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1.
The equilibria and periodic orbits around a dumbbell-shaped body 总被引：1，自引：0，他引：1
This paper investigates the equilibria, their stability, and the periodic orbits in the vicinity of a rotating dumbbell-shaped body. First, the geometrical model of dumbbell-shaped body is established. The gravitational potential fields are obtained by the polyhedral method for several dumbbell-shaped bodies with various length–diameter ratios. Subsequently, the equilibrium points of these dumbbell-shaped bodies are computed and their stabilities are analyzed. Periodic orbits around equilibrium points are determined by the differential correction method. Finally, in order to understand further motion characteristic of dumbbell-shaped body, the effect of the rotating angular velocity of the dumbbell-shaped bodies is investigated. This study extends the research work of the orbital dynamics from simple shaped bodies to complex shaped bodies and the results can be applied to the dynamics of orbits around some asteroids. 相似文献
2.
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
3.
Dynamic environment near heterogeneous asteroids is worth studying since many small bodies have varied internal structures. In this paper, we investigated the effect of temporary resonance with the heterogeneous Itokawa. Zero-power curves divide the space into four regions. The test particle experiences orbital energy-enhancing in the Region I and Region III, but receding in the Region II and Region IV. Moreover, there are differences in zero-power curves between the heterogeneous and homogeneous cases. The absolute values of gravity power in the gravitational field of heterogeneous Itokawa are more significant than those of the homogeneous one. It means the particle suffers from stronger energy change near the heterogeneous body. Numerical simulations conducted in Region II and Region III verify the difference. Thus, vicinal ejecta is easier to run away from a heterogeneous Itokawa, which may lead to a more frequent exchange of materials on the surface. These results give a better understanding of dust’s motion near a heterogeneous body. Moreover, the performance of temporary resonance near a heterogeneous body might serve as a guiding principle for probe orbiting an asteroid with a varied internal structure. 相似文献
4.
《Planetary and Space Science》2007,55(4):512-516
The existence and linear stability of equilibrium points in the Robe's restricted three body problem have been studied after considering the full buoyancy force as in Plastino and Plastino and by assuming the hydrostatic equilibrium figure of the first primary as an oblate spheroid. The pertinent equations of motion are derived and existence of all equilibrium points is discussed. It is found that there is an equilibrium point near the centre of the first primary. Further there can be one more equilibrium point on the line joining the centre of the first primary and second primary and infinite number of equilibrium points lying on a circle in the orbital plane of the second primary provided the parameters occurring in the problem satisfy certain conditions. So, there can be infinite number of equilibrium points contrary to the classical restricted three body problem. 相似文献
5.
Eva Tresaco Jean Paulo S. Carvalho Antonio F. B. A. Prado Antonio Elipe Rodolpho Vilhena de Moraes 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):9
This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from \(J_2\) up to \(J_6\), and the tesseral harmonics \(\overline{C}_{22}\) that is of the same magnitude than zonal \(J_2\). In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury–Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury’s gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits. 相似文献
6.
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
7.
Przemysław Bartczak Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》2003,86(2):131-141
We propose a new, simple model to describe the gravity field of irregular, nonspherical celestial bodies, like small moons or minor asteroids. The simple idea of Duboshin to use a material straight segment for such bodies is extended by combining two perpendicular segments of different lengths and masses. In typical situations, when the longest axis of the body coincides with one segment, the remaining segment must have an imaginary length. The potential remains a real function even if one segment is imaginary. The new model is confronted with the exact form of an ellipsoid's potential and with two alternative simple models for a two-axial and a three-axial ellipsoid. 相似文献
8.
This paper analyzes Robe??s circular restricted three-body problem when the hydrostatic equilibrium figure of the first primary is assumed to be an oblate spheroid, the shape of the second primary is considered as a triaxial rigid body, and the full buoyancy force of the fluid is taken into account. It is found that there is an equilibrium point near the center of the first primary, another equilibrium point exists on the line joining the centers of the primaries and there exist infinite number of equilibrium points on an ellipse in the orbital plane of the second primary. It is also observed that under certain conditions, all these equilibrium points can be stable. The most interesting and distinguishable results of this study are the existence of elliptical points and their stability. 相似文献
9.
The paper discusses the possibilty of interpreting the magnetic fields of astronomical bodies in the framework of a unified field theory.Using one of the solutions of the generalized field theory, a direct relation between the polar magnetic field, the angular velocity and the gravitational potential of the body considered, is obtained. The geometric model used for applications has spherical symmetry and is of the type (FIGI).The predictions of the theoretical formula, obtained from the model, are compared with available observational data, and with the empirical formula of Blackett. The theoretical formula gives a possible interpretation of a seed magnetic field which will develop and produce the large-scale magnetic field observed for celestial objects. The formula shows that the field is generated as a result of rotation of a massive object. 相似文献
10.
Milan Burša 《Earth, Moon, and Planets》1993,62(2):149-159
The orbital gravitational potential energies of the planets and of the satellites have been estimated and compared to the gravitational potential energies of the bodies themselves and to the gravitational potential energy of the Sun. From the point of view of the gravitational potential energy distribution two quite different groups of the planets can be distinguished clearly. However, the gravitational potential energy of the systems is mainly concentrated within the central bodies, only about 10–5 in orbiting bodies. 相似文献
11.
M. Bahgat El-Shaarawy 《Earth, Moon, and Planets》1989,47(3):217-230
In a series of papers, the equilibrium configurations of highly rotating fluid bodies have been derived. The deformation of these inhomogeneous self-gravitating fluid, of arbitrary internal structure are due to centrifugation potential. These level surfaces are expressed in terms of fourth-order sectorial harmonics.In this paper, the main equations of the problem — such as the surface of the distorted body, the gravitational potential at an arbitrary point and the disturbing potential — have been expanded to the fourth-order in terms of the even-order sectorial harmonics.This work will hereafter be referred to as Paper I. 相似文献
12.
Victor Szebehely Arthur L. Whipple 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):125-133
The restricted problem of three bodies is generalized to the restricted problem of 2+n bodies. Instead of one body of small mass and two primaries, the system is modified so that there are several gravitationally interacting bodies with small masses. Their motions are influenced by the primaries but they do not influence the motions of the primaries. Several variations of the classical problem are discussed. The separate Jacobian integrals of the minor bodies are lost but a conservative (time-independent) Hamiltonian of the system is obtained. For the case of two minor bodies, the five Lagrangian points of the classical problem are generalized and fourteen equilibrium solutions are established. The four linearly stable equilibrium solutions which are the generalizations of the triangular Lagrangian points are once again stable but only for considerably smaller values of the mass parameter of the primaries than in the classical problem. 相似文献
13.
S. A. Naroenkov D. O. Glazachev A. P. Kartashova O. P. Popova I. S. Turuntaev 《Solar System Research》2018,52(6):534-546
Quick assessment of hazardous effects from impacts of large celestial bodies is achieved through the development of a new consequence calculator. A distinctive feature of this calculator is a new block, the Hazardous-Orbit Constructor, which simulates the conditions of entry of a celestial body into the Earth’s atmosphere and determines the orbital parameters of the body based on given atmospheric entry conditions. This block is used to simulate the atmospheric entry conditions of known asteroids and meteoroids and to determine the orbital parameters of known bolides leading to meteorite fall events. For the case of asteroid 2008 TC3 and the P?ibram meteorite, it is shown that within the potential impact area of the celestial body, the atmospheric entry angle may vary considerably. 相似文献
14.
We examine the stability of the orbit of an artificial moon of a small celestial body in the presence of an external massive
perturbing body in terms of the restricted three-body problem. The orbit of this moon is shown to be dependent on the shape
of the small body and central gravitational field of the external body. We study how these factors interact with each other
and how they affect the stability of the orbit. 相似文献
15.
In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun–Jupiter and Sun–Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with. 相似文献
16.
V. I. Ferronsky S. A. Denisik S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1981,23(3):243-267
The Hamiltonian form of Jacobi's virial equation, which permits obtaining solution of the equation while considering both gravitational and Coulomb interactions, is given for the system of the material points constituting a celestial body.On the basis of the numerical solutions, in the framework of the plasma model of a celestial body, it is shown that for the Coulomb interactions of charged particles the product of the form-factors and , entering expressions for the potential energy and the moment of inertia, remains constant.Without any model restrictions this conclusion is confirmed in case of the asymptotic time limit of simultaneous collision of all the charged particles of the system.A relationship between the potential energy of a spherically symmetrical celestial body and its mass through a phenomenological parameter, which is the sound velocity, is found from the consideration of the hydrostatic equilibrium condition of the body, taking the Coulomb interactions into account. 相似文献
17.
18.
V. I. Ferronsky S. A. Denisik S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1984,32(2):173-183
Generalized Jacobi's equation is derived by introducing the friction force into the equations of motion of mass points constituting the system.The exact solution of the equation of virial oscillations of celestial bodies written for non-conservative systems is obtained using non-linear time scale in the course of the change of variables for a particular friction force law.The nature of the undamped virial oscillations of celestial bodies is though to be related to the system unstability near the state determined by the virial theorem. Thus, the friction force changes its sign near the unstable equilibrium state and due to dissipation of energy during evolution of the system the undamped virial oscillations can be described as self-exited oscillations. 相似文献
19.
引力波是爱因斯坦和其他物理学家提出的关于广义相对论的四大预言之一。除了PSR1 91 3 + 1 6引力辐射阻尼的观测提供了引力波存在的间接证据外 ,科学家至今仍没有在实验室中确证引力波的存在。由于人类目前的技术水平还不可能在实验室中产生强度可供探测的引力波 ,而宇宙中存在大量大质量、高速运动的天体 ,有可能产生较强的引力波 ,天体引力波源自然成为现阶段科学家研究引力波的首选。本文介绍广义相对论框架下预言的引力波性质 ,引力波探测的理论依据 ,共振型棒式天线和激光干涉仪两大类探测器的基本原理 ,引力波探测实验的现状和面临的困难 ,科学家采取的对策 ,以及爆发型和连续型两类天体引力波源。最后介绍了正在计划中的几个引力波探测空间实验 相似文献
20.
Simulation of the full two rigid body problem using polyhedral mutual potential and potential derivatives approach 总被引：3，自引：0，他引：3
Eugene G. Fahnestock Daniel J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):317-339
Herein we investigate the coupled orbital and rotational dynamics of two rigid bodies modelled as polyhedra, under the influence of their mutual gravitational potential. The bodies may possess any arbitrary shape and mass distribution. A method of calculating the mutual potential’s derivatives with respect to relative position and attitude is derived. Relative equations of motion for the two body system are presented and an implementation of the equations of motion with the potential gradients approach is described. Results obtained with this dynamic simulation software package are presented for multiple cases to validate the approach and illustrate its utility. This simulation capability is useful both for addressing questions in dynamical astronomy and for enabling spacecraft missions to binary asteroid systems. 相似文献