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1.
The temporary capture of the dust grains in the exterior resonances with planets is studied in the frames of the planar circular three-body problem with Poynting-Robertson (PR) drag. For the Earth and particles ~ 10 Μm the resonances 4/5, 5/6, 6/7, 7/8 are shown to be most effective. The capture is only temporary (of order 105 years) and the position of resonance may be calculated from semi-analytical model using averaged disturbing function. These semi-analytical results are confirmed by numerical integration. For various planet this picture changes as with increasing planetary mass the more exterior resonances become more important. We showed that for Jupiter (at least in the space between Jupiter and Saturn) the resonance 1/2 plays the dominant role. The capture time is here several myr but again eccentricity is evolving to eccentricity e 0 ~ 0.48 of libration point for this resonance.  相似文献   

2.
The temporary capture of the dust grains in the exterior resonances with planets is studied in the frames of the planar circular three-body problem with Poynting-Robertson (PR) drag. For the Earth and particles ~ 10 m the resonances 4/5, 5/6, 6/7, 7/8 are shown to be most effective. The capture is only temporary (of order 105 years) and the position of resonance may be calculated from semi-analytical model using averaged disturbing function. These semi-analytical results are confirmed by numerical integration. For various planet this picture changes as with increasing planetary mass the more exterior resonances become more important. We showed that for Jupiter (at least in the space between Jupiter and Saturn) the resonance 1/2 plays the dominant role. The capture time is here several myr but again eccentricity is evolving to eccentricity e 0 ~ 0.48 of libration point for this resonance.  相似文献   

3.
A small generalization of the equation of motion for the Poynting-Robertson effect is tested in order to find the significance of new terms. The test is made for dust particles ejected at perihelia of the orbit of the comet Encke. The particles are released at the speed of 40 m s?1. Gravitational perturbations of planets, Poynting-Robertson effect and solar corpuscular radiation (solar wind) are considered. Other nongravitational effects may be represented by new terms in the suggested form of the nongravitational force. Various values of normal and transversal components of the perturbing nongravitational force are used. The final results of numerical integrations are compared with those obtained on the basis of the Poynting-Robertson effect.  相似文献   

4.
A small generalization of the equation of motion for the Poynting-Robertson effect is tested in order to find the significance of new terms. The test is made for dust particles ejected at perihelia of the orbit of the comet Encke. The particles are released at the speed of 40 m s–1. Gravitational perturbations of planets, Poynting-Robertson effect and solar corpuscular radiation (solar wind) are considered. Other nongravitational effects may be represented by new terms in the suggested form of the nongravitational force. Various values of normal and transversal components of the perturbing nongravitational force are used. The final results of numerical integrations are compared with those obtained on the basis of the Poynting-Robertson effect.  相似文献   

5.
We review here some relevant problems connected to the evolution of circumstellar dust grains, subjected to Poynting-Robertson (PR) drag, and perturbed by first-order resonances with a planet on a circular orbit. We show that only outer mean motion resonances are able to counteract the damping effect of PR drag. However, the high orbital eccentricities reached by the particle lead to orbit crossings with the planet. This is a serious difficulty for a permanent trapping to be achieved. In any case, we show that the time spent in the resonance is long enough for statistical effects (accumulation at the resonant radius) to be significant. We underline some difficulties associated with this problem, namely, the non-adiabaticity of motion in the resonance phase space and the existence of close encounters with the planet at high eccentricities.  相似文献   

6.
The dynamical evolution of dust particles forming a circumstellar disk around Pictoris is followed by numerical simulations on a Connection Machine. The disk appears to be cleared inside a radius of about 20 AU. We integrate simultaneously the orbits of 8,000 dust particles subjected to Poynting-Robertson drag and perturbed by one alleged planet. The simulations show that a planet revolving about Pictoris at a mean distance of 20 AU with a mass of at least 2 * 10–5 central stellar mass can confine the disk by outer resonance trapping. The azimuthal density distribution of particles which shows very strong variations. appears to be stationary in a frame rotating with the planet.  相似文献   

7.
Jiang & Yeh proposed gas-drag-induced resonant capture as a mechanism able to explain the dominant 3:2 resonance observed in the trans-Neptunian belt. Using a model of a disc–star–planet system they concluded that gaseous drag in a protoplanetary disc can trap trans-Neptunian object (TNO) embryos into the 3:2 resonance rather easily although it could not trap objects into the 2:1 resonance. Here we further investigate this scenario using numerical simulations within the context of the planar restricted four-body problem by including both present-day Uranus and Neptune. Our results show that mean motion and corotation resonances are possible and trapping into both the 3:2 and 2:1 resonances as well as other resonances is observed. The associated corotation centres may easily form larger planetesimals from smaller ones. Corotation resonances evolve into pure Lindblad resonances in a time-scale of 0.5 Myr. The non-linear corotation and mean motion resonances produced are very size selective. The 3:2 resonance is dominant for submetric particles but for larger particles the 2:1 resonance is stronger. In summary, our calculations show that confined chaotic motion around the resonances not only increases trapping efficiency but also the orbital eccentricities of the trapped material, modifying the relative abundance of trapped particles in different resonances. If we assume a more compact planetary system, instead of using the present-day values of the orbital elements of Uranus and Neptune, our results remain largely unchanged.  相似文献   

8.
We analyze the process of resonance trapping due to Poynting–Robertson drag and Stokes drag in the frame of the restricted 3-body problem and in the case of external mean motion resonances. The numerical simulations presented are computed by using the 3-dimensional extended Schubart averaging (ESA) integrator developed by Moons (1994) for all mean motion resonances. We complete it by adding the contributions of the dissipative forces. To follow the philosophy of the initial integrator, we average the drag terms, but we do not make any expansion in series of eccentricity or inclination. We show our results, especially capture around asymmetric equilibria, and compare them to those found by Beaué and Ferraz-Mello (1993, 1994) and Liou et al. (1979).  相似文献   

9.
The hardware-software complex of the SBG telescope of the Kourovka astronomical observatory of the Ural Federal University is described. The area-to-mass ratio of high-orbit objects was estimated from the results of positional observations at the SBG telescope. Positions and sizes of resonance zones are determined from the numerical simulation results depending on the area-to-mass ratio in the case of low-order resonances (1 : 1, 1 : 2, and 1 : 3). Secular perturbations of semimajor axes of orbits, caused by the Poynting-Robertson effect, are estimated in the neighborhood of low-order resonance zones at different area-to-mass ratios.  相似文献   

10.
A correct understanding of the dynamical effect of solar radiation exerted on fluffy dust particles can be achieved with assistance of a light scattering theory as well as the equation of motion. We reformulate the equation of motion so that the radiation pressure and the Poynting-Robertson effect on fluffy grains are given in both radial and nonradial directions from the center of the Sun. This allows numerical estimates of these radiation forces on fluffy dust aggregates in the framework of the discrete dipole approximation, in which the first term of the scattering coefficients in Mie theory determines the polarizability of homogeneous spheres forming the aggregates.The nonsphericity in shape turns out to play a key role in the dynamical evolution of dust particles, while its consequence depends on the rotation rate and axis of the grains. Unless a fluffy dust particle rapidly revolves on its randomly oriented axis, the nonradial radiation forces may prevent, apart from the orbital eccentricity and semimajor axis, the orbital inclination of the particle from being preserved in orbit around the Sun. However, a change in the inclination is most probably controlled by the Lorentz force as a consequence of the interaction between electric charges on the grains and the solar magnetic field. Although rapidly and randomly rotating grains spiral into the Sun under the Poynting-Robertson effect in spite of their shapes and structures, fluffy grains drift inward on time scales longer at submicrometer sizes and shorter at much larger sizes than spherical grains of the same sizes. Numerical calculations reveal that the dynamical lifetimes of fluffy particles are determined by the material composition of the grains rather than by their morphological structures and sizes. The Poynting-Robertson effect alone is nevertheless insufficient for giving a satisfactory estimate of lifetimes for fluffy dust grains since their large ratios of cross section to mass would reduce the lifetimes by enhancing the collisional probabilities. We also show that the radiation pressure on a dust particle varies with the orbital velocity of the particle but that this effect is negligibly small for dust grains in the Solar System.  相似文献   

11.
Both the Poynting-Robertson drag and resonant orbits appear to be very important for the motion of small grains in the early solar system. While orbital resonances are very often stable and tend to force bodies into noncircular orbits, the Poynting-Robertson drag produces secular variations in the semimajor axis and tends to circularize the orbits. We study numerically the competition between the Poynting-Robertson drag and the gravitational interaction of grains with Jupiter near the 2/1 resonance. Computations are based on the plane-restricted problem. Numerical investigations show that the grains always cross the resonance region without any oscillation, except in the special case where the grains were initially inside the resonance. In both cases the variations of the osculating elements exhibit a drastic step, which can be explained by Greenberg's and Schubart's theories.  相似文献   

12.
Motion of the interplanetary dust particle under the action of collisions with much smaller interplanetary dust particles is investigated. The equation of motion is derived. Perturbation equations of celestial mechanics are also discussed. The results are compared with the Poynting-Robertson effect and the effect of solar wind on the motion of the interplanetary dust particles, from the point of view of observational data.  相似文献   

13.
Correct and complete (to terms of orderv/c) derivation of the Poynting-Robertson effect is presented. It is based on the idea that aberration of light is an important part in the effect of radiation on the motion of (interplanetary) dust particle. Derivations are presented for spherical particles, however, not only for perfectly absorbing ones. It follows from the presented derivations that the Poynting-Robertson effect is purely relativistic phenomenon and cannnot be treated in nonrelativistic manner, although results in orderv/c are sufficient for calculation in the Solar System studies.  相似文献   

14.
We use a non-singular potential that appears in the literature under the influence of which the Poynting-Robertson effect is studied. For that, dust particles originating within the asteroid belt are used, in circular and elliptic orbits, and expressions for the semimajor axis as a function of time are obtained. The derived expressions are written in terms of the two basic dust particle parameters, namely the density and the diameter. In both cases, we obtain expressions for the time that the dust particles take to reach the orbit of Earth under the action of the non-singular potential and solar radiation. For the non-singular potential, dust particles of diameter 10−3 m in circular and elliptical orbits require times of the order of 4.058×107 and 2.823×107 y to reach the orbit of the Earth respectively. Finally, the derived expressions and numerical results are compared with those of the Newtonian potential.  相似文献   

15.
The orbit-averaged differential equations of motion of dust particles under gravity, radiation pressure and Poynting-Robertson drag were given by Wyatt and Whipple (1950). An integral of motion enables the system of two equations in semi-major axis a and eccentricity e to be reduced to one equation, the solution of which is presented here in terms of analytical formulae. An efficient numerical algorithm to compute the solution is given. Listings of two FORTRAN routines are included.  相似文献   

16.
Abrupt or gradual disintegration of the interplanetary dust particle causes increase of its distance from the Sun due to the solar radiation pressure. The problem of the orbital evolution of the interplanetary dust particles under such disintegration processes is discussed. The process of gradual disintegration due to the solar wind particles is calculated in detail. Obtained results represent corrections to the changes of orbital elements for the Poynting-Robertson effect and effect of the solar wind.  相似文献   

17.
Francois Mignard 《Icarus》1982,49(3):347-366
The dynamics of small dust grains orbiting a planet are investigated when solar radiation pressure forces are added to the planet's gravitational central field. In the first part a set of differential equations is derived in a reference frame linked to the solar motion. The complete solution of these equations is given for particles lying in the planet's orbital plane, and we show that the orbital eccentricity may undergo considerable variation. At the same time the pericenter longitude librates or circulates according to initial conditions. With this result we establish a criterion for any orbiting particle (because of its highly eccentric orbit) to collide with its planet's atmosphere. The case of inclined orbit is studied through a numerical integration and allows us to draw conclusions related to the stability of the orbital plane. All solutions are periodic, with the period being independent of the initial conditions. This last point permits us to investigate the different time scales involved in that problem. Finally, the Poynting-Robertson drag is included, along with the radial radiation pressure forces, and the secular trend is considered. A coupling effect between the two components is ascertained, yielding a systematic behavior in the eccentricity and thus in the pericenter distance. Our solutions generalize the results of S. J. Peale (1966, J. Geophys. Res.71, 911–933) and J. A. Burns, P. Lamy, and S. Soter (1979, Icarus40, 1–48) by allowing eccentricities to be large (of order 1) and inclinations to be nonzero and by considering Poynting-Robertson drag.  相似文献   

18.
The area-to-mass ratio of high-orbit space objects is estimated on the basis of positional observations from the SBG telescope at the Kourovka astronomical observatory of the Ural Federal University. The properties of regions where high-order resonances are located are analyzed. The position and sizes of the resonance zones depending on the area-to-mass ratio of objects are determined on the basis of numerical modeling. It is shown that a system transits through the high-order resonances due to secular perturbations of the semimajor axis under the Poynting-Robertson effect. The high-order resonances weakly influence the formation of the stochastic trajectories. The stochastic properties are mostly manifested in evolution of the semimajor axis of the orbit.  相似文献   

19.
A migrating planet can capture planetesimals into mean motion resonances. However, resonant trapping can be prevented when the drift or migration rate is sufficiently high. Using a simple Hamiltonian system for first- and second-order resonances, we explore how the capture probability depends on the order of the resonance, drift rate and initial particle eccentricity. We present scaling factors as a function of the planet mass and resonance strength to estimate the planetary migration rate above which the capture probability drops to less than half. Applying our framework to multiple extrasolar planetary systems that have two planets locked in resonance, we estimate lower limits for the outer planet's migration rate, allowing resonance capture of the inner planet.
Mean motion resonances are comprised of multiple resonant subterms. We find that the corotation subterm can reduce the probability of capture when the planet eccentricity is above a critical value. We present factors that can be used to estimate this critical planet eccentricity. Applying our framework to the migration of Neptune, we find that Neptune's eccentricity is near the critical value that would make its 2 : 1 resonance fail to capture twotinos. The capture probability is affected by the separation between resonant subterms and so is also a function of the precession rates of the longitudes of periapse of both planet and particle near resonance.  相似文献   

20.
We study the evolution of a system consisting of two protoplanets still embedded in a protoplanetary disk. Results of two different numerical approaches are presented. In the first kind of model the motion of the disk material is followed by fully viscous hydrodynamical simulations, and the planetary motion is determined by N-body calculations including exactly the gravitational potential from the disk material. In the second kind we only solve the N-body part and add additional analytically given forces which model the effect of the torques of the disk. This type of modeling is of course orders of magnitudes faster than the full hydro-model. Another advantage of this two-fold approach is the possibility of adjusting the otherwise unknown parameters of the simplified model.The results give very good agreement between the methods. Using two different initial setups for the planets and disk, we obtain in the first case a resonant trapping into the 3:1 resonance, and in the second case a trapping into the 2:1 resonance. Resonant capture leads to a rise in the eccentricity and to an alignment of the spatial orientation of orbits. The characteristics of the numerical results agree very favorably with those of three observed planetary systems (GJ 876, HD 82943, and 55 Cnc) known to be in mean motion resonances.  相似文献   

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