共查询到20条相似文献，搜索用时 15 毫秒
1.
2.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1993,56(4):563-599
A mapping model is constructed to describe asteroid motion near the 3 : 1 mean motion resonance with Jupiter, in the plane. The topology of the phase space of this mapping coincides with that of the real system, which is considered to be the elliptic restricted three body problem with the Sun and Jupiter as primaries. This model is valid for all values of the eccentricity. This is achieved by the introduction of a correcting term to the averaged Hamiltonian which is valid for small values of the ecentricity.We start with a two dimensional mapping which represents the circular restricted three body problem. This provides the basic framework for the complete model, but cannot explain the generation of a gap in the distribution of the asteroids at this resonance. The next approximation is a four dimensional mapping, corresponding to the elliptic restricted problem. It is found that chaotic regions exist near the 3 : 1 resonance, due to the interaction between the two degrees of freedom, for initial conditions close to a critical curve of the circular model. As a consequence of the chaotic motion, the eccentricity of the asteroid jumps to high values and close encounters with Mars and even Earth may occur, thus generating a gap. It is found that the generation of chaos depends also on the phase (i.e. the angles andv) and as a consequence, there exist islands of ordered motion inside the sea of chaotic motion near the 3 : 1 resonance. Thus, the model of the elliptic restricted three body problem cannot explain completely the generation of a gap, although the density in the distribution of the asteroids will be much less than far from the resonance. Finally, we take into account the effect of the gravitational attraction of Saturn on Jupiter's orbit, and in particular the variation of the eccentricity and the argument of perihelion. This generates a mixing of the phases and as a consequence the whole phase space near the 3 : 1 resonance becomes chaotic. This chaotic zone is in good agreement with the observations. 相似文献
3.
J. P. S. Carvalho R. Vilhena de Moraes A. F. B. A. Prado 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):371-388
In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites.
We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a
third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to
the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute
the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied
to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the
case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed,
considering that the perturbations are acting together or one at a time. 相似文献
4.
We consider the dynamics of a test particle co-orbital with a satellite of mass m
s which revolves around a planet of mass M
0 m
s with a mean motion n
s and semi-major axis a
s. We study the long term evolution of the particle motion under slow variations of (1) the mass of the primary, M
0, (2) the mass of the satellite, m
s and (3) the specific angular momentum of the satellite J
s. The particle is not restricted to small harmonic oscillations near L
4 or L
5, and may have any libration amplitude on tadpole or horseshoe orbits. In a first step, no torque is applied to the particle, so that its motion is described by a Hamiltonian with slowly varying parameters. We show that the torque applied to the satellite, as measured by s = js/(n
s
J
s) induces an distortion of the phase space which is entirely described by an asymmetry coefficient = s/, where = m
s/M. The adiabatic invariance of action implies furthermore that the long term evolution of the particle co-orbital motion depends only on the variation of m
s
a
s with time. Applying a constant torque to the particle, as measured by s = js/(n
s
J
p) is then merely equivalent to replacing = s/ by = (s – p)/. However, if the torque acting on the particle exhibits a radial gradient, then the action is no more conserved and the evolution of the particle orbit is no more controlled by m
s
a
s only. We show that even mild torque gradients can dominate the orbital evolution of the particle, and eventually decide whether the latter will be pulled towards the stable equilibrium points L
4 or L
5, or driven away from them. Finally, we show that when the co-orbital bodies are two satellites with comparable masses m
1 and m
2, we can reduce the problem to that of a test particle co-orbital with a satellite of mass m
1 + m
2. This new problem has then parameters varying at rates which are combinations, with appropriate coefficients, of the changes suffered by each satellite. 相似文献
5.
Michèle Moons Alessandro Morbidelli 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):99-108
We study the motion of asteroids in the main mean motion commensurabilities in the frame of the planar restricted three-body problem. No assumption is made about the size of the eccentricity of the asteroid. At small to moderate eccentricity, we recover existing results (shape of the phase space and location of secondary resonances). We also provide global pictures of the dynamics in the region of secondary resonances. At high eccentricity, the phase space portraits of the integrable part of the Hamiltonian show new families of stable orbits for the 3:2 and 2:1 cases and the secular resonances 5 and 6 are located. 相似文献
6.
An analysis of ordered and chaotic regions of motion in the outer asteroid belt has shown that once the eccentricity of Jupiter is introduced the chaotic regions of the circular model are quite easily depleted. This suggests that also objects in neighbouring regions must be strongly perturbed. Therefore it is not surprising that many outer belt asteroids have been reported in the literature as resonant or anyway dynamically protected. By using the planar elliptic restricted 3-body model we have investigated the motion of outer belt asteroids which had not been suspected to librate. We find 3 cases of libration and 11 cases of e, coupling that can be explained within the theory of secular resonances. It is thus established that in the outer belt only resonant and dynamically protected asteroids can have lifetimes of the same order as the age of the Solar System. 相似文献
7.
The global semi-numerical perturbation method proposed by Henrard and Lemaître (1986) for the 2/1 resonance of the planar elliptic restricted three body problem is applied to the 3/1 resonance and is compared with Wisdom's perturbative treatment (1985) of the same problem. It appears that the two methods are comparable in their ability to reproduce the results of numerical integration especially in what concerns the shape and area of chaotic domains. As the global semi-numerical perturbation method is easily adapted to more general types of perturbations, it is hoped that it can serve as the basis for the analysis of more refined models of asteroidal motion. We point out in our analysis that Wisdom's uncertainty zone mechanism for generating chaotic domains (also analysed by Escande 1985 under the name of slow Hamiltonian chaotic layer) is not the only one at work in this problem. The secondary resonance
p
= 0 plays also its role which is qualitatively (if not quantitatively) important as it is closely associated with the random jumps between a high eccentricity mode and a low eccentricity mode. 相似文献
8.
Makoto Yoshikawa 《Celestial Mechanics and Dynamical Astronomy》1992,54(1-3):287-290
Motions of asteroids in mean motion resonances with Jupiter are studied in three-dimensional space. Orbital changes of fictitious asteroids in the Kirkwood gaps are calculated by numerical integrations for 105 – 106 years. The main results are as follows: (1) There are various motions of resonant asteroids, and some of them are very complicated and chaotic and others are regular. (2) The eccentricity of some asteroids becomes very large, and the variation of the inclination is large while the eccentricity is large. (3) In the 3:1 resonance, there is a long periodic change in the variation of the inclination, when (7 : ) is a simple ratio (7: longitude of perihelion, : longitude of node). (4) In the 7:3 resonance, the variation of the inclination of some resonant asteroids is so large that prograde motion becomes retrograde. Some asteroids in the 7:3 resonance can collide with the Sun as well as with the inner planets. 相似文献
9.
《天文和天体物理学研究(英文版)》2017,(4)
A new non-simplified model of formation flying is derived in the presence of an oblate mainbody and third-body perturbation.In the proposed model,considering the perturbation of the thirdbody in an inclined orbit,the effect of obliquity(axial tilt) of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite.From a new point of view,J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit,are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion.To validate the accuracy of the model presented in this study,an auxiliary model was constructed as the Main-body Center based Relative Motion(MCRM) model.Finally,the importance of the main-body's obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping.The main-body's obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit(PCO) formations. 相似文献
10.
O. M. Kochetova 《Solar System Research》2004,38(1):66-75
Masses of 19 asteroids have been determined from the analysis of their gravitational effect on the motion of perturbed bodies. The following asteroids were selected as perturbed bodies: (1) those which had single close encounters with the perturbing asteroid; (2) those whose mean motion was in a 1 : 1 commensurability with that of the perturber and which had close or moderate recurrent encounters with the perturber. The perturber mass was determined from observations of several tens of perturbed asteroids that were selected from these two groups. The selection criterion was the error of the mass determined from observations of only one asteroid. Positional observations of the asteroids on the interval 1900–2002 were used. The masses were determined with errors by an order-half an order of magnitude smaller than the masses found. The results are compared with those of other authors. 相似文献
11.
Yoshihide Kozai 《Celestial Mechanics and Dynamical Astronomy》1985,36(1):47-69
Secular perturbations of asteroids are derived for mean motion resonance cases under the assumptions that the disturbing planets are moving along circular orbits on the same plane and that critical arguments are fixed at stable equilibrium points. Under these assumptions the equations of motion are reduced to those of one degree of freedom with the energy integral. Then equi-energycurves on (2g-X) plane (g and X being, respectively, the argument of perihelion and (1–e2)1/2) are derived for given values of the two constant parameters, the semi-major axis and =(1–e2)1/2 cos i, and the variations of the eccentricity and the inclination as functions of the argument of perihelion are graphically estimated. In fact this method is applied to numbered asteroids with commensurable mean motions to estimate the ranges of the variations of orbital elements.The same method is also applied to the Pluto-Neptune system and the results are found to agree with those of numerical integrations and show that the argument of perihelion of Pluto librates around 90°. 相似文献
12.
M. A. Vashkov’yak 《Astronomy Letters》2003,29(8):543-551
We suggest a nonstandard methodology for studying the influence of Jupiter on the secular orbital evolution of a distant satellite of Saturn. This influence is tangible only in short time spans near the times of the smallest separation between Jupiter and Saturn, i.e., when the heliocentric longitudes of the two planets coincide. These times are spaced about 20 years apart. To describe the jumplike behavior of perturbations, we suggest approximating the principal part of the perturbing function averaged over the satellite’s motion by a two-parameter exponential wavelet-type (burst) function. The subsequent averaging (smoothing) of the perturbing function allows us to eliminate the 20-year-period terms and obtain an approximate analytical solution in a special case of the problem. The results are illustrated by plots of the variations in the averaged perturbing function and the orbital eccentricity of Saturn’s outer satellite S/2000 S1, which is most strongly perturbed by Jupiter. 相似文献
13.
Alexandre Pousse Philippe Robutel Alain Vienne 《Celestial Mechanics and Dynamical Astronomy》2017,128(4):383-407
In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit. 相似文献
14.
M. A. Vashkovjak 《Celestial Mechanics and Dynamical Astronomy》1976,13(3):313-324
The restricted problem of the motion of a point of negligible mass (asteroid) in anN-planetary system is considered. It is assumed that all the planets move about the central body (Sun) along circular orbits in the same plane and the mean motions of the asteroid and the planets are incommensurable. The asteroid orbit evolution is described as a first approximation by secular equations with the perturbing function averaged by the mean longitudes of the asteroid and the planets. For small values of the asteroid orbit eccentricity an expression for the secular part of the perturbing function has been obtained. This expression holds for the arbitrary values of the asteroid orbit semiaxis which are different from those of the planet orbit radii. The stability of the asteroid circular orbits in a linear approximation with respect to the eccentricity is studied. The critical inclinations for a Solar system model are calculated. 相似文献
15.
Christos Efthymiopoulos 《Celestial Mechanics and Dynamical Astronomy》2013,117(1):101-112
We present estimates of the size of the analytic domain of stability for co-orbital motions obtained by a high order normal form in the framework of the elliptic restricted three body problem. As a demonstration example, we consider the motion of a Trojan body in an extrasolar planetary system with a giant planet of mass parameter $\mu =0.005$ μ = 0.005 and eccentricity $e^{\prime }=0.1$ e ′ = 0.1 . The analysis contains three basic steps: (i) derivation of an accurate expansion of the Hamiltonian, (ii) computation of the normal form up to an optimal order (in the Nekhoroshev sense), and (iii) computation of the optimal size of the remainder at various values of the action integrals (proper elements) of motion. We explain our choice of variables as well as the method used to expand the Hamiltonian so as to ensure a precise model. We then compute the normal form up to the normalisation order $r=50$ r = 50 by use of a computer-algebraic program. We finally estimate the size $||R||$ | | R | | of the remainder as a function of the normalization order, and compute the optimal normalization order at which the remainder becomes minimum. It is found that the optimal value $\log (||R_{opt}||)$ log ( | | R o p t | | ) can serve in order to construct a stability map for the domain of co-orbital motion using only series. This is compared to the stability map found by a purely numerical approach based on chaotic indicators. 相似文献
16.
N. Delsate P. Robutel A. Lemaître T. Carletti 《Celestial Mechanics and Dynamical Astronomy》2010,108(3):275-300
We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed
by a third body, assumed to lay in the equatorial plane (Sun or Jupiter for example) using a Hamiltonian formalism. We are
able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain
constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed
theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo
mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally,
we also bring to the light that the coefficient J
2 is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect and the coefficient J
3 determines a shift of the equilibria. 相似文献
17.
Makoto Yoshikawa 《Celestial Mechanics and Dynamical Astronomy》1987,40(3-4):233-272
When asteroids are in the secular resonance 6, the variation of the eccentricity becomes very large. In this paper, the dynamics of this secular resonance 6 is investigated by a simple analytical model, in which the third degree terms of the eccentricity and inclination are taken into account. The eccentricity variations of asteroids located near this resonance are represented clearly by the diagrams of equi-Hamiltonian curves on the plane of
versuse (
the longitude of perihelion of asteroids and Saturn,e: the eccentricity of asteroids). These diagrams predict that the eccentricity of these asteroids suffers a large increase or decrease, and that the secular resonance argument
librates about 0° and 180°. In order to confirm these predictions, numerical integrations are carried out over one million years. By these integrations, it is found that the eccentricity of secular resonant asteroids becomes more than 0.8, and that the libration about 0° also exists, as well as the libration about 180°. The strongly depopulated region in the asteroidal belt, which corresponds to the position of the secular resonance 6, is also explained well by this analytical model. 相似文献
18.
The simplest model of a resonant problem of second order is the planar and circular case. Simplification like this is very old and for 3/1 resonance, several authors have studied this problem with different purposes. In this work, we test this model for the available asteroids, by applying Hori's perturbation method. Explicit solutions of the intermediate orbit are obtained. In the plane of two constants of the problem, all types of motion are described. By testing the model, it is shown that, in general, one can confirm results of numerical integrations indicating libration for a few number of asteroids and circulation for most of them. However, agreement in numerical values for amplitude and period of librations seems to be not possible mainly if Jupiter's eccentricity is neglected. On the other hand, even though there might be some physical reasons determining that only asteroids with high eccentricity may librate, it is shown that, from mathematical point of view, libration may occur even in the case of small eccentricities provided that some relations are satisfied. 相似文献
19.
G. E. O. Giacaglia 《Celestial Mechanics and Dynamical Astronomy》1977,15(2):191-215
The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power ofr/r, r being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the Moon or Sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations. 相似文献
20.
R. Dvorak 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):71-80
We present numerical results of the so-called Sitnikov-problem, a special case of the three-dimensional elliptic restricted three-body problem. Here the two primaries have equal masses and the third body moves perpendicular to the plane of the primaries' orbit through their barycenter. The circular problem is integrable through elliptic integrals; the elliptic case offers a surprisingly great variety of motions which are until now not very well known. Very interesting work was done by J. Moser in connection with the original Sitnikov-paper itself, but the results are only valid for special types of orbits. As the perturbation approach needs to have small parameters in the system we took in our experiments as initial conditions for the work moderate eccentricities for the primaries' orbit (0.33e
primaries
0.66) and also a range of initial conditions for the distance of the 3
rd
body (= the planet) from very close to the primaries orbital plane of motion up to distance 2 times the semi-major axes of their orbit. To visualize the complexity of motions we present some special orbits and show also the development of Poincaré surfaces of section with the eccentricity as a parameter. Finally a table shows the structure of phase space for these moderately chosen eccentricities. 相似文献