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61.
D. J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2006,94(3):317-349
Equilibrium conditions for a mutually attracting general mass distribution and point mass are derived and their stability
computed. The equilibrium conditions can be reduced to six equations in six unknowns, plus the existence of four integrals
of motion consisting of the total angular momentum and energy of the system. The equilibrium conditions are further reduced
to two independent equations, and their theoretical properties are studied. We derive three distinct conditions for a relative
equilibrium which can be used to derive robust algorithms for solving these problems for non-symmetric gravity fields: a set
of necessary conditions, a set of sufficient conditions, and a set of necessary and sufficient conditions. Each of these conditions
is well suited for the computation of certain classes of equilibria. These equations are solved for non-symmetric gravity
fields of interest, using a real asteroid shape model for the general gravity fields. Explicit conditions for the spectral
and energetic stability of the resulting equilibria are also derived and computed for the shape of interest. 相似文献
62.
We predict that when Asteroid 2004 MN4 passes 5.6±1.4 Earth radii from Earth's center on April 13, 2029, terrestrial torques during the flyby will alter its spin state in a dramatic manner that will be observable using groundbased telescopes. Although the asteroid will most likely not undergo catastrophic disruption, it may be subject to localized failure across its surface and interior, providing a unique opportunity to measure otherwise inaccessible mechanical properties of an asteroid. 相似文献
63.
In this paper we study the statistical effect of planetary flybys on the rotation rates and states of Near Earth Objects (NEOs). Our approach combines numerical and analytical methods within a Monte Carlo model that simulates the evolution of the NEO spin rates. We take as input for the simulation a source distribution of spin states and evolve it to find their steady state distribution. In performing this evolution we track the changes in the spin rate and state distribution for the different components of the NEO population. We show that the cumulative effect of planetary encounters is to spin up the overall population of NEOs. This spin up effect holds on average only, and particular members of the population may experience an overall decrease in rotation rate. This effect is clearly seen across all components of the NEO population and is significant both statistically and physically. For initially slow rotators the spin up effect is strong, lowering the mean rotation period by 32%. For faster rotating populations the effect is less, lowering the spin period by 15% for the intermediate case, 6% for fast rotating rubble piles, and 8% for fast rotating monoliths. Physically, the spin up effect pushes 1% of the fast rotating rubble-pile NEOs over the disruption limit, while 6% of these bodies experience a sub-disruption event that could modify their physical structure. For monolithic NEOs, the spin up effect is self-limiting, reaching a minimum spin period of 1.1 hr, with a strong cut-off between 2-3 hr. This has two implications. First, it may not be necessary to invoke the rubble-pile hypothesis to recover a cut-off in spin period. Second, it shows that planetary flybys cannot account for the extremely rapid rotation rates of some small NEOs. We also tested a different balance between the effects of Earth and Venus by treating the Aten sub-class of asteroids separately. Due to increased interactions with the planets, the spin up effect is more pronounced (10%) and disruptions increase by a factor of three. The slow rotation tails of the spin distributions are increased to longer periods, in general, with rotation periods of over 100 hr occurring for a few tenths of a percent for some component populations. Thus, this mechanism may account for some of the noted excess in slow rotators among the NEOs. Planetary flybys also cause NEOs to enter a tumbling state, with approximately 0.5% of the population being placed into a long-axis rotation mode. Finally, based on the evolution of spin states of different components of the NEO population, we compared the evolved states with the measured distribution of NEOs to estimate the relative populations of these components that comprise the NEOs. 相似文献
64.
A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is
given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar
radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape
and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous
orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the
energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation
pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be
averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology
is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are
presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their
evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise
models for their orbital evolution. 相似文献
65.
We present a numerical method that incorporates particle sticking in simulations using the N-body code pkdgrav to study motions in a local rotating frame, such as a patch of a planetary ring. Particles stick to form non-deformable but breakable aggregates that obey the (Eulerian) equations of rigid-body motion. Applications include local simulations of planetary ring dynamics and planet formation, which typically feature hundreds of thousands or more colliding bodies. Bonding and breaking thresholds are tunable parameters that can approximately mimic, for example, van der Waals forces or interlocking of surface frost layers. The bonding and breaking model does not incorporate a rigorous treatment of internal fracture; rather the method serves as motivation for first-order investigation of how semi-rigid bonding affects the evolution of particle assemblies in high-density environments.We apply the method to Saturn’s A ring, for which laboratory experiments suggest that interpenetration of thin, frost-coated surface layers may lead to weak cohesive bonding. These experiments show that frost-coated icy bodies can bond at the low impact speeds characteristic of the rings. Our investigation is further motivated by recent simulations that suggest a very low coefficient of restitution is needed to explain the amplitude of the azimuthal brightness asymmetry in Saturn’s A ring, and the hypothesis that fine structure in Saturn’s B ring may in part be caused by large-scale cohesion.This work presents the full implementation of our model in pkdgrav, as well as results from initial tests with a limited set of parameters explored. We find a combination of parameters that yields aggregate size distribution and maximum radius values in agreement with Voyager data for ring particles in Saturn’s outer A ring. We also find that the bonding and breaking parameters define two strength regimes in which fragmentation is dominated either by collisions or other stresses, such as tides. We conclude our study with a discussion of future applications of and refinements to our model. 相似文献
66.
Michael W. Busch Steven J. Ostro Lance A.M. Benner Jon D. Giorgini Daniel J. Scheeres Michael C. Nolan Patrick A. Taylor Walter Brisken 《Icarus》2011,212(2):649-660
We observed the near-Earth ASTEROID 2008 EV5 with the Arecibo and Goldstone planetary radars and the Very Long Baseline Array during December 2008. EV5 rotates retrograde and its overall shape is a 400 ± 50 m oblate spheroid. The most prominent surface feature is a ridge parallel to the asteroid’s equator that is broken by a concavity about 150 m in diameter. Otherwise the asteroid’s surface is notably smooth on decameter scales. EV5’s radar and optical albedos are consistent with either rocky or stony-iron composition. The equatorial ridge is similar to structure seen on the rubble-pile near-Earth asteroid (66391) 1999 KW4 and is consistent with YORP spin-up reconfiguring the asteroid in the past. We interpret the concavity as an impact crater. Shaking during the impact and later regolith redistribution may have erased smaller features, explaining the general lack of decameter-scale surface structure. 相似文献
67.
Marina Brozovic Steven J. Ostro Jon D. Giorgini Randy Rose Alice A. Hine Daniel J. Scheeres 《Icarus》2009,201(1):153-166
Near-Earth Asteroid 4660 Nereus has been identified as a potential spacecraft target since its 1982 discovery because of the low delta-V required for a spacecraft rendezvous. However, surprisingly little is known about its physical characteristics. Here we report Arecibo (S-band, 2380-MHz, 13-cm) and Goldstone (X-band, 8560-MHz, 3.5-cm) radar observations of Nereus during its 2002 close approach. Analysis of an extensive dataset of delay-Doppler images and continuous wave (CW) spectra yields a model that resembles an ellipsoid with principal axis dimensions X=510±20 m, Y=330±20 m and . The pole direction is approximately located at ecliptic pole longitude and latitude of λ=+25°, β=+80° with the uncertainty radius of 10°. Our modeling yields a refined rotation period of 15.16±0.04 h. Nereus has a circular polarization (SC/OC) ratio of 0.74±0.08, which implies substantial near-surface centimeter-to-decimeter scale roughness. Dynamical analysis of our model suggests that YORP alteration of the rotation period may become evident within a few years. Nereus has two stable synchronous orbits where natural material may remain in orbit, while most asteroids observed to date do not have such stable synchronous orbits. We also find that spacecraft orbits about Nereus are feasible. 相似文献
68.
Stability of the planar full 2-body problem 总被引：1，自引：0，他引：1
D. J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):103-128
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
69.
八达岭基性岩和高Ba—Sr花岗岩地球化学特征及成因探讨：华北和大别—苏鲁造山带中生代岩浆岩的对比 总被引：27，自引：15，他引：27
八达岭杂岩侵位于华北北部，由辉长闪长岩岩、石英闪长岩、石英二长岩、二长闪长岩、二长花岗岩、碱长花岗岩和石英正长岩等组成，主要属高钾钙碱性系列。除了含V-Ti磁铁矿的堆晶辉长闪长岩，整套岩石的主量元素变化范围较大，SiO2=46.5%-75.3%,MgO=5.6%-0.2%，中酸性岩石的K2O/NaO为0.59-1.09。碱长花岗岩和少数石英二长岩Ba和Sr含量较低，且具有明显（Eu）负异常。大多数中酸性岩石（高Ba-Sr花岗岩）具有如下显著的微量元素地球化学特征：Ba,Sr和轻稀土（LREE）富集，Y和重稀土（HREE）亏损，LREE/HREE强烈分离，Sr/Y和La/Yb比值较高；在原始地幔标准化的蛛网图中具有显著的Nb,Ta和Ti亏损，不具明显的Sr和Eu亏损。在Harker图解中，基性岩石和高Ba-Sr花岗岩的主量元素相关性明显，两者还具有相似的微量元素和稀土（REE）分配特征，并且，REE,Y,Sr,P和Ti含量从基性到酸性逐渐降低。辉长闪长岩和高Ba-Sr花岗岩的Sr-Nd同位素初始值呈EMI特征（Isr=0.7051-0.7068,εNdi=-8.2-20.2），大致呈负相关。地球化学特征表明基性岩浆为富集的大陆岩石圈地幔部分熔融形成，而高Ba-Sr花岗岩则为基性岩浆通过陆壳混染和结晶分离形成；富P和Ti的副矿物（如磷灰石和的榍石）的分离结晶导致了REE,P和Ti丰度的逐渐降低。另外，华北板块内部和大别-苏鲁造山带基性岩和高Ba-Sr花岗岩分别具有相似的地球化学特征，这表明，上述地区燕山期大规模岩浆活动具有相似的地球动力学机制，大别-苏鲁造山带岩浆岩的地球化学特征并不反映其地幔源区一定受到过来自深俯冲的扬子板块的流体的富集作用。岩石圈的拆沉和减簿作用可能导致了华北板块和大别-苏鲁造山带下古老岩石圈地幔的部分熔融，岩石圈地幔的富集作用可能主要性发生于元古代。 相似文献
70.
Stability in the Full Two-Body Problem 总被引：3，自引：3，他引：0
D. J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):155-169
Stability conditions are established in the problem of two gravitationally interacting rigid bodies, designated here as the full two-body problem. The stability conditions are derived using basic principles from the N-body problem which can be carried over to the full two-body problem. Sufficient conditions for Hill stability and instability, and for stability against impact are derived. The analysis is applicable to binary small-body systems such as have been found recently for asteroids and Kuiper belt objects. 相似文献