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1.
Rudolf Dvorak 《Celestial Mechanics and Dynamical Astronomy》1997,68(1):63-73
We report on the different results concerning the stability of the hierarchical triple systems where a close binary is accompanied
by a third star. There are different possible approaches to answer the question of the stability limits for such triple stars:
the most direct investigations can be undertaken in integrating numerically the respective equations of motion for many different
initial conditions. It is then difficult to take into account all the important parameters like eccentricities, inclination,
phases and masses. Analytical approaches and qualitative methods are more approriate to deal with this problem; the respective
results confirm the numerically found results that:
1. for prograde orbits the ratio semimajor axis of the inner orbits to the periastron position of the outer orbit is approximately
3.2
2. for retrograde orbits this ratio is just some 10 percents smaller
3. the results are not sensitive in what concerns the masses involved
4. There is a tendency that the inclinations and eccentricities change slightly the stability limits mentioned above.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
We have numerically investigated the stability of retrograde orbits/trajectories around Jupiter and the smaller of the primaries in binary systems RW-Monocerotis (RW-Mon) and Krüger-60 in the presence of radiation. A trajectory is considered as stable if it remains around the smaller mass for at least few hundred binary periods. In case of circular binary orbit, we find that the third order resonance provides the basis for reduction of stability region of retrograde motion of particle in RW-Mon and Sun-Jupiter system both in the presence and absence of radiation. Considering finite ellipticity in Sun-Jupiter system we find that for distant retrograde orbits, radiation from the Sun increases the width of the stable region and covers a significant portion of the region obtained in the absence of solar radiation. Further, due to solar radiation pressure, the stable region in the neighborhood of Jupiter has been found to shift much below the characteristic asymptotic line for the periodic retrograde orbits. In case of Krüger-60 we observe the distant retrograde orbits around the smaller of the primaries get affected considerably with increase in radiation parameter β1. Further the range of velocities for which stable motion may persist narrows down for distant retrograde orbits in this system. 相似文献
3.
This paper contains an analysis of the attitude stability of a spinning axisymmetric satellite whose mass center moves in any known planar periodic orbit of the restricted three-body problem while the spin axis remains normal to the orbit plane. A procedure based on Floquet theory is developed for constructing attitude instability charts, and examples of these are presented for two stable periodic orbits of the Earth-Moon system—one direct and one retrograde. The physical significance of these instability predictions is then explored by means of numerical integration of the full nonlinear equations of motion. Finally, an analysis based on averaging is performed, leading to approximate instability charts and indicating a possible connection between certain orbital-attitude resonance conditions and unstable attitude motions. 相似文献
4.
The mechanism by which ‘vertical’ branches consisting of symmetric, three-dimensional periodic orbits bifurcate from families of plane orbits at ‘veertical self-resonant’ orbits is discussed, with emphasis on the relationship between symmetry properties and multiplicity, and methods for the numerical determination of such branches are described. As examples, eight new families of all symmetry classes which branch vertically from the familyf of retrograde satellite orbits in the Sun-Jupiter case of the restricted problem (μ=0.000 95), are given in their entirety; these branches are found, as expected, to occur in pairs, each pair arising from the same self-resonant orbit, and their symmetry properties following the predicted pattern. The stability and other properties of the branch orbits are discussed. 相似文献
5.
Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow
modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous
(on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing,
centrally symmetric ellipses (2: 1 orbits). Depending on the density distribution in the system and the degree of halo inhomogeneity,
the orbit precession can be both prograde and retrograde, in contrast to systems with 1: 1 elliptical orbits where the precession
is unequivocally retrograde. In the first paper, we show that in the case where at least some of the orbits have a prograde
precession and the stellar distribution function is a decreasing function of angular momentum, an instability that turns into
the well-known radial orbit instability in the limit of low angular momenta can develop in the system. We also explore the
question of whether the so-called spoke approximation, a simplified version of the slow mode approximation, is applicable
for investigating the instability of stellar systems with highly elongated orbits. Highly elongated orbits in clusters with
nonsingular gravitational potentials are known to be also slowly precessing 2: 1 ellipses. This explains the attempts to use
the spoke approximation in finding the spectrum of slow modes with frequencies of the order of the orbit precession rate.
We show that, in contrast to the previously accepted view, the dependence of the precession rate on angular momentum can differ
significantly from a linear one even in a narrow range of variation of the distribution function in angular momentum. Nevertheless,
using a proper precession curve in the spoke approximation allows us to partially “rehabilitate” the spoke approach, i.e.,
to correctly determine the instability growth rate, at least in the principal (O(α
T−1/2) order of the perturbation theory in dimensionless small parameter α
T, which characterizes the width of the distribution function in angular momentum near radial orbits. 相似文献
6.
M. Hénon 《Celestial Mechanics and Dynamical Astronomy》1976,13(3):267-285
We describe a one-parameter family of periodic orbits in the planar problem of three bodies with equal masses. This family begins with Schubart's (1956) rectilinear orbit and ends in retrograde revolution, i.e. a hierarchy of two binaries rotating in opposite directions. The first-order stability of the orbits in the plane is also computed. Orbits of the retrograde revolution type are stable; more unexpectedly, orbits of the interplay type at the other end of the family are also stable. This indicates the possible existence of triple stars with a motion entirely different from the usual hierarchical arrangement. 相似文献
7.
8.
Using inter-satellite range data,the combined autonomous orbit determination problem of a lunar satellite and a probe on some special orbits is studied in this paper.The problem is firstly studied in the circular restricted three-body problem,and then generalized to the real force model of the Earth-Moon system.Two kinds of special orbits are discussed:collinear libration point orbits and distant retrograde orbits.Studies show that the orbit determination accuracy in both cases can reach that of the observations.Some important properties of the system are carefully studied.These findings should be useful in the future engineering implementation of this conceptual study. 相似文献
9.
V. V. Markellos 《Celestial Mechanics and Dynamical Astronomy》1974,10(1):87-134
The familyf of simple-periodic retrograde satellites of Jupiter is used as the generating family in order to find periodic orbits of the second generation of up to order eight. Thirteen new families of long-periodic orbits of the type of retrograde satellites are found and the significane of their characteristic family curves for the determination of regions of stability is investigated. The use of these, family curves is suggested for the direct discovery of such regions in a two-dimensional space of parameters. 相似文献
10.
Winston L. Sweatman 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):37-65
We locate members of an important category of periodic orbits in the Newtonian four-body problem. These systems perform an interplay motion similar to that of the periodic three-body orbit discovered by Schubart. Such orbits, when stable, have been shown to be a key feature and influence on the dynamics of few-body systems. We consider the restricted case where the masses are collinear and are distributed symmetrically about their centre of mass. A family of orbits is generated from the known (three-dimensionally) unstable equal masses case by varying the mass ratio, whilst maintaining the symmetry. The stability of these orbits to perturbation is studied using linear stability analysis, analytical approximation of limiting cases and nonlinear simulation. We answer the natural question: are there any stable periodic orbits of this kind? Three ranges of the mass ratio are found to have stable orbits and three ranges have unstable orbits for three-dimensional motion. The systems closely resemble their three-body counterparts. Here the family of interplay orbits is simpler requiring just one parameter to characterise the mass ratio. Our results provide a further insight into three-body orbits studied previously. 相似文献
11.
The distant retrograde orbits (DROs) can serve as the parking orbits for a long-term cis-lunar space station. This paper gives a comprehensive study on the transfer problem from DROs to Earth orbits, including low Earth orbits (LEOs), medium Earth orbits (MEOs), and geosynchronous orbits (GSOs), in the bicircular restricted four-body problem (BR4BP) via optimizations within a large solution space. The planar transfer problem is firstly solved by grid search and optimization techniques, and two types of transfer orbits, direct ones and low-energy ones, are both constructed. Then, the nonplanar transfer problem to Earth orbits with inclinations between 0 and 90 degrees are solved via sequential optimizations based on the planar transfers. The transfer characteristics in the cases of different destination orbit inclinations are discussed for both the direct and the low-energy transfer orbits. The important role of the lunar gravity in the low-energy transfers is also discussed, which can overcome the increase of transfer cost caused by the high inclination of Earth orbits. The distinct features of different transfer scenarios, including multiple revolutions around the Earth and Moon, the exterior phase, and the lunar flyby, are discovered. The energy of transfer orbits is exploited to discuss the effects of close lunar flybys. The results will be helpful for the transfer design in future manned or unmanned return missions, and can also provide valuable information for selecting proper parking DROs for cis-lunar space stations.
相似文献12.
Victor Szebehely 《Celestial Mechanics and Dynamical Astronomy》1978,18(4):383-389
A quantitative measure of stability based on Hill's definition is evaluated for direct and retrograde satellite orbits. These orbits are known as Poincaré's first kind in the restricted problem of three bodies. Onsets of possible instabilities and captures are established. A critical (maximum) value of the satellite's orbital radius is found for stability as a remarkably simple function of the massparameter. The results are applied to the natural satellites of the solar system. 相似文献
13.
J. J. Rawal 《Earth, Moon, and Planets》1986,36(2):135-138
On the basis of works of King and Innanen, the limiting direct and retrograde orbits around the planets Mercury and Venus have been calculated. Synthesizing this concept with the concept of synchronous orbits around the planets and tidal drags acting within them it is shown that Venus may not have retained any satellite direct or retrograde but Mercury may have retained a retrograde satellite at a distance between 225000 and 252700 km from its center. It is urged that this satellite may be investigated observationally. 相似文献
14.
Ian W. Walker 《Celestial Mechanics and Dynamical Astronomy》1983,29(2):117-148
The stability parameters developed and discussed in the first paper of this series (Walkeret al., 1980) are used to determine empirically, by means of numerical integration experiment, regions of stability for corotational, coplanar, hierarchical three-body systems. The initially circular case of these systems is studied: the components of the close binary are taken to move initially in circular orbits with respect to their common mass-centre, the third mass initially moving in a circular orbit with respect to the same mass-centre such that its orbit lies wholly outside those of the former two masses. The stability of these systems is then studied by reference to the empirical stability parameters and the initial ratio of the semi-major axes of the orbit of the close binary to that of the third mass about the binary's mass-centre, which is less than unity. For given values of the stability parameters it is determined how the stability of a system is affected by changes in the ratio of the semi-major axes. It is found that an upper limit to this ratio exists which determines the region of stability for such systems. It is also found possible, in the region of instability, to predict how unstable a system will be i.e. crudely speaking, the number of orbits it may be expected to execute before some gross instability sets in. The effect commensurabilities in mean motion have on the stability of these systems is also considered. It is generally found that these commensurabilities enhance the stability of these systems. The predictive powers of the method are then tested: using many test cases it is seen how accurately the stability or instability of a system may be predicted. 相似文献
15.
16.
T.A. Heppenheimer 《Icarus》1975,24(2):172-180
The problem of the origin of Jupiter's outer satellites is treated within the framework of the theory of capture through collinear libration points. Lower bounds for the satellites' semimajor axes are found from a corrected rederivation of Bailey's capture theory. Upper bounds are found from a new derivation of the stability limit for satellites, based on Floquet stability theory.It is shown that if the bodies had near-zero relative velocity when passing the libration point, direct orbits would lie outside retrograde orbits, which is not the case for Jupiter. It is found that the dimensions and distributions of the direct group are well explained by libration-point capture with solar mass, which is interpreted as indicating capture soon after Jupiter's formation. But ad hoc assumptions are required for this capture model to explain the retrograde group. It is concluded that the direct and retrograde groups may have had different mechanisms of origin. 相似文献
17.
This paper introduces a new set of compatible orbits called “Two-Way Orbits,” whose ground track path is a closed-loop trajectory that intersects at certain points with tangent intersections. The spacecraft passes over these tangent intersections once in a prograde mode and once in a retrograde mode. Motivations are found for the need to have simultaneous observations of the same target area in both Earth observation and reconnaissance systems. The general mathematical model to design a Two-Way Orbit is presented for the specific case where the tangent points are experienced at the orbit extremes, perigee and apogee. As for the general case, Two-Way Orbit conditions are formulated and numerically solved. Results show that, in general, Two-Way Orbits could be formed over any point on Earth. Since Two-Way Orbits use compatible orbits, the theory of Flower Constellations can be applied to them. Using these Two-Way Orbits, this paper also introduces the Two-Way Flower Constellations that have one spacecraft prograde and one retrograde passing simultaneously over the tangent intersection. 相似文献
18.
P. Delibaltas 《Astrophysics and Space Science》1976,45(1):207-233
Several families of planar planetary-type periodic orbits in the general three-body problem, in a rotating frame of reference, for the Sun-Jupiter-Saturn mass-ratio are found and their stability is studied. It is found that the configuration in which the orbit of the smaller planet is inside the orbit of the larger planet is, in general, more stable.We also develop a method to study the stability of a planar periodic motion with respect to vertical perturbations. Planetary periodic orbits with the orbits of the two planets not close to each other are found to be vertically stable. There are several periodic orbits that are stable in the plane but vertically unstable and vice versa. It is also shown that a vertical critical orbit in the plane can generate a monoparametric family of three-dimensional periodic orbits. 相似文献
19.
J. I. Read M. I. Wilkinson N. W. Evans G. Gilmore Jan T. Kleyna 《Monthly notices of the Royal Astronomical Society》2006,366(2):429-437
We present an improved analytic calculation for the tidal radius of satellites and test our results against N -body simulations.
The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and the orbit of the star within the satellite . We demonstrate that this last point is critical and suggest using three tidal radii to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power-law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically.
Over short times (≲1–2 Gyr ∼1 satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic. 相似文献
The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and the orbit of the star within the satellite . We demonstrate that this last point is critical and suggest using three tidal radii to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power-law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically.
Over short times (≲1–2 Gyr ∼1 satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic. 相似文献
20.
We analyze nearly periodic solutions in the plane problem of three equal-mass bodies by numerically simulating the dynamics of triple systems. We identify families of orbits in which all three points are on one straight line (syzygy) at the initial time. In this case, at fixed total energy of a triple system, the set of initial conditions is a bounded region in four-dimensional parameter space. We scan this region and identify sets of trajectories in which the coordinates and velocities of all bodies are close to their initial values at certain times (which are approximately multiples of the period). We classify the nearly periodic orbits by the structure of trajectory loops over one period. We have found the families of orbits generated by von Schubart’s stable periodic orbit revealed in the rectilinear three-body problem. We have also found families of hierarchical, nearly periodic trajectories with prograde and retrograde motions. In the orbits with prograde motions, the trajectory loops of two close bodies form looplike structures. The trajectories with retrograde motions are characterized by leafed structures. Orbits with central and axial symmetries are identified among the families found. 相似文献