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1.
Tidal disruption is a potentially important process for the accumulation of the planets from planetesimals. The fact that stable equilibria do not exist for circular orbits inside the Roche limit has often been hypothesized to mean that any object that passes within the Roche limit is totally disrupted. We have disproven this hypothesis by solving the dynamic problem of the tidal disruption of a dissipative planetestimal during a close encounter with a protoplanet. The solution consists of a numerical integration of the three-dimensional, nonlinear equations of motion, including an approximate treatment of viscous dissipation in the solid regions of the planetesimal. The numerical methods have been extensively tested on a series of one-, two- (Jeans), and three-(Roche) dimensional test problems involving the equilibrium of a body subjected to tidal forces. The results may be scaled to planetesimals of arbitrary size, providing that the scaled equation of state applied. The calculations show that a strongly dissipative planetesimal which passes by the Earth on a parabolic orbit with a perigee within the Roche limit (≈3REarth) is not tidally disrupted (even for grazing incidence), and loses no more than a few percent of its mass. This result applies to bodies of radius R which have a kinematic viscosity ν ? 1012(R/1000km)2 cm2sec?1. Less dissipative planetesimals (ν ≈ 1013(R/1000 km)2 cm2sec?1) may lose up to about 20% of their mass. There are two coupled reasons why this result differs from previous hypotheses: (1) in a dynamic encounter, there is insufficient time to disrupt the planetesimal, and (2) even in circular orbit, the small velocities in the solid region imply that many orbital periods are necessary to completely disrupt the planetesimal. Hence solid and partially molten planetesimals will not experience substantial tidal disruption; completely molten bodies may be sufficiently inviscid to undergo tidal disruption. 相似文献
2.
A new scenario is offered for the origin of the Moon. It is assumed that the Earth formed initially with about the maximum amount of angular momentum consistent with dynamical stability. This state is approximated by the secularly unstable Maclaurin spheroids (highly flattened, hamburger-shaped bodies). It is shown that the Earth cannot depart from this state at a resonable rate as long as its viscosity is in the range of liquid rock. Since core formation supplies about 1600 kJ kg?1 the Earth will not leave this state until core formation is complete. When cooling produces a rise in viscosity, the Earth will necessarily evolve along a path which is approximated by the Riemann ellipsoids (which have rapid internal motion). The evolution is toward a Jacobi ellipsoid, but it is intercepted by the development of a third-harmonic (pearshaped) instability, which is catastrophic and leads to fission. The process of fission itself may be fundamentally analogous to the breaking of a wave in water. We cannot exclude the possibility that some other planets evolved similarly. 相似文献
3.
We present a calculation of the sedimentation of grains in a giant gaseous protoplanet such as that resulting from a disk instability of the type envisioned by Boss [Boss, A.P., 1998. Earth Moon Planets 81, 19-26]. Boss [Boss, A.P., 1998. Earth Moon Planets 81, 19-26] has suggested that such protoplanets would form cores through the settling of small grains. We have tested this suggestion by following the sedimentation of small silicate grains as the protoplanet contracts and evolves. We find that during the course of the initial contraction of the protoplanet, which lasts some 4×105 years, even very small (>1 μm) silicate grains can sediment to create a core both for convective and non-convective envelopes, although the sedimentation time is substantially longer if the envelope is convective, and grains are allowed to be carried back up into the envelope by convection. Grains composed of organic material will mostly be evaporated before they get to the core region, while water ice grains will be completely evaporated. These results suggest that if giant planets are formed via the gravitational instability mechanism, a small heavy element core can be formed due to sedimentation of grains, but it will be composed almost entirely of refractory material. Including planetesimal capture, we find core masses between 1 and 10 M⊕, and a total high-Z enhancement of ∼40 M⊕. The refractories in the envelope will be mostly water vapor and organic residuals. 相似文献
4.
J. N. Tokis 《Earth, Moon, and Planets》1974,10(3-4):337-355
In a previous paper of this series (Tokis, 1974b), we have discussed the solution of the Eulerian equation which governs the axial rotation, applied to the effects of viscous friction exhibited in binary systems which consist of a close pair of fluid bodies of arbitrary structure. The aim of the present paper will be to give an application of those results to the Earth-Moon system. It is shown that synchronism between the axial rotation of the Earth and the revolution of the Moon will occur at the value of 650 h, in a time scale which depends strongly on the value of the mean viscosity of the Earth (regarded as spherical or spheroidal). In particular, the variation of rotational angular velocity of the Earth over the next ten centuries commencing from 1900 A.D., depends sensitively on the value of viscosity. On the other hand, the time for synchronism of axial rotation of the Moon is not affected by the viscosity for values between 1024g cm?1 s?1 and 1027g cm?1 s?1. 相似文献
5.
J. C. B. Papaloizou 《Celestial Mechanics and Dynamical Astronomy》2005,91(1-2):33-57
We study and review disk protoplanet interactions using local shearing box simulations. These suffer the disadvantage of having
potential artefacts arising from periodic boundary conditions but the advantage, when compared to global simulations, of being
able to capture much of the dynamics close to the protoplanet at high resolution for low computational cost. Cases with and
without self sustained MHD turbulence are considered. The conditions for gap formation and the transition from type I migration
are investigated and found to depend on whether the single parameter M
p
R
3/(M*
H
3), with M
p, M*, R, and H being the protoplanet mass, the central mass, the orbital radius and the disk semi-thickness, respectively, exceeds a number
of order unity. We also investigate the coorbital torques experienced by a moving protoplanet in an inviscid disk. This is
done by demonstrating the equivalence of the problem for a moving protoplanet to one where the protoplanet is in a fixed orbit
which the disk material flows through radially as a result of the action of an appropriate external torque. For sustainable
coorbital torques to be realized a quasi steady state must be realized in which the planet migrates through the disk without
accreting significant mass. In that case, although there is sensitivity to computational parameters, in agreement with earlier
work by Masset and Papaloizou [2003, ApJ, 588, 494] based on global simulations, the coorbital torques are proportional to
the migration speed and result in a positive feedback on the migration, enhancing it and potentially leading to a runaway.
This could lead to fast migration for protoplanets in the Saturn mass range in massive disks and may be relevant to the mass
period correlation for extrasolar planets which gives a preponderance of sub Jovian masses at short orbital periods. 相似文献
6.
S.J. Peale 《Icarus》2006,181(2):338-347
In determining Mercury's core structure from its rotational properties, the value of the normalized moment of inertia, C/MR2, from the location of Cassini 1 is crucial. If Mercury's spin axis occupies Cassini state 1, its position defines the location of the state, where the axis is fixed in the frame precessing with the orbit. Although tidal and core-mantle dissipation drive the spin to the Cassini state with a time scale O(105) years, the spin might still be displaced from the Cassini state if the variations in the orbital elements induced by planetary perturbations, which change the position of the Cassini state, cause the spin to lag behind as it attempts to follow the state. After being brought to the state by dissipative processes, the spin axis is expected to follow the Cassini state for orbit variations with time scales long compared to the 1000 year precession period of the spin about the Cassini state because the solid angle swept out by the spin axis as it precesses is an adiabatic invariant. Short period variations in the orbital elements of small amplitude should cause displacements that are commensurate with the amplitudes of the short period terms. The exception would be if there are forcing terms in the perturbations that are nearly resonant with the 1000 year precession period. The precision of the radar and eventual spacecraft measurements of the position of Mercury's spin axis warrants a check on the likely proximity of the spin axis to the Cassini state. How confident should we be that the spin axis position defines the Cassini state sufficiently well for a precise determination of C/MR2? By following simultaneously the spin position and the Cassini state position during long time scale orbital variations over past 3 million years [Quinn, T.R., Tremaine, S., Duncan, M., 1991. Astron. J. 101, 2287-2305] and short time scale variations for 20,000 years [JPL Ephemeris DE 408; Standish, E.M., private communication, 2005], we show that the spin axis will remain within one arcsec of the Cassini state after it is brought there by dissipative torques. In this process the spin is located in the orbit frame of reference, which in turn is referenced to the inertial ecliptic plane of J2000. There are no perturbations with periods resonant with the precession period that could cause large separations. We thus expect Mercury's spin to occupy Cassini state 1 well within the uncertainties for both radar and spacecraft measurements, with correspondingly tight constraints on C/MR2 and the extent of Mercury's molten core. Two unlikely caveats for this conclusion are: (1) an excitation of a free spin precession by an unknown mechanism or (2) a displacement by a dissipative core mantle interaction that exceeds the measurement uncertainties. 相似文献
7.
We follow the contraction and evolution of a typical Jupiter-mass clump created by the disk instability mechanism, and compute the rate of planetesimal capture during this evolution. We show that such a clump has a slow contraction phase lasting ∼3×105 yr. By following the trajectories of planetesimals as they pass through the envelope of the protoplanet, we compute the cross-section for planetesimal capture at all stages of the protoplanet's evolution. We show that the protoplanet can capture a large fraction of the solid material in its feeding zone, which will lead to an enrichment of the protoplanet in heavy elements. The exact amount of this enrichment depends upon, but is not very sensitive to the size and random speed of the planetesimals. 相似文献
8.
The main points are presented of a new hypothesis of the origin of the Earth—Moon system, developed on the basis of Savi's (1961) theory of the origin of rotation of celestial bodies. The cooling off and contraction due to gravitational attraction on vast particle systems, with the pushing out of electrons from atom shells result in a continually increasing density. Depending on the amount of mass, this pushing out can lead to the expulsion of electrons and the creation of a magnetic field by which a rotational motion is brought about. These conditions are satisfied for the Earth's mass and all larger masses. If the Earth and the Moon formed a unique body, the protoplanet, then once rotational motion had begun, the primeval spherical body must have taken the shape of a large Jacobi ellipsoid. New condensation followed, however no longer solely around the centre of the protoplanet, but also along the edge of the ellipsoid, the process leading to the creation of the dual Earth—Moon system. 相似文献
9.
A spectrum of Jupiter between 6000 and 12 000 cm? at high resolution (0.05 cm?) was recorded with a Michelson interferometer at Palomar Mountain in October 1974. An analysis of the R branch of the 3ν3CH4 band with the reflecting-layer model, taking into account the H2 absorption which occurs in the same spectral range, leads to a Lorentzian half-width of 0.09 ± 0.02 cm?1, a rotational temperature of 175 ± 10° K, and a CH4 abundance of order 52m atm. Five lines of the 13CH43ν3 band have been identified; a comparison with new laboratory spectra indicates that the 13CH4/12CH4 ratio in the Jupiter atmosphere is close to the terrestrial ratio. 相似文献
10.
For models of planetary accumulation in the presence of solar nebular gas, the initial surface temperature of the Earth is controlled by the grain opacity of the atmosphere. The surface temperature in turn controls the quantity of neon dissolved and trapped within the interior of the Earth. To compare accumulation theory with observation calculations have been made of the grain opacity expected to be associated with accumulation in a gaseous nebula. There are two parameters that are in principle determined by the theory, but actually are at present uncertain: the mean eccentricity e of the planetesimal swarm, and the fraction ξ of the accretional energy that is expended in the release of grains into the atmosphere by ablation of the incoming planetesimal. It is found that if the eccentricity of swarm is low (10?3), rather low values of ξ(10?5) are required to match the observed neon data. In contrast higher values of ξ are required (10?1) for the most probable case, intermediate eccentricity (10?2). For the high eccentricity case (e ～ 0.1) ξ must be >10?2. The results show that avoidance of excess trapped neon of solar composition places restrictive, but not necessarily impossible, conditions on the parameters of the accumulation theory. 相似文献
11.
Peter Bodenheimer Allen S. Grossman William M. DeCampli Geoffrey Marcy James B. Pollack 《Icarus》1980,41(2):293-308
Evolutionary calculations are presented for spherically symmetric protoplanetary configurations with a homogeneous solar composition and with masses of 10?3, 1.5 × 10?3, 2.85 × 10?4, and 4.2 × 10?4M⊙. Recent improvements in equation-of-state and opacity calculations are incorporated. Sequences start as subcondensations in the solar nebula with densities of ～10?10 to 10?11 g cm?3, evolve through a hydrostatic phase lasting 105 to 107 years, undergo dynamic collapse due to dissociation of molecular hydrogen, and regain hydrostatic equilibrium with densities ～1 g cm?3. The nature of the objects at the onset of the final phase of cooling and contraction is discussed and compared with previous calculations. 相似文献
12.
In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider f(R)=R+?R 2 model and assume hydrostatic equilibrium of the axial self-gravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, Γ 1, that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the f(R) model affect the instability ranges. 相似文献
13.
Paul S. Wesson 《Astrophysics and Space Science》1975,37(1):101-114
Recent computer simulations by Haggerty (1974) and Haggerty and Janin (1974) on the gravitational clumping of bodies into clusters and superclusters in Newtonian cosmology have given an approximate value of Θ=1.9 for the thinning factor (defined for two systems of sizesR 1,R 2 and densities? 1,? 2 by? 1/? 2 = (R 2/R 1)θ), close to the observed value of Θ=1.7. To get an almost exact value of Θ in a general relativistic hierarchy, algebraic conditions on the metric tensor are employed: the result is Θ=2, with the hierarchy characterized by a dimensionless constantη 1 (?G?b 2/c2) of valueη 1 ? 2 x 10-7 (?=density,b=characteristic dimension, of any system at any level of the hierarchy). A condition on the rotation of systems is also found for objects of sufficiently high angular momentum. 相似文献
14.
Yu. V. Barkin H. Hanada K. Matsumoto S. Sasaki M. Yu. Barkin 《Solar System Research》2014,48(6):403-419
An analytical theory of lunar physical librations based on its two-layer model consisting of a non-spherical solid mantle and ellipsoidal liquid core is developed. The Moon moves on a high-precision orbit in the gravitational field of the Earth and other celestial bodies. The defined fourth mode of a free libration is caused by the influence of the liquid core, with a long period of 205.7 yr, with amplitude S = 0″0395 and with an initial phase Π0 = ?134° (for the initial epoch 2000.0). Estimates of dynamic (meridional) oblatenesses of a liquid core of the Moon have been estimated: ?D = 4.42 × 10?4, μD = 2.83 × 10?4 (?D + μD = 7.24 × 10?4). These results have been obtained as a result of comparison of the developed analytical theory of physical librations of the Moon with the empirical theory of librations of the Moon constructed on the basis of laser observations. 相似文献
15.
The propagation and modulation of electrons in the heliosphere play an important part in improving our understanding and assessment of the modulation processes. A full three-dimensional numerical model is used to study the modulation of galactic electrons, from Earth into the inner heliosheath, over an energy range from 10 MeV to 30 GeV. The modeling is compared with observations of 6–14 MeV electrons from Voyager 1 and observations at Earth from the PAMELA mission. Computed spectra are shown at different spatial positions. Based on comparison with Voyager 1 observations, a new local interstellar electron spectrum is calculated. We find that it consists of two power-laws: In terms of kinetic energy E, the results give E ?1.5 below ～500 MeV and E ?3.15 at higher energies. Radial intensity profiles are computed also for 12 MeV electrons, including a Jovian source, and compared to the 6–14 MeV observations from Voyager 1. Since the Jovian and galactic electrons can be separated in the model, we calculate the intensity of galactic electrons below 100 MeV at Earth. The highest possible differential flux of galactic electrons at Earth with E=12 MeV is found to have a value of 2.5×10?1 electrons m?2?s?1?sr?1?MeV?1 which is significantly lower (a factor of 3) than the Jovian electron flux at Earth. The model can also reproduce the extraordinary increase of electrons by a factor of 60 at 12 MeV in the inner heliosheath. A lower limit for the local interstellar spectrum at 12 MeV is estimated to have a value of (90±10) electrons m?2?s?1?sr?1?MeV?1. 相似文献
16.
Alan Paul Boss 《Icarus》1985,61(1):3-9
The presolar nebula may have formed from the collapse of a very slowly rotating interstellar cloud. The first three-dimensional, hydrodynamical calculations of the collapse of such clouds are presented. The models include radiative transfer in the Eddington approximation, as well as detailed equations of state appropriate for the nonisothermal regime of protostellar evolution. Very slowly rotating clouds, i.e., those with initial ratios of rotational energy to gravitational energy of 10?3 or less, avoid fragmentation and instead collapse to form single central objects, containing quasistatic cores with densities of about 10?10 g cm?3. These cores are, however, surrounded by significantly nonaxisymmetric regions, such that the presolar nebula would have been bar-like over the scale of the present solar system. This nonaxisymmetry, coupled with differential rotation, results in gravitational torques that produce rapid outward transfer of angular momentum. The center of the presolar nebula should then be able to contract and collapse to pre-main-sequence densities without suffering fission or fragmentation. 相似文献
17.
Peter Bodenheimer 《Icarus》1974,23(3):319-325
The evolution of the protoplanet Jupiter is followed, using a hydrodynamic computer code with radiative energy transport. Jupiter is assumed to have formed as a subcondensation in the primitive solar nebula at a density just high enough for gravitational collapse to occur. The initial state has a density of 1.5 × 10?11 g cm?3 and a temperature of 43 K; the calculations are carried to an equilibrium state where the central density reaches 0.5 g cm?3 and the central temperature reaches 2.5 × 104 K. During the early part of the evolution the object contracts in quasi-hydrostatic equilibrium; later on hydrodynamic collapse occurs, induced by the dissociation of hydrogen molecules. After dissociation is complete, the planet regains hydrostatic equilibrium with a radius of a few times the present value. Further evolution beyond this point is not treated here; however the results are consistent with the existence of a high-luminosity phase shortly after the planet settles into its final quasistatic contraction. 相似文献
18.
Libyan Desert Glass contains meteoritic material and, therefore, its origin is most likely associated with an impact event. However, the impact crater has not been found. We performed numerical simulations of impacts of stony and cometary bodies in order to confirm the version that this glass was formed from silica heated by radiation from aerial bursts near the ground. Asteroids were treated as strengthless bodies from dunite with a density of 3.3 g cm?3, and comets as icy bodies with a density of 1 g cm?3. The simulations based on hydrodynamic equations included the equations of radiation transfer. Melting and vaporization of a silica target under action of radiation incident on a planar surface were modeled using a one‐dimensional hydrodynamic equation of energy and equations of radiation transfer in two‐flux approximation. We selected those variants of simulations in which a crater is not formed, a fireball touches the earth surface, and the area of a molten target corresponds to the area of the Libyan Desert Glass strewn field. Appropriate options include the impact of an asteroid with a diameter of 300 m, an entry speed of 35 km s?1, and an entry angle of 8°, and cometary bodies with diameters from 150 to 300 m, speeds of 50–70 km s?1, and entry angles from 15° to 45°. Impact options with crater formation are also discussed. The maximum depth of molten silica at ground zero reaches 10 cm with the cometary impacts and 3–4 cm with the asteroidal impact. Melting occurs during a period of time from 50 to 400 s. 相似文献
19.
20.
Tidally forced viscous heating in a partially molten Io 总被引：1，自引：0，他引：1
We investigate tidal dissipative heating in two different models of Io. The partially molten asthenosphere model consists of a rigid inner core and a thin (less than 40 km thick) partially molten “decoupling” layer (asthenosphere) surrounded by an elastic lithosphere. In the partially molten interior model the interior beneath the lithosphere is partially molten throughout. The partially molten region in each model assumed to possess negligible shear strength and to be characterized by a Newtonian viscosity. Tidal deformation and dissipation in the core of the thin asthenosphere model are assumed negligible. Fluid in the viscous layers is forced to circulate by the tidal distortion of the outer shell, modeled here as a sinusoidal variation with time of the distortion amplitude. As a result, heat is generated in the fluid by viscous dissipation. There are two heating mechanisms in our models: “elastic” dissipation in the lithosphere ∞ 1/Q and viscous dissipation in the partially molten region. Numerical calculatons are carried out for a 90-km-thick lithosphere with Q = 100. This thickness maximizes dissipation in a decoupled lithosphere; other reasonable values of lithosphere thickness do not alter our conclusions. Under the constraint that total dissipation equals the observed radiated heat loss we derived the iscosity of the partially molten region in each model. We a posteriori evaluate the assumption that the lithosphere is decoupled from the interior by calculating the distortion of an elastic shell due to the viscous stresses on the lower surface of the outr shell. If the interior viscosity is such that the total dissipation is equal to the observed heat flux from Io, viscous stresses produce negligible distortion of a 90-km-thick shell. This validates the assumption of a decoupled shell. The derived viscosity for both models is characteristic of a partially molten rock. In the thin asthenosphere model the derived viscosity is so low that a very high degree of partial melt is necessary, about 40% crystal fraction in a 400-km-thick asthenosphere and about 0% in a 1-km-thick asthenosphere. In the partially molten interior model the derived viscosity corresponds to a magma with about 60% crystals. Consideration of convective efficiencies demonstrates the plausibility of a stable thermal steady state for both models. A significant portion (75% for Q = 100) of Io's tidal heating can be the result of viscous dissipation in a partially molten region that decouples the outer shell from the interior. The partially molten layer can be considered a “global magma ocean”. 相似文献