共查询到20条相似文献，搜索用时 125 毫秒
1.
Claudio Vidal 《Celestial Mechanics and Dynamical Astronomy》1998,71(1):15-33
We consider four bodies in space with same masses forming two binaries, each one symmetric with respect to a fixed axis and
moving under Newtonian gravitation in opposite directions about this axis. It is given a direct proof that all singularities
of this model are due to collisions, and it is proved that the singularities due to simultaneous double collisions are regularizable.
The set of equilibrium points on the total collision manifold is studied as well as the possible connections among them. We
show that the set of initial conditions on a given energy surface going to quadruple collision is a union of twenty submanifolds:
twelve of them have dimension 2 and the others have dimension 3. Similarly for ejection orbits from quadruple collision.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Theoretical consideration and observations by other authors indicate that small asteroids are capable of maintaining irregular shapes, notably the shape of a cigar and even of a dumb-bell. This paper presents a model which describes the changes in the shape of an asteroid due to collisions of smaller objects (meteoroids) with the asteroid. The following assumptions must be approximately valid: (1) collisions are not uncommon; (2) collisions between a (relatively) large asteroid and small objects (meteroids) are more common than collisions between asteroids; (3) the cumulative probability of the collision of a meteoroid on a point on the surface of an asteroid is proportional to the zenith angle of the horizon as seen by that point; (4) obliquities of all but the major asteroids are random, so that there is not a preferred side on which collisions occur; (5) a considerable percentage of collision ejecta achieves escape velocity; and (6) the rate of erosion of each point on the surface of an asteroid is proportional to the cumulative probability of collision.Generalized conclusions that are obtained from the computer running of the model indicate that both cigars and dumb-bells are possible outcomes. Sharp corners are smoothed away, the radius of curvature of rounded surfaces increases to the point of going from convexity to concavity, and flat surfaces develop into gentle concavities.Collisions of an asteroid with an object of sufficient size such that the impact causes the breakage of the asteroid or the formation of a large crater, are not discussed in this paper. Previous work, however, suggests that the crater will undergo geomorphological changes of different geometry than a similar crater on the Moon. 相似文献
3.
Lennard F. Bakker Tiancheng Ouyang Duokui Yan Skyler Simmons Gareth E. Roberts 《Celestial Mechanics and Dynamical Astronomy》2010,108(2):147-164
We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous
binary collision orbits in the symmetric collinear four-body problem with masses 1, m, m, 1, and also in a symmetric planar
four-body problem with equal masses. In both problems, the assumed symmetries reduce the determination of linear stability
to the numerical computation of a single real number. For the collinear problem, this verifies the earlier numerical results
of Sweatman for linear stability with respect to collinear and symmetric perturbations. 相似文献
4.
E. Gaburov A. Gualandris S. Portegies Zwart 《Monthly notices of the Royal Astronomical Society》2008,384(1):376-385
We study the circumstances under which first collisions occur in young and dense star clusters. The initial conditions for our direct N -body simulations are chosen such that the clusters experience core collapse within a few million years, before the most massive stars have left the main sequence. It turns out that the first collision is typically driven by the most massive stars in the cluster. Upon arrival in the cluster core, by dynamical friction, massive stars tend to form binaries. The enhanced cross-section of the binary compared to a single star causes other stars to engage the binary. A collision between one of the binary components and the incoming third star is then mediated by the encounters between the binary and other cluster members. Due to the geometry of the binary–single star engagement the relative velocity at the moment of impact is substantially different than in a two-body encounter. This may have profound consequences for the further evolution of the collision product. 相似文献
5.
A two-dimensional hydrodynamic code has been developed for numerical studies of stellar collisions. The motivation for the study has been the suggestion by Colgate that collisions among stars in a dense galactic core can lead to growth of stellar masses by coalescence and thus to an enhanced rate of supernova activity. The specific results reported here refer to head-on collisions between identical polytropes of index 3 having solar mass and radius. If the polytropes were initially at rest at infinity, then about five percent of the combined mass is lost by ejection following collision. The volatilized mass fraction rises to about 18% for an initial relative collision velocity of 1000 km s–1 at infinite separation, and to about 60% for the 2000 km s–1 case. Since the initial kinetic and gravitational energies balance for a relative velocity of 1512 km s–1 at infinity, it may be seen that net coalescence persists to velocities somewhat in excess of this figure. Mass ejection takes place in two ways simultaneously: (1) by a rapid sideward expulsion of fluid in a massive lateral sheet normal to the collision axis, and (2) as a result of two recoil shocks which lead momentum flows backwards along this axis. The lateral effect has similarities to the expansion of gas into a vacuum; that is, shocks are not involved. However, the ejection of material from the rear colliding hemisphere due to the recoil shocks predominates at low collision velocities. As the velocity increases, both effects strengthen, but the lateral expulsion intensifies more rapidly than the recoil shocks. 相似文献
6.
《New Astronomy》2017
This paper attempts to formulate a way for calculating the intensity of gravitational wave from two point masses in Keplerian circular and elliptic orbits. The intensity is calculated with the assumption that the orbital plane of the binary undergoes small oscillation about the equilibrium x-y plane. This problem is simplification of a physically possible orbit where one of the point masses is spinning whereby the spin-orbit force drives the orbital plane to wobble in a complicated manner. It is shown that the total energy of gravitational wave emitted by the binary in this case is dominated by the parameters which take into account the oscillation of the plane. The results presented are in fact a generalization of the classic results of Landau and Lifshitz. 相似文献
7.
P. Delibaltas 《Celestial Mechanics and Dynamical Astronomy》1983,29(2):191-204
In the general three-body problem, in a rotating frame of reference, a symmetric periodic solution with a binary collision is determined by the abscissa of one body and the energy of the system. For different values of the masses of the three bodies, the symmetric periodic collision orbits form a two-parametric family. In the case of equal masses of the two bodies and small mass of the third body, we found several symmetric periodic collision orbits similar to the corresponding orbits in the restricted three-body problem. Starting with one symmetric periodic collision orbit we obtained two families of such orbits. Also starting with one collision orbit in the Sun-Jupiter-Saturn system we obtained, for a constant value of the mass ratio of two bodies, a family of symmetric periodic collision orbits. 相似文献
8.
Joerg Waldvogel 《Celestial Mechanics and Dynamical Astronomy》1972,6(2):221-231
A new method of simultaneously regularizing the three types of binary collisions in the planar problem of three bodies is developed: The coordinates are transformed by means of certain fourth degree polynomials, and a new independent variable is introduced, too. The proposed transformation is in each binary collision locally equivalent to Levi-Civita's transformation, whereas the singularity corresponding to a triple collision is mapped into infinity. The transformed Hamiltonian is a polynomial of degree 12 in the regularized variables.Presented before the Division of Dynamical Astronomy at the 133rd meeting of the American Astronomical Society, Tampa, Florida, December 6–9, 1970.Department of Aerospace Engineering and Engineering Mechanics. 相似文献
9.
We report on a very large set of simulations of collisions between two main-sequence (MS) stars. These computations were carried out with the smoothed particle hydrodynamics method. Realistic stellar structure models for evolved MS stars were used. In order to sample an extended domain of initial parameters space (masses of the stars, relative velocity and impact parameter), more than 14 000 simulations were carried out. We considered stellar masses ranging between 0.1 and 75 M⊙ and relative velocities up to a few thousand km s−1 . To limit the computational burden, a resolution of 1000–32 000 particles per star was used. The primary goal of this study was to build a complete data base from which the result of any collision can be interpolated. This allows us to incorporate the effects of stellar collisions with an unprecedented level of realism into dynamical simulations of galactic nuclei and other dense stellar clusters. We make the data describing the initial condition and outcome (mass and energy loss, angle of deflection) of all our simulations available on the Internet. We find that the outcome of collisions depends sensitively on the stellar structure and that, in most cases, using polytropic models is inappropriate. Published fitting formulae for the collision outcomes, established from a limited set of collisions, prove of limited use because they do not allow robust extrapolation to other stellar structures or relative velocities. 相似文献
10.
Massimo Meneghetti Naoki Yoshida Matthias Bartelmann Lauro Moscardini Volker Springel Giuseppe Tormen Simon D. M. White 《Monthly notices of the Royal Astronomical Society》2001,325(1):435-442
We carry out ray tracing through five high-resolution simulations of a galaxy cluster, to study how its ability to produce giant gravitationally lensed arcs is influenced by the collision cross-section of its dark matter. In three cases typical dark matter particles in the cluster core undergo between 1 and 100 collisions per Hubble time; two more explore the long ('collisionless') and short ('fluid') mean free path limits. We study the size and shape distributions of arcs and compute the cross-section for producing 'extreme' arcs of various sizes. Even a few collisions per particle modifies the core structure enough to destroy the ability of the cluster to produce long, thin arcs. For larger collision frequencies the cluster must be scaled up to unrealistically large masses before it regains the ability to produce giant arcs. None of our models with self-interacting dark matter (except the 'fluid' limit) is able to produce radial arcs; even the case with the smallest scattering cross-section must be scaled to the upper limit of observed cluster masses before it produces radial arcs. Apparently the elastic collision cross-section of dark matter in clusters must be very small, below 0.1 cm2 g−1 , to be compatible with the observed ability of clusters to produce both radial arcs and giant arcs. 相似文献
11.
We study a symmetric collinear restricted 3-body problem, where the equal mass primaries perform elliptic collisions, while
a third massless body moves in the line between the primaries, during the time between two consecutive elliptic collisions.
After desingularizing binary and triple collisions, we prove the existence of a transversal heteroclinic orbit beginning and
ending in triple collision. This orbit is the unique homothetic orbit that the problem possess. Finally, we describe the topology
of the compact extended phase space.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
Lennard F. Bakker Tiancheng Ouyang Duokui Yan Skyler Simmons 《Celestial Mechanics and Dynamical Astronomy》2011,110(3):271-290
We analytically prove the existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise
symmetric equal mass four-body problem. This is an extension of our previous proof of the analytic existence of a symmetric
periodic simultaneous binary collision orbit in a regularized planar fully symmetric equal mass four-body problem. We then
use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar
pairwise symmetric 1, m, 1, m four-body problem for m between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability
when 0.54 ≤ m ≤ 1, and are linearly unstable when 0 < m ≤ 0.53. 相似文献
13.
This paper gives an analytic proof of the existence of Schubart-like orbit, a periodic orbit with singularities in the symmetric
collinear four-body problem. In each period of the Schubart-like orbit, there is a binary collision (BC) between the inner
two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized
and the existence is proved by using a “turning point” technique and a continuity argument on differential equations of the
regularized Hamiltonian. 相似文献
14.
We present the results of our study of two collisions of binary elliptical galaxies, NGC 4782/4783 and NGC 2672/2673. Each pair has a high relative velocity (>500 km s–1 along the line-of-sight) but the two pairs differ in mass ratio (1 for the first pair, and 10 for the second). CCD images and velocities obtained from digital spectra are used to constrain simulations of the galaxy collisions. Once a solution has been found and its uniqueness verified, we derive the binary orbital elements, the orientation of the orbit in the sky, the time since pericenter, and the dynamical mass of the pair. This method provides a quantitative determination of galaxy masses on the scale of the binary separations free from uncertainties due to projection effects. We also derive accurate timing of the collision and information about the fate of the pairs (merger/escape). Among our conclusions, we find that the dumb-bell galaxy NGC 4782/4783 isnot a supermassive galaxy as claimed from the high relative velocity and the high central dispersions, but has a moderateM/L
B10. Its trajectory has been changed from hyperbolic to elliptical as a result of energy lost during the collision. NGC 2672/2673 provides an interesting example of how the collision probes the internal structure and dynamics of a galaxy. It also has a moderateM/L
B7.Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., for the National Aeronautics and Space Administration, MA, U.S.A.Kitt Peak National Observatory, National Optical Astronomy Observatories, operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation, AR, U.S.A. 相似文献
15.
Mass depletion of bodies through successive collisional disruptions (i.e., collision cascade) is one of the most important processes in the studies of the asteroids belt, the Edgeworth-Kuiper belt, debris disks, and planetary formation. The collisional disruption is divided into two types, i.e., catastrophic disruption and cratering. Although some studies of the collision cascades neglected the effect of cratering, it is unclear which type of disruption makes a dominant contribution to the collision cascades. In the present study, we construct a simple outcome model describing both catastrophic disruption and cratering, which has some parameters characterizing the total ejecta mass, the mass of the largest fragment, and the power-law exponent of the size distribution of fragments. Using this simple outcome model with parameters, we examine the model dependence of the mass depletion time in collision cascades for neglect of coalescence of colliding bodies due to high collisional velocities. We find the cratering collisions are much more effective in collision cascades than collisions with catastrophic disruption in a wide region of the model parameters. It is also found that the mass depletion time in collision cascades is mainly governed by the total ejecta mass and almost insensitive to the mass of the largest fragment and the power-law exponent of fragments for a realistic parameter region. The total ejecta mass is usually determined by the ratio of the impact energy divided by the target mass (i.e. Q-value) to its threshold value for catastrophic disruption, as well as in our simple model. We derive a mass depletion time in collision cascades, which is determined by of the high-mass end of collision cascades. The mass depletion time derived with our model would be applicable to debris disks and planetary formation. 相似文献
16.
Recent surveys have identified seven hypervelocity stars (HVSs) in the halo of the Milky Way. Most of these stars may have originated from the breakup of binary star systems by the nuclear black hole SgrA*. In some instances, the breakup of the binary may lead to a collision between its member stars. We examine the dynamical properties of these collisions by simulating thousands of different binary orbits around SgrA* with a direct N -body integration code. For some orbital parameters, the two stars collide with an impact velocity lower than their escape velocity and may therefore coalesce. It is possible for a coalescing binary to have sufficient velocity to escape the galaxy. Furthermore, some of the massive S-stars near Sgr A* might be the merger remnants of binary systems, however this production method can not account for most of the S-stars. 相似文献
17.
M M E Irigoyen 《Celestial Mechanics and Dynamical Astronomy》1974,9(4):491-506
The analytical study of the evolution in the rectilinear problem of three bodies, leads us to consider the collision between two bodies,M 2 andM 3, in the presence of the third body,M 1. This problem, which seems to be difficult to approach in the general case, can be partly solved if the masses ofM 2 andM 3 are equal and can be neglected in regard toM 1. In this particular case of the general problem, the mechanical study of a collision betweenM 2 andM 3, leads to two distinct types of collisions: ‘instantaneous collisions’, and ‘collisions with repetition’, according to the value of a parameter which depends on the position and the speed of the binaryM 2 M 3, relative toM 1, in the collision. In the first type, the collision exchanges the speeds ofM 2 andM 3, while in the second type, there is a series of collisions succeeding each other. 相似文献
18.
Studying the origin and evolution of the Solar system is among the fundamental problems of modern natural science. This problem is interdisciplinary and requires the development of mathematical models for the physical structure and evolution of a gas–dust accretion disk from the initial stages of its formation to the formation of a planetary system. One of the key problems is the formation and growth of bodies in a protoplanetary disk, the basis for which is a study of the collisional processes of the solidbody component. We have performed a parametric analysis of the cluster–cluster collision processes occurring in a protoplanetary disk within the model of permeable particles being developed by us. The outcome of such collisions is shown to be affected significantly by the topological properties of colliding dust clusters with a fractal internal structure. The results of our parametric analysis show that for sufficiently “dense” fractal dust clusters, at low relative collision velocities, there exists a range in which the colliding clusters bounce. At the same time, for “porous” fractal clusters the bounce is impossible for any sets of collision parameters. As the relative collision velocities increase, the cluster coalescence processes begin to dominate due to a rearrangement of the fractal structure in the contact zone. However, as the kinetic energy of collisions increases further, a critical threshold is reached beyond which the collision energy exceeds the particle binding energy in clusters and the fractal dust cluster destruction processes are switched on during collisions. Thus, our parametric analysis imposes quite definite constraints on the dynamics and chronology of the evolution processes during the formation of primordial solid bodies and planetesimals. The proposed approach and the results obtained are fairly realistic and open prospects for more comprehensive model studies of the initial evolutionary phase of a protoplanetary disk. 相似文献
19.
A study of collisions between spiral and elliptical galaxies (approximated as composite spherical masses) is made to assess the changes undergone by the elliptical. Results indicate that unless the spiral is extremely massive compared to the elliptical, the elliptical is almost unaffected, while the spiral is strongly affected. For the frequent type of collision between equally massive spiral and elliptical galaxies, the elliptical is negligibly affected, while disruptive effects set in the spiral. However, the stellar pattern of the elliptical is changed and the stars are found to crowd in faint shells after the collision. The consequences of these results are explored in the context of the morphology-density relationship and the elliptical companions of ring galaxies. 相似文献
20.
An analysis of the collisional transition between the lower atmosphere and the collisionless exosphere is carried out based upon an integral formulation of the Boltzmann equation. This investigation utilizes a collision model which is a combination of Lorentz-gas and relaxation collision models. The results of this analysis indicate that intermolecular collisions act in two ways to affect the atmosphere. First, there is a critical layer, similar to the apparent photospheric surface of the Sun, from which the material escaping from the planet originates. This layer is determined by collision suffered by particles moving on orbits which skim tangentially by the planet. Secondly, collisions reduce the vertical flux of material in a manner analogous to the diffusion processes which occur in the lower atmosphere. 相似文献