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1.
F. MarzariH. Scholl 《Icarus》2002,159(2):328-338
We have numerically explored the mechanisms that destabilize Jupiter's Trojan orbits outside the stability region defined by Levison et al. (1997, Nature385, 42-44). Different models have been exploited to test various possible sources of instability on timescales on the order of ∼108 years.In the restricted three-body model, only a few Trojan orbits become unstable within 108 years. This intrinsic instability contributes only marginally to the overall instability found by Levison et al.In a model where the orbital parameters of both Jupiter and Saturn are fixed, we have investigated the role of Saturn and its gravitational influence. We find that a large fraction of Trojan orbits become unstable because of the direct nonresonant perturbations by Saturn. By shifting its semimajor axis at constant intervals around its present value we find that the near 5:2 mean motion resonance between the two giant planets (the Great Inequality) is not responsible for the gross instability of Jupiter's Trojans since short-term perturbations by Saturn destabilize Trojans, even when the two planets are far out of the resonance.Secular resonances are an additional source of instability. In the full six-body model with the four major planets included in the numerical integration, we have analyzed the effects of secular resonances with the node of the planets. Trojan asteroids have relevant inclinations, and nodal secular resonances play an important role. When a Trojan orbit becomes unstable, in most cases the libration amplitude of the critical argument of the 1:1 mean motion resonance grows until the asteroid encounters the planet. Libration amplitude, eccentricity, and nodal rate are linked for Trojan orbits by an algebraic relation so that when one of the three parameters is perturbed, the other two are affected as well. There are numerous secular resonances with the nodal rate of Jupiter that fall inside the region of instability and contribute to destabilize Trojans, in particular the ν16. Indeed, in the full model the escape rate over 50 Myr is higher compared to the fixed model.Some secular resonances even cross the stability region delimited by Levison et al. and cause instability. This is the case of the 3:2 and 1:2 nodal resonances with Jupiter. In particular the 1:2 is responsible for the instability of some clones of the L4 Trojan (3540) Protesilaos.  相似文献   

2.
The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T J = T S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β1 ≈ 0.8403504° (Saturn) and β2 ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.  相似文献   

3.
Four-color photographic photometry of Saturn for the 1977–1979 apparitions has been analyzed to determine the dependence of ring brightness on wavelength, solar phase angle, ring particle orbital phase angle (azimuthal effect), declination of the Earth relative to the ring plane (tilt angle), and radial distance from Saturn. Azimuthal brightness variations up to ±20% relative to the ansae are clearly apparent for the maximum of ring A, but are not detectable for ring B or the outer portion of ring A. The shape of the intensity (I) versus orbital phase angle (θ) curve varies with ring tilt (B) and probably with wavelength, and shows 180° symmetry. As characterized by its slope near the ansae, this curve suggests that the azimuthal effect increases as B decreases from 26 to ≈11°. The phase curves l(α) for the ansae show very little dependence on ring tilt (26° > B > 6°), on wavelength, or on radial distance from Saturn; possibly the curves are somewhat steeper at the smallest tilt angles and for ring A relative to ring B. The radial profile of both rings becomes flatter with decreasing tilt angle and with decreasing wavelength. The latter effect is a natural result of the classical, many-particle-thick ring model.  相似文献   

4.
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5.
We investigate the relevance of the Yarkovsky effect for the origin of kilometer and multikilometer near-Earth asteroids (NEAs). The Yarkovsky effect causes a slow migration in semimajor axis of main belt asteroids, some of which are therefore captured into powerful resonances and transported to the NEA space. With an innovative simulation scheme, we determine that in the current steady-state situation 100-160 bodies with H < 18 (roughly larger than 1 km) enter the 3/1 resonance per million years and 40-60 enter the ν6 resonance. The ranges are due to uncertainties on relevant simulation parameters such as the time scales for collisional disruption and reorientation, their size dependence, and the strength of the Yarkovsky and YORP effects. These flux rates to the resonances are consistent with those independently derived by Bottke et al. (2002, Icarus 156, 399-433) with considerations based only on the NEA orbital distribution and dynamical lifetime. Our results have been obtained assuming that the main belt contains 1,300,000 asteroids with H < 18 and linearly scale with this number. Assuming that the cumulative magnitude distribution of main belt asteroids is N(< H) ∝ 10γ′H with γ′ = 0.25 in the 15.5 < H < 18 range (consistent with the results of the SDSS survey), we obtain that the bodies captured into the resonances should have a similar magnitude distribution, but with exponent coefficient γ = 0.33-0.40. The lowest value is obtained taking into account the YORP effect, while higher values correspond to a weakened YORP or to YORP-less cases. These values of γ are all compatible with the debiased magnitude distributions of the NEAs according to Rabinowitz et al. (2000, Nature 403, 165-166), Bottke et al. (2000b, Science 288, 2190-2194), and Stuart (2001, Science 294, 1691-1693). Hence the Yarkovsky and YORP effects allow us to understand why the magnitude distribution of NEAs is only moderately steeper than that of the main belt population. The steepest main belt distribution that would still be compatible with the NEA distribution has exponent coefficient γ′ ∼ 0.3.  相似文献   

6.
Early ground-based and spacecraft observations suggested that the temperature of Saturn's main rings (A, B and C) varied with the solar elevation angle, B′. Data from the composite infrared spectrometer (CIRS) on board Cassini, which has been in orbit around Saturn for more than five years, confirm this variation and have been used to derive the temperature of the main rings from a wide variety of geometries while B′ varied from near −24° to 0° (Saturn's equinox).Still, an unresolved issue in fully explaining this variation relates to how the ring particles are organized and whether even a simple mono-layer or multi-layer approximation describes this best. We present a set of temperature data of the main rings of Saturn that cover the ∼23°—range of B′ angles obtained with CIRS at low (α∼30°) and high (α≥120°) phase angles. We focus on particular regions of each ring with a radial extent on their lit and unlit sides. In this broad range of B′, the data show that the A, B and C rings’ temperatures vary as much as 29-38, 22-34 and 18-23 K, respectively. Interestingly the unlit sides of the rings show important temperature variations with the decrease of B′ as well. We introduce a simple analytical model based on the well known Froidevaux monolayer approximation and use the ring particles’ albedo as the only free parameter in order to fit and analyze this data and estimate the ring particle's albedo. The model considers that every particle of the ring behaves as a black body and warms up due to the direct energy coming from the Sun as well as the solar energy reflected from the atmosphere of Saturn and on its neighboring particles. Two types of shadowing functions are used. One analytical that is used in the latter model in the case of the three rings and another, numerical, that is applied in the case of the C ring alone. The model lit side albedo values at low phase are 0.59, 0.50 and 0.35-0.38 for the A, B and C rings, respectively.  相似文献   

7.
We study the short-term effects of “shepherding” satellites on narrow rings, in the general case where all bodies move along eccentric orbits. We do this by following numerically a ring of test particles as their orbits evolve under the gravitational perturbations of the shepherds. Planar motion is assumed. Our numerical scheme vastly improves (by a factor of ～104) the computation speed over conventional orbital integration methods by constructing a table of the perturbation integrals and then utilizing it over and over. The approach is applicable to any narrow ring with a nearby satellite, such as a ring confined by the shepherding mechanism of P. Goldreich and S. Tremaine [Nature277, 97–99 (1979)]. We arrive at results for a variety of orbital configurations, and then apply these to the F-ring of Saturn. Several features of the numerical integration are reminiscent of the kinks and clumps observed by Voyager. If the ring-to-satellite distance changes significantly due to eccentricities, then the ring can break up into periodic clumps in an azimuthal domain which trails the satellite. This region may lag somewhat in longitude. The perturbations may also cause the ring to vary significantly in width, being narrowest near the point of closest approach of the shepherd and widest at the opposite side. It is as yet unclear whether this effect is, or could be, observed in the Voyager images. And finally, the perturbations of the shepherds can impact a significant, but probably time variable, eccentricity to the ring. The short-term tendency is not toward alignment of ring and satellite apsides; longer time effects have not been explored.  相似文献   

8.
The aim of this work is to understand the absence of objects along the orbits of Mimas and Enceladus in contrast to their presence at the orbits of neighbouring Tethys and Dione from the point of view of dynamical stability. Large scale numerical simulations of 360 test particles within the coorbital regions of these four saturnian satellites were carried out for 4×105 yr or 1.6×108 revolutions of the innermost moon Mimas. The tidal forcing of the satellites' orbits was not taken into account in these simulations. We have quantitatively reproduced the Mimas-Tethys 4:2 and Enceladus-Dione 2:1 mean motion resonances in the system and devised a scheme by which the parameter space of the coorbital resonance is sampled uniformly by our test particles. We observe that 6 out of the 36 integrated horseshoe particles of Enceladus escaped the coorbital region. All 54 tadpole particles remained stable. The main cause of instability for Enceladus coorbitals appears to be the overlap between the coorbital resonance and the 2:1 mean motion resonance between the particle and Dione. This leads particles with starting semimajor axes near the horseshoe-tadpole separatrix to be ejected from the resonance, as proposed by Morais [Morais, M.H.M., 2000. The effect of secular perturbations and mean motion resonances on trojan dynamics. Ph.D. thesis, Univ. of London], over timescales of ∼8×107 revolutions of Enceladus. For Mimas we observe a larger number of coorbital escapes overall, both of tadpole (7/54) and horseshoe (29/36) librators. An analysis of the observed dynamical evolution suggests a two-stage process at work: The semimajor axis of particles with starting conditions near the horseshoe-tadpole separatrix undergoes a slow random walk over timescales of 105 yr through a mechanism similar to that at Enceladus but involving the 4:2 inclination resonance with Tethys. These particles are eventually injected into a region of short-term (?104 yr) instability just inside the nominal boundary of stable, symmetric horseshoe motion. The presence of the 4:2 eccentricity triplet at that location is the most likely culprit for the instability. In both the cases of Mimas and Enceladus small-amplitude tadpoles remain stable until the end of the integration. The existence of fast escapers at Mimas provides a dynamical avenue for the short-term survival of impact ejecta in horseshoe orbits within Mimas' coorbital region.  相似文献   

9.
Model calculations were carried out to determine the extent of the effects on the rotational bursting of F-coronal dust in eccentric orbits due to their interaction with the flow of coronal mass ejections (CMEs). The model included an initial limiting perihelion distance of 8 solar radii (RS) for all particles used. The parameters of the CMEs (velocity and proton number density) along with the various parameters of the dust particles (size and median density) were taken into consideration. By keeping these parameters the same and varying one of them, it was found that the velocity of the CMEs protons plays a major role in determining at which heliocentric distance the particle bursts. To a lesser degree, the median density of the particle also had a similar effect. Depending on the values of the dust particles orbital eccentricity, limiting sizes of the dust particles were found beyond which the particles do not burst. More particles bursted in regions close to their perihelion passage, however very few particles bursted near 8RS from which we conclude that the majority of the fragmented particles were outside the F-corona region. The results show that rotational bursting of the dust in eccentric orbits inside the F-corona forces the particles to fragment outside 8RS.  相似文献   

10.
In this paper, the orbital dynamics of the gravitational field in Bardeen space-time are investigated. The equations of the particle’s orbital motion are given by solving the Lagrangian equation, and the stability and types of orbits are studied by means of analysing the effective potential of particles. Also, with the help of phase-plane method, the closed and non-closed orbits of test particle are analysed. We find that the stability and types of orbits in the Bardeen space-time are determined not only by the particles’ energy but also by the angular momentum. And for q=0.5M and b<3.3731M, absorbed by the black hole is the only fate of the test particle. We also find that the position of the innermost stable circular orbit of Bardeen black hole occurs at r min =5.5722M.  相似文献   

11.
V. Carruba  J.A. Burns  W. Bottke 《Icarus》2003,162(2):308-327
Asteroid families are groupings of minor planets identified by clustering in their proper orbital elements; these objects have spectral signatures consistent with an origin in the break-up of a common parent body. From the current values of proper semimajor axes a of family members one might hope to estimate the ejection velocities with which the fragments left the putative break-up event (assuming that the pieces were ejected isotropically). However, the ejection velocities so inferred are consistently higher than N-body and hydro-code simulations, as well as laboratory experiments, suggest. To explain this discrepancy between today’s orbital distribution of asteroid family members and their supposed launch velocities, we study whether asteroid family members might have been ejected from the collision at low speeds and then slowly drifted to their current positions, via one or more dynamical processes. Studies show that the proper a of asteroid family members can be altered by two mechanisms: (i) close encounters with massive asteroids, and (ii) the Yarkovsky non-gravitational effect. Because the Yarkovsky effect for kilometer-sized bodies decreases with asteroid diameter D, it is unlikely to have appreciably moved large asteroids (say those with D > 15 km) over the typical family age (1-2 Gyr).For this reason, we numerically studied the mobility of family members produced by close encounters with main-belt, non-family asteroids that were thought massive enough to significantly change their orbits over long timescales. Our goal was to learn the degree to which perturbations might modify the proper a values of all family members, including those too large to be influenced by the Yarkovsky effect. Our initial simulations demonstrated immediately that very few asteroids were massive enough to significantly alter relative orbits among family members. Thus, to maximize gravitational perturbations in our 500-Myr integrations, we investigated the effect of close encounters on two families, Gefion and Adeona, that have high encounter probabilities with 1 Ceres, by far the largest asteroid in the main belt. Our results show that members of these families spreads in a of less than 5% since their formation. Thus gravitational interactions cannot account for the large inferred escape velocities.The effect of close encounters with massive asteroids is, however, not entirely negligible. For about 10% of the simulated bodies, close encounters increased the “inferred” ejection velocities from sub-100 m/s to values greater than 100 m/s, beyond what hydro-code and N-body simulations suggest are the maximum possible initial ejection velocity for members of Adeona and Gefion with D > 15 km. Thus this mechanism of mobility may be responsible for the unusually high inferred ejection speeds of a few of the largest members of these two families.To understand the orbital evolution of the entire family, including smaller members, we also performed simulations to account for the drift of smaller asteroids caused by the Yarkovsky effect. Our two sets of simulations suggest that the two families we investigated are relatively young compared to larger families like Koronis and Themis, which have estimated ages of about 2 Byr. The Adeona and Gefion families seems to be no more than 600 and 850 Myr old, respectively.  相似文献   

12.
The variation in infrared equilibrium brightness temperature of Saturn's A, B, and C rings is modeled as a function of solar elevation B′ with respect to the ring plane. The basic model includes estimates of minimum and maximum interparticle shadowing in a monolayer approximation. Simple laboratory observations of random particle distributions at various illumination angles provide more realistic shadowing functions. Radiation balance calculations yield the physical (kinetic) temperature of particles in equilibrium with radiation from the Sun, Saturn, and neighboring particles. Infrared brightness temperatures as a function of B′ are then computed and compared to the available 20-μm data (Pioneer results are also briefly discussed). The A and B rings are well modeled by an optically thick monolayer, or equivalently, a flat sheet, radiating from one side only. This points to a temperature contrast between the two sides, possibly due to particles with low thermal inertia. Other existing models for the B ring are discussed. The good fit for the monolayer model does not rule out the possibility that the A and B rings are many particles thick. It could well be that a multilayer ring produces an infrared behavior (as a function of tilt angle) similar to that of a monolayer. The C ring brightness increases as B′ decreases. This contrast in behavior can be understood simply in terms of the low C ring optical depth and small amount of interparticle shadowing. High-albedo particles (A?0.5) can fit the C ring infrared data if they radiate mostly from one hemisphere due to slow rotation or low thermal inertia (or both). Alternatively, particles isothermal over their surface (owing to a rapid spin, high inertia, or small size), and significantly darker (A?0.3) than the A and B ring particles, can produce a similar brightness variation with ring inclination. In any case, the C ring particles have significantly hotter physical temperatures than the particles in the A and B rings, whether or not the rings form a monolayer.  相似文献   

13.
Y. Kawata  W.M. Irvine 《Icarus》1975,24(4):472-482
Models of Saturn's B ring have been investigated which include the shadowing mechanism, realistic phase functions for the ring particles, and the effects of multiple scattering and a particle size dispersion. These models are based on the assumption that the rings form a layer many particles thick. A power law relation dn ∝ ??s is used for the size dispersion law of the ring particles, where dn is the number of particles with radii between ? and ? + d?. In the calculation of the infrared brightness temperature of the rings, the effect of mutual heating among the ring particles is considered quantitatively for the first time. The parameters of the polydisperse s = 2 model can be chosen to satisfy both optical (λ ? 1.1 μ) and infrared data, but the situation could be much clarified if a good phase curve for the rings were available in the red, if the ring brightness were known accurately for λ > 1 μ, and if it could be established whether the ring particles are rotating synchronously.  相似文献   

14.
The stability of an imaginary planet located in the present main asteroid belt is studied with a 7-body model (Sun, Mars, Jupiter, Saturn, Uranus, Neptune and the imaginary planet). The fourth-order Hermite algorithm P(EC)3 is used, which has a very small secular energy error for the integration of periodic orbits with a constant time-step. The evolution of orbits is followed up to 108 years. Our numerical results show that the low-order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper limit of the imaginary planet's mass that can survive in the main belt is around 1025 kg, i.e., about the Earth's mass.  相似文献   

15.
Abstract— We give a nonmathematical review of recent work regarding the Yarkovsky effect on asteroidal fragments. This effect may play a critical, but underappreciated, role in delivering meteorites to Earth. Two variants of the effect cause drifts in orbital elements, notably semimajor axes. The “classic” or “diurnal” Yarkovsky effect is associated with diurnal rotation at low obliquity. More recently, a “seasonal” effect has also been described, associated with high obliquity. Studies of these Yarkovsky effects are combined with studies of resonance effects to clarify meteorite delivery. If there were no Yarkovsky drift, asteroid fragments could reach a resonance only if produced very near that resonance. However, objects in resonances typically reach Earth-crossing orbits within a few million years, which is inconsistent with stone meteorites' cosmic-ray exposure (CRE) ages (5–50 Ma) and iron meteorites' CRE ages (100–1000 Ma). In the new view, on the other hand, large objects in the asteroid belt are “fixed” in semimajor axis, but bodies up to 100 m in diameter are in a constant state of mixing and flow, especially if the thermal conductivity of their surface layers is low. Thus, small asteroid fragments may reach the resonances after long periods of drift in the main belt. Yarkovsky drift effects, combined with resonance effects, appear to explain many meteorite properties, including: (1) the long CRE ages of iron meteorites (due to extensive drift lifetimes in the belt); (2) iron meteorites' sampling of numerous parent bodies; (3) the shorter CRE ages of most stone meteorites (due to faster drift, coupled with weaker strength and more rapid collisional erosion); and (4) the abundance of falls from discrete impact events near resonances, such as the 8 Ma CRE age of H chondrites. Other consequences include: the delivery of meteorite parent bodies to resonances is enhanced; proportions of stone and iron meteorites delivered to Earth may be different from the proportions at the same sizes left in the belt, which in turn may differ from the ratio produced in asteroidal collisions; Rabinowitz's 10–100 m objects may be preferentially delivered to near-Earth space; and the delivery of C-class fragments from the outer belt may be inhibited, compared to classes in other parts of the belt. Thus, Yarkovsky effects may have important consequences in meteoritics and asteroid science.  相似文献   

16.
In extending the analysis of the four secular resonances between close orbits in Li and Christou (Celest Mech Dyn Astron 125:133–160, 2016) (Paper I), we generalise the semianalytical model so that it applies to both prograde and retrograde orbits with a one-to-one map between the resonances in the two regimes. We propose the general form of the critical angle to be a linear combination of apsidal and nodal differences between the two orbits \( b_1 \Delta \varpi + b_2 \Delta \varOmega \), forming a collection of secular resonances in which the ones studied in Paper I are among the strongest. Test of the model in the orbital vicinity of massive satellites with physical and orbital parameters similar to those of the irregular satellites Himalia at Jupiter and Phoebe at Saturn shows that \({>}20\) and \({>}40\%\) of phase space is affected by these resonances, respectively. The survivability of the resonances is confirmed using numerical integration of the full Newtonian equations of motion. We observe that the lowest order resonances with \(b_1+|b_2|\le 3\) persist, while even higher-order resonances, up to \(b_1+|b_2|\ge 7\), survive. Depending on the mass, between 10 and 60% of the integrated test particles are captured in these secular resonances, in agreement with the phase space analysis in the semianalytical model.  相似文献   

17.
Irregular satellites—moons that occupy large orbits of significant eccentricity e and/or inclination I—circle each of the giant planets. The irregulars often extend close to the orbital stability limit, about 1/3-1/2 of the way to the edge of their planet's Hill sphere. The distant, elongated, and inclined orbits suggest capture, which presumably would give a random distribution of inclinations. Yet, no known irregulars have inclinations (relative to the ecliptic) between 47 and 141°.This paper shows that many high-I orbits are unstable due to secular solar perturbations. High-inclination orbits suffer appreciable periodic changes in eccentricity; large eccentricities can either drive particles with ∼70°<I<110° deep into the realm of the regular satellites (where collisions and scatterings are likely to remove them from planetocentric orbits on a timescale of 107-109 years) or expel them from the Hill sphere of the planet.By carrying out long-term (109 years) orbital integrations for a variety of hypothetical satellites, we demonstrate that solar and planetary perturbations, by causing particles to strike (or to escape) their planet, considerably broaden this zone of avoidance. It grows to at least 55°<I<130° for orbits whose pericenters freely oscillate from 0 to 360°, while particles whose pericenters are locked at ±90° (Kozai mechanism) can remain for longer times.We estimate that the stable phase space (over 10 Myr) for satellites trapped in the Kozai resonance contains ∼10% of all stable orbits, suggesting the possible existence of a family of undiscovered objects at higher inclinations than those currently known.  相似文献   

18.
We investigate the survivability of Trojan-type companions of Neptune during primordial radial migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. We adopt the usual planet migration model in which the migration speed decreases exponentially with a characteristic time scale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus ∼1000 test particle Neptune Trojans with initial distributions of orbital eccentricity, inclination, and libration amplitude similar to those of the known jovian Trojans asteroids. We analyze these simulations to measure the survivability of Neptune's Trojans as a function of migration rate. We find that orbital migration with the characteristic time scale τ=106 years allows about 35% of preexisting Neptune Trojans to survive to 5τ, by which time the giant planets have essentially reached their final orbits. In contrast, slower migration with τ=107 years yields only a ∼5% probability of Neptune Trojans surviving to a time of 5τ. Interestingly, we find that the loss of Neptune Trojans during planetary migration is not a random diffusion process. Rather, losses occur almost exclusively during discrete prolonged episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranus with Neptune. These secondary resonances arise when the circulation frequencies, f, of critical arguments for Uranus-Neptune mean-motion near-resonances (e.g., fUN1:2, fUN4:7) are commensurate with harmonics of the libration frequency of the critical argument for the Neptune-Trojan 1:1 mean-motion resonance (fNT1:1). Trojans trapped in the secondary resonances typically have their libration amplitudes amplified until they escape the 1:1 resonance with Neptune. Trojans with large libration amplitudes are susceptible to loss during sweeping by numerous high-order secondary resonances (e.g., fUN1:2≈11fNT1:1). However, for the slower migration, with τ=107 years, even tightly bound Neptune Trojans with libration amplitudes below 10° can be lost when they become trapped in 1:3 or 1:2 secondary resonances between fUN1:2 and fNT1:1. With τ=107 years the 1:2 secondary resonance was responsible for the single greatest episode of loss, ejecting nearly 75% of existing Neptune Trojans. This episode occurred during the late stages of planetary migration when the remnant planetesimal disk would have been largely dissipated. We speculate that if the number of bodies liberated during this event was sufficiently high they could have caused a spike in the impact rate throughout the Solar System.  相似文献   

19.
Gravitational accretion in the rings of Saturn is studied with local N-body simulations, taking into account the dissipative impacts and gravitational forces between particles. Common estimates of accretion assume that gravitational sticking takes place beyond a certain distance (Roche distance) where the self-gravity between a pair of ring particles exceeds the disrupting tidal force of the central object, the exact value of this distance depending on the ring particles' internal density. However, the actual physical situation in the rings is more complicated, the growth and stability of the particle groups being affected also by the elasticity and friction in particle impacts, both directly via sticking probabilities and indirectly via velocity dispersion, as well as by the shape, rotational state and the internal packing density of the forming particle groups. These factors are most conveniently taken into account via N-body simulations. In our standard simulation case of identical 1 m particles with internal density of solid ice, ρ=900 kg m−3, following the Bridges et al., 1984 elasticity law, we find accretion beyond a=137,000-146,000 km, the smaller value referring to a distance where transient aggregates are first obtained, and the larger value to the distance where stable aggregates eventually form in every experiment lasting 50 orbital periods. Practically the same result is obtained for a constant coefficient of restitution εn=0.5. In terms of rp parameter, the sum of particle radii normalized by their mutual Hill radius, the above limit for perfect accretion corresponds to rp<0.84. Increased dissipation (εn=0.1), or inclusion of friction (tangential force 10% of normal force) shifts the accretion region inward by about 5000 km. Accretion is also more efficient in the case of size distribution: with a q=3 power law extending over a mass range of 1000, accretion shifts inward by almost 10,000 km. The aggregates forming in simulations via gradual accumulation of particles are synchronously rotating.  相似文献   

20.
To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets - Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N = 1000-2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the “Nice model”. We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars’ mass is too large by a factor of 5-10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e = 0.07-0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. Our simulations leave us with a problem: we can reasonably satisfy the observed constraints (except for Earth’s water) with a configuration of Jupiter and Saturn that is at best marginally consistent with models of the outer Solar System, as it does not allow for any outer planet migration after a few Myr. Alternately, giant planet configurations which are consistent with the Nice model fail to reproduce Mars’ small size.  相似文献   

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