gravity field at scales smaller than 500 km. This is
shown based on the analysis of spectral signal power of various gravity field components and on the comparison with current
knowledge and expected performance of GRACE and GOCE. Both, accuracy and resolution can be improved by future dedicated gravity
satellite missions. For applications in geodesy, the spectral omission error due to the limited spatial resolution of a gravity
satellite mission is a limiting factor. The recommended strategy is to extend as far as possible the spatial resolution of
future missions, and to improve at the same time the modelling of the very small scale components using terrestrial gravity
information and topographic models.We discuss the geodetic needs in improved gravity models in the areas of precise height
systems, GNSS levelling, inertial navigation and precise orbit determination. Today global height systems with a 1 cm accuracy
are required for sea level and ocean circulation studies. This can be achieved by a future satellite mission with higher spatial
resolution in combination with improved local and regional gravity field modelling. A similar strategy could improve the very
economic method of determination of physical heights by GNSS levelling from the decimeter to the centimeter level. In inertial
vehicle navigation, in particular in sub-marine, aircraft and missile guidance, any improvement of global gravity field models
would help to improve reliability and the radius of operation. 相似文献
15.
B. C. Low 《Solar physics》1980,67(1):57-77
A method is prescribed for generating exact solutions of magnetostatic equilibrium describing a cylindrically symmetric magnetic flux tube oriented vertically in a stratified medium. Given the geometric shape of the field lines, compact formulae are presented for the direct calculation of all the possible distributions of pressure, density, temperature and magnetic field strength compatible with these field lines under the condition of static equlibrium. The plasma satisfies the ideal gas law and gravity is uniform in space. A particular solution is obtained by this method for a medium sized sunspot whose magnetic field obeys the similarity law of Schlüter and Temesváry (1958). With this solution, it is possible for the first time to illustrate explicitly the confinement of the magnetic field of the cool sunspot by the hotter external plasma in an exact relationship involving both magnetic pressure and field tension as well as the support of the weight of the plasma by pressure gradients. It is found that the cool region of the sunspot is not likely to extend much more than a few density scale heights below the photosphere. The sunspot field approaches being potential in the neighbourhood of the photosphere so that the Lorentz force exerting on the photosphere is less than what the magnetic pressure would suggest. This accounts for how the sunspot field can be confined in the photosphere where its magnetic pressure is often observed to even exceed the normal photospheric pressure. The energy mechanism operating in the sunspot and the question of mechanical stability are not treated in this paper.Normally at Lau Kuei Huat (Singapore) Private Limited, 55 Shipyard Road, Singapore 22, Singapore. 相似文献
16.
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
17.
Some properties of the dumbbell satellite attitude dynamics 总被引：1，自引：0，他引：1
Alessandra Celletti Vladislav Sidorenko 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):105-126
The dumbbell satellite is a simple structure consisting of two point masses connected by a massless rod. We assume that it moves around the planet whose gravity field is approximated by the field of the attracting center. The distance between the point masses is assumed to be much smaller than the distance between the satellite’s center of mass and the attracting center, so that we can neglect the influence of the attitude dynamics on the motion of the center of mass and treat it as an unperturbed Keplerian one. Our aim is to study the satellite’s attitude dynamics. When the center of mass moves on a circular orbit, one can find a stable relative equilibrium in which the satellite is permanently elongated along the line joining the center of mass with the attracting center (the so called local vertical). In case of elliptic orbits, there are no stable equilibrium positions even for small values of the eccentricity. However, planar periodic motions are determined, where the satellite oscillates around the local vertical in such a way that the point masses do not leave the orbital plane. We prove analytically that these planar periodic motions are unstable with respect to out-of-plane perturbations (a result known from numerical investigations cf. Beletsky and Levin Adv Astronaut Sci 83, 1993). We provide also both analytical and numerical evidences of the existence of stable spatial periodic motions. 相似文献
18.
We have studied the radiative stability of thermally isolated coronal loops with free-flow boundary conditions by nonlinear numerical simulation. We first establish a chromosphere-to-corona loop equilibrium (including the option of a deep chromosphere) by following the nonlinear evolution from an initial isothermal state with rigid boundaries. We then change the end conditions, to allow free flow and to fix the temperature, and investigate the response to non-isobaric perturbations. Within a family of loops of the same pressure, we find long hot loops to be stable and short cool loops to be unstable to the thermal chromosphericexpansion mode. The stable cases remain so, even when long chromospheric ends and/or gravity are added. In those cases which are unstable, we follow the subsequent nonlinear evolution which exhibits swelling of the chromosphere until the entire loop becomes cool and dense. 相似文献
19.
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
20.
Keith A. Holsapple 《Icarus》2004,172(1):272-303
The study of the equilibrium and stability of spinning ellipsoidal fluid bodies with gravity began with Newton in 1687, and continues to the present day. However, no smaller bodies of the Solar System are fluid. Here I model those bodies as elastic-plastic solids using a cohesionless Mohr-Coulomb yield envelope characterized by an angle of friction. This study began in Holsapple 2001. Here new closed-form algebraic formulas for the spin limits of ellipsoidal shapes are derived using an energy method. The fluid results of Maclaurin and Jacobi are again recovered as special cases. I then consider the stability of those equilibrium states. For elastic-plastic solids the common methods cannot be used, because the constitutive equations lack sufficient smoothness at the limiting plastic states. Therefore, I propose and study a new measure of the stability of dynamic processes in general bodies. An energy-based approach is introduced which is shown to include stability approaches used in the statics of nonlinear elastic and elastic-plastic bodies, spectral definitions and the Liapunov methods used for finite-dimensional dynamical systems. The method is applied to spinning, solid, strained bodies. In contrast to the special fluid case, it is found that the strain energy term of solid materials generally induces stability of all equilibrium shapes, except for two possible cases. First, strain softening in the elastic-plastic law can result in instability at the plastic limit spin. Second, a loss of shear stiffness can give unstable states at specific spins less than the limit equilibrium spins. In the latter case, a solid spinning ellipsoidal body without elastic shear stiffness can spin no faster than with a period of about 3.7 hr, else it will fail by shearing deformations. That is distinctly slower than the oft-quoted limit of 2.1 hr at which material would be flung off the equator by tensile forces. However, the final conclusion is that neither cohesion nor tensile strength is required for the shapes and spins of almost all of the larger observed asteroids: we cannot rule out rubble-pile structures. 相似文献