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1.
D.J. Scheeres 《Icarus》2007,189(2):370-385
The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.  相似文献   

2.
Stability of Binary Asteroids   总被引：1，自引：0，他引：1  
D.J. Scheeres 《Icarus》2002,159(2):271-283
The stability and final outcome of a strongly interacting binary asteroid system is considered. We discuss the implications of the system transferring energy and angular momentum between rotational and translational motion while conserving the total system energy and angular momentum. Using these results we can develop a set of sufficient conditions for stability against escape and impact. These allow us to delineate several classes of final outcomes for a binary asteroid system, each of which may have implications for asteroid observations. The effects of energy dissipation on an asteroid binary system are also considered and are shown to be able to change the stability of the system against escape and impact. An example computation for the near-Earth asteroid binary 1996 FG3 is given along with a series of numerical explorations of an evolving binary system consisting of an ellipsoid and a sphere of equal mass.  相似文献   

3.
Stability of the planar full 2-body problem   总被引：1，自引：0，他引：1  
The stability of the Full Two-Body Problem is studied in the case where both bodies are non-spherical, but are restricted to planar motion. The mutual potential is expanded up to second order in the mass moments, yielding a highly symmetric yet non-trivial dynamical system. For this system we identify all relative equilibria and determine their stability properties, with an emphasis on finding the energetically stable relative equilibria and conditions for Hill stability of the system. The energetically stable relative equilibria always correspond to the classical “gravity gradient” configuration with the long ends of the two bodies pointed at each other, however there always exists a second equilibrium in this configuration at a closer separation that is unstable. For our model system we precisely map out the relations between these different configurations at a given value of angular momentum. This analysis identifies the fundamental physical constraints and limitations that exist on such systems, and has immediate applications to the stability of asteroid systems that are fissioned due to a rapid spin rate. Specifically, we find that all contact binary asteroids which are spun to fission will initially lie in an unstable dynamical state and can always re-impact. If the total system energy is positive, the fissioned system can disrupt directly from this relative equilibrium, while if it is negative the system is bound together.  相似文献   

4.
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5.
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   

6.
The distribution of escape energy, escape velocity and final binary eccentricity in the breakup of a three-body system have been studied, using a recent survey of 25 000 numerical experiments. The dependence of these distributions on the initial parameters have been analysed and were found to agree well with analytical predictions in some cases. The escape velocity depends mainly on the total energy and angular momentum of the system, while the eccentricity is markedly different between planar and three-dimensional systems.  相似文献   

7.
Near-Earth Asteroid (66391) 1999 KW4 was the subject of the recently published first extensive radar imaging, shape and mutual orbit modeling, and physical and dynamical characterization of a binary asteroid. In this paper we present in detail our numerical simulation of KW4 behind that work. Our propagations of the system with some variation in estimated parameters cover the set of KW4's possible current dynamical states consistent with the body models and other information obtained directly from the observations. We also apply our implementation of this simulation capability to address some of the dynamical mechanisms by which KW4 may be moved into the more energetically excited of those possible current states, particularly solar gravity interaction. Through comparison of the results with certain features of the observation data, we conclude that the actual KW4 system is not in the most energetically relaxed configuration but must be moderately excited. The system occupies a generalized Cassini state 2 which is different from that considered in most previously published treatments of Cassini states in that it involves co-precession of the primary's spin frame and the mutual orbit rather than co-precession of a satellite's spin frame and that satellite's orbit about the primary. We present a simple analytical theory describing the system's dynamics, which should be applicable to any other binary systems, of which KW4 is representative, in which a massive, roughly oblate primary is spinning rapidly relative to the rate of its mutual orbit with an on-average synchronous, elongated secondary. We examine separately both the effect of the larger binary component's oblateness, and the effect of the smaller component's roughly triaxial ellipsoid shape. The simple analytical formulae obtained agree with full-detail numerical simulation results, and can be used for remote estimation of binary mass properties from observed system motion.  相似文献   

8.
In this paper we examine the possible outcome of the tidal evolution of a close binary system using a method from which the outline has already been given by Counselman (1973). If the value of the total angular momentum of the system is sufficiently large, two equilibrium states corresponding to synchronism between stellar rotation and orbital motion are possible. In one of these states the total energy attains no extreme value. The considered evolution can be visualized geometrically by the motion of a point along a hyperbolic cylinder in three-dimensional space. A comparison with some observational data reveals that most of the synchronously rotating detached systems have attained a stable equilibrium state of minimum total energy for the given value of total angular momentum.  相似文献   

9.
Photometric data on 17 binary near-Earth asteroids (15 of them are certain detections, two are probables) were analysed and characteristic properties of the near-Earth asteroid (NEA) binary population were inferred. We have found that binary systems with a secondary-to-primary mean diameter ratio Ds/Dp?0.18 concentrate among NEAs smaller than 2 km in diameter; the abundance of such binaries decreases significantly among larger NEAs. Secondaries show an upper size limit of Ds=0.5-1 km. Systems with Ds/Dp?0.5 are abundant but larger satellites are significantly less common. Primaries have spheroidal shapes and they rotate rapidly, with periods concentrating between 2.2 to 2.8 h and with a tail of the distribution up to ∼4 h. The fast rotators are close to the critical spin for rubble piles with bulk densities about 2 g/cm3. Orbital periods show an apparent cut-off at Porb∼11 h; closer systems with shorter orbital periods have not been discovered, which is consistent with the Roche limit for strengthless bodies. Secondaries are more elongated on average than primaries. Most, but not all, of their rotations appear to be synchronized with the orbital motion; nonsynchronous secondary rotations may occur especially among wider systems with Porb>20 h. The specific total angular momentum of most of the binary systems is similar to within ±20% and close to the angular momentum of a sphere with the same total mass and density, rotating at the disruption limit; this suggests that the binaries were created by mechanism(s) related to rotation near the critical limit and that they neither gained nor lost significant amounts of angular momentum during or since formation. A comparison with six small asynchronous binaries detected in the main belt of asteroids suggests that the population extends beyond the region of terrestrial planets, but with characteristics shifted to larger sizes and longer periods. The estimated mean proportion of binaries with Ds/Dp?0.18 among NEAs larger than 0.3 km is 15±4%. Among fastest rotating NEAs larger than 0.3 km with periods between 2.2 and 2.8 h, the mean proportion of such binaries is (66+10−12)%.  相似文献   

10.
The evolutionary process of semi-detached binary systems is examined on the basis of non-conservation of orbital angular momentum. We conclude that the semi-detached binary systems follow Type B evolution.  相似文献   

11.
The orbital period modulation, observed in close binary systems with late-type secondary stars, is considered in the framework of a general model that allows us to test the hypothesis proposed by Applegate. It relates the orbital period variation to the modulation of the gravitational quadrupole moment of their magnetically active secondary stars produced by angular momentum exchanges within their convective envelopes. By considering the case of RS CVn binary systems, it is found that the surface angular velocity variation of the secondary component required by Applegate's hypothesis is between 4 and 12 per cent, i.e. too large to be compatible with the observations and that the kinetic energy dissipated in its convection zone ranges from 4 to 43 times that supplied by the stellar luminosity along one cycle of the orbital period modulation. Similar results are obtained for other classes of close binary systems by applying a scaling relationship based on a simplified internal structure model. The effect of rapid rotation is briefly discussed finding that it is unlikely that the rotational quenching of the turbulent viscosity may solve the discrepancy. Therefore, the hypothesis proposed by Applegate is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary.  相似文献   

12.
The locations of the fully despun, double synchronous end states of tidal evolution, where the rotation rates of both the primary and secondary components in a binary system synchronize with the mean motion about the center of mass, are derived for spherical components. For a given amount of scaled angular momentum J/J′, the tidal end states are over-plotted on a tidal evolution diagram in terms of mass ratio of the system and the component separation (semimajor axis in units of primary radii). Fully synchronous orbits may not exist for every combination of mass ratio and angular momentum; for example, equal-mass binary systems require J/J′ > 0.44. When fully synchronous orbits exist for prograde systems, tidal evolution naturally expands the orbit to the stable outer synchronous solution. The location of the unstable inner synchronous orbit is typically within two primary radii and often within the radius of the primary itself. With the exception of nearly equal-mass binaries, binary asteroid systems are in the midst of lengthy tidal evolutions, far from their fully synchronous tidal end states. Of those systems with unequal-mass components, few have even reached the stability limit that splits the fully synchronous orbit curves into unstable inner and stable outer solutions.Calculations of material strength based on limiting the tidal evolution time to the age of the Solar System indicate that binary asteroids in the main belt with 100-km-scale primary components are consistent with being made of monolithic or fractured rock as expected for binaries likely formed from sub-catastrophic impacts in the early Solar System. To tidally evolve in their dynamical lifetime, near-Earth binaries with km-scale primaries or smaller created via a spin-up mechanism must be much weaker mechanically than their main-belt counterparts even if formed in the main belt prior to injection into the near-Earth region. Small main-belt binaries, those having primary components less than 10 km in diameter, could bridge the gap between the large main-belt binaries and the near-Earth binaries, as, depending on the age of the systems, small main-belt binaries could either be as strong as the large main-belt binaries or as weak as the near-Earth binaries. The inherent uncertainty in the age of a binary system is the leading source of error in calculation of material properties, capable of affecting the product of rigidity μ and tidal dissipation function Q by orders of magnitude. Several other issues affecting the calculation of μQ are considered, though these typically affect the calculation by no more than a factor of two. We also find indirect evidence within all three groups of binary asteroids that the semimajor axis of the mutual orbit in a binary system may evolve via another mechanism (or mechanisms) in addition to tides with the binary YORP effect being a likely candidate.  相似文献   

13.
The dynamical evolution of triple systems with equal and unequal-mass components and different initial velocities is studied. It is shown that, in general, the statistical results for the planar and three-dimensional triple systems do not differ significantly. Most (about 85%) of the systems disrupt; the escape of one component occurs after a triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (about 15%) of stable or long-lived systems is formed if the angular momentum is non-zero. Averages, distributions and coefficients of correlations of evolutionary characteristics are presented: the life-time, angular momentum, numbers of wide and close triple approaches of bodies, relative energy of escapers, minimum perimeter during the last triple approach resulting in escape, elements of orbits of the final binary and escaper.  相似文献   

14.
P. Descamps  F. Marchis 《Icarus》2008,193(1):74-84
We describe in this work a thorough study of the physical and orbital characteristics of extensively observed main-belt and trojan binaries, mainly taken from the LAOSA (Large Adaptive Optics Survey of Asteroids [Marchis, F., Baek, M., Berthier, J., Descamps, P., Hestroffer, D., Kaasalainen, M., Vachier, F., 2006c. In: Workshop on Spacecraft Reconnaissance of Asteroid and Comet Interiors. Abstract #3042]) database, along with a selection of bifurcated objects. Dimensionless quantities, such as the specific angular momentum and the scaled primary spin rate, are computed and discussed for each system. They suggest that these asteroidal systems might be the outcome of rotational fission or mass shedding of a parent body presumably subjected to an external torque. One of the most striking features of separated binaries composed of a large primary (Rp>100 km) with a much smaller secondary (Rs<20 km) is that they all have total angular momentum of ∼0.27. This value is quite close to the Maclaurin-Jacobi bifurcation (0.308) of a spinning fluid body. Alternatively, contact binaries and tidally locked double asteroids, made of components of similar size, have an angular momentum larger than 0.48. They compare successfully with the fission equilibrium sequence of a rotating fluid mass. In conclusion, we find that total angular momentum is a useful proxy to assess the internal structure of such systems.  相似文献   

15.
Ground observations have found that asynchronous systems constitute most of the population of the near-Earth binary asteroids. This paper concerns the trajectory of a particle in the asynchronous system which is systematically described using periodic ellipsoidal and spherical body models. Due to the non-autonomous characteristics of the asynchronous system, Lagrangian coherent structures (LCS) are employed to identify the various dynamical behaviors. To enhance the accuracy of LCS, a robust LCS finding algorithm is developed incorporating hierarchical grid refinement, one-dimensional search and variational theory verification. In this way, the intricate dynamical transport boundaries are detected efficiently. These boundaries indicate that a total of 15 types of trajectories exist near asynchronous binary asteroids. According to their Kepler energy variations, these trajectories can be grouped into four basic categories, i.e., transitory, escape, impact and flyby trajectories. Furthermore, the influence of the ellipsoid’s spin period on the dynamical behavior is discussed in the context of the change of dynamical regions. We found that the transitory and impact motions occur easily in the synchronous-like binary systems, in which the rotation period of the ellipsoid is nearly equal to that of the mutual orbit. Meanwhile, the results confirm a positive correlation between the spinning rate of the ellipsoid and the probability of the escape and flyby trajectories. The LCS also reveal a marked increase in trajectory diversity after a larger initial energy is selected.  相似文献   

16.
The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 107 yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.  相似文献   

17.
We present numerical simulations of near-Earth asteroid (NEA) tidal disruption resulting in bound, mutually orbiting systems. Using a rubble pile model we have constrained the relative likelihoods for possible physical and dynamical properties of the binaries created. Overall 110,500 simulations were run, with each body consisting of ∼1000 particles. The encounter parameters of close approach distance and velocity were varied, as were the bodies' spin, elongation and spin axis direction. The binary production rate increases for closer encounters, at lower speeds, for more elongated bodies, and for bodies with greater spin. The semimajor axes for resultant binaries are peaked between 5 to 20 primary radii, and there is an overall trend for high eccentricity, with 97% of binaries having e > 0.1. The secondary-to-primary size ratios of the simulated binaries are peaked between 0.1 and 0.2, similar to trends among observed asteroid binaries. The spin rates of the primary bodies are narrowly distributed between 3.5- and 6-h periods, whereas the secondaries' periods are more evenly distributed and can exceed 15-h periods. The spin axes of the primary bodies are very closely aligned with the angular momenta of the binary orbits, whereas the secondary spin axes are nearly random. The shapes of the primaries show a large distribution of axis ratios, where those with low elongation (ratio of long and short axis) are both oblate and prolate, and nearly all with large elongation are prolate. This work presents results that suggest tidal disruption of gravitational aggregates can make binaries physically similar to those currently observed in the NEA population. As well, tidal disruption may create an equal number of binaries with qualities different from those observed, mostly binaries with large separation and with elongated primaries.  相似文献   

18.
We present spatial orientations of angular momentum vectors of galaxies in three merging binary clusters A1750, A3395 and A3528. The axial ratio and intrinsic flatness of galaxy are used to convert two-dimensional given parameters into three-dimensional angular momentum vector of the galaxy. We have performed K-S, Kuiper and Fourier tests in order to examine non-random effects. The merging binary cluster A3395 that exhibits strongly distorted feature in its maps of temperature and surface brightness showed a random orientation in the spatial orientation of angular momentum vectors of galaxies. A weak anisotropic distribution in the angular momentum vectors of galaxies is noticed in the sub-structures of A3528. We suspect a relation between the stages of merging and the non-random alignments of galaxies in the sub-structures of the binary clusters. Possible explanation of the results will be discussed.  相似文献   

19.
We investigate the dynamical evolution of 100 000 rotating triple systems with equal-mass components. The system rotation is specified by the parameter ω=?c2E, where c and E are the angular momentum and total energy of the triple system, respectively. We consider ω=0.1,1, 2, 4, 6 and study 20 000 triple systems with randomly specified coordinates and velocities of the bodies for each ω. We consider two methods for specifying initial conditions: with and without a hierarchical structure at the beginning of the evolution. The evolution of each system is traced until the escape of one of the bodies or until the critical time equal to 1000 mean system crossing times. For each set of initial conditions, we computed parameters of the final motions: orbital parameters for the final binary and the escaping body. We analyze variations in the statistical characteristics of the distributions of these parameters with ω. The mean disruption time of triple systems and the fraction of the systems that have not been disrupted in 1000 mean crossing times increase with ω. The final binaries become, on average, wider at larger angular momenta. The distribution of their eccentricities does not depend on ω and generally agrees with the theoretical law f(e)=2e. The velocities of the escaping bodies, on average, decrease with increasing angular momentum of the triple system. The fraction of the angles between the escaping-body velocity vector and the triple-system angular momentum close to 90° increases with ω. Escapes in the directions opposite to rotation and prograde motions dominate at small and large angular momenta, respectively. For slowly rotating systems, the angular momentum during their disruption is, on average, evenly divided between the escaping body and the final binary, whereas in rapidly rotating systems, about 80% of the angular momentum is carried away by the escaping component. We compare our numerical simulations with the statistical theory of triple-system disruption.  相似文献   

20.
We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.  相似文献   

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