首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 765 毫秒
1.
Using numerical simulations, we studied several coupled translational and rotational solutions of the two-finite-body problem with one spherical and one triaxial body. The aim was to investigate which types of orbits and planetary bodies could produce spin-induced orbital perturbations relevant enough to add to models dealing with other perturbations. To fully assess the strengths and consequences of this perturbation, we did not include any other perturbation even when a more realistic scenario would have required it. Interesting results concern planet–star mass ratios like a hot Jupiter or a super-Jupiter around a star like the Sun or the red dwarf Proxima Centauri. The short-period chaotic effect of the gravitational spin–orbit perturbation on highly eccentric orbits in the vicinity of the Roche limit can be a prominent feature. It should be taken into account when studying the tidal evolution of such a planet or its interactions with any companion in the neighborhood of the star.  相似文献   

2.
Some aspects and consequences of the theory of gravitational accretion of the terrestrial planets are examined. The concept of a “closed feeding zone” is somewhat unrealistic, but provides a lower bound on the accretion time. Safronov's relative velocity relation for planetesimals is not entirely consistent with the feeding zone model. A velocity relation which includes an initial velocity component is suggested. The orbital parameters of the planetesimals and the dimensions of the feeding zone are related to their relative velocities. The assumption of an initial velocity does not seriously change the accretion time.Mercury, Venus, and the Earth have accretion times on the order of 108yr. Mars requires well over 109yr to accrete by the same assumptions. Currently available data do not rule out a late formation of Mars, but the lunar cratering history makes it unlikely. If Mars is as old as the Earth, nongravitational forces or a violation of the feeding zone concept is required. One such possibility is the removal of matter from the zone of Mars by Jupiter's influence. The final sweeping up by Mars after this event would result in the scattering of a considerable mass among the other terrestrial planets. The late postaccretional bombardments infrerred for the Moon and Mercury may have had this source.  相似文献   

3.
The discovery of a terrestrial planet orbiting Proxima Centauri has led to a lot of papers discussing the possible conditions on this planet. Since the main factors determining space weather in the Solar System are the solar wind and cosmic rays (CRs), it seems important to understand what the parameters of the stellar wind, Galactic and stellar CRs near exoplanets are. Based on the available data, we present our estimates of the stellar wind velocity and density, the possible CR fluxes and fluences near Proxima b. We have found that there are virtually no Galactic CRs near the orbit of Proxima b up to particle energies ~1 TeV due to their modulation by the stellar wind. Nevertheless, more powerful and frequent flares on Proxima Centauri than those on the Sun can accelerate particles to maximum energies ~3150αβ GeV (α, β < 1). Therefore, the intensity of stellar CRs in the astrosphere may turn out to be comparable to the intensity of low-energy CRs in the heliosphere.  相似文献   

4.
The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods perform the terminal fine tuning of the optimization parameters.  相似文献   

5.
Stephen J. Kortenkamp 《Icarus》2005,175(2):409-418
Numerical simulations of the gravitational scattering of planetesimals by a protoplanet reveal that a significant fraction of scattered planetesimals can become trapped as so-called quasi-satellites in heliocentric 1:1 co-orbital resonance with the protoplanet. While trapped, these resonant planetesimals can have deep low-velocity encounters with the protoplanet that result in temporary or permanent capture onto highly eccentric prograde or retrograde circumplanetary orbits. The simulations include solar nebula gas drag and use planetesimals with diameters ranging from ∼1 to ∼1000 km. Initial protoplanet eccentricities range from ep=0 to 0.15 and protoplanet masses range from 300 Earth-masses (M⊕) down to 0.1M⊕. This mass range effectively covers the final masses of all planets currently thought to be in possession of captured satellites—Jupiter, Saturn, Neptune, Uranus, and Mars. For protoplanets on moderately eccentric orbits (ep?0.1) most simulations show from 5-20% of all scattered planetesimals becoming temporarily trapped in the quasi-satellite co-orbital resonance. Typically, 20-30% of the temporarily trapped quasi-satellites of all sizes came within half the Hill radius of the protoplanet while trapped in the resonance. The efficiency of the resonance trapping combined with the subsequent low-velocity circumplanetary capture suggests that this trapped-to-captured transition may be important not only for the origin of captured satellites but also for continued growth of protoplanets.  相似文献   

6.
Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. [1986. Satellites. Univ. of Arizona Press, Tucson, pp. 89-116], heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as ∼RH/2. At first, the net angular momentum of this proto-satellite swarm is small, and collisions among satellitesimals leads to loss of mass from the outer disk, and delivers mass to the inner disk (where regular satellites form) in a timescale ?105 years. This mass loss may be offset by continued collisional capture of sufficiently small <1 km interlopers resulting from the disruption of planetesimals in the feeding zone of the giant planet. As the planet's feeding zone is cleared in a timescale ?105 years, enough angular momentum may be delivered to the proto-satellite swarm to account for the angular momentum of the regular satellites of Jupiter and Saturn. This feeding timescale is also roughly consistent with the independent constraint that the Galilean satellites formed in a timescale of 105-106 years, which may be long enough to accommodate Callisto's partially differentiated state [Anderson et al., 1998. Science 280, 1573; Anderson et al., 2001. Icarus 153, 157-161]. In turn, this formation timescale can be used to provide plausible constraints on the surface density of solids in the satellitesimal disk (excluding satellite embryos for satellitesimals of size ∼1 km), which yields a total disk mass smaller than the mass of the regular satellites, and means that the satellites must form in several ∼10 collisional cycles. However, much more work will need to be conducted concerning the collisional evolution both of the circumplanetary satellitesimals and of the heliocentric planetesimals following giant planet formation before one can assess the significance of this agreement. Furthermore, for enough mass to be delivered to form the regular satellites in the required timescale one may need to rely on (unproven) mechanisms to replenish the feeding zone of the giant planet. We compare this model to the solids-enhanced minimum mass (SEMM) model of Mosqueira and Estrada [2003a. Icarus 163, 198-231; 2003b. Icarus 163, 232-255], and discuss its main consequences for Cassini observations of the saturnian satellite system.  相似文献   

7.
A model of planetary formation in a binary system with a small relative mass of primary is computed on the assumption of a mass transfer from the less massive component to the more massive one with no mass and angular momentum carried away from the system under consideration. At the last stage of mass transfer the condensed Moon-like objects (planetoids) are ejected through the inner Lagrange point of the primary Roche lobe with the outflow of gaseous matter.The whole system is considered in the plane of binary star rotation. Newtonian equations of motion are integrated with the initial conditions for the planetoids referred to as the coordinates and velocity of the inner Lagrangian point at the moments of planetoid ejections, all the pairwise gravitational interactions being included in computations but without a gas-drag. The mass transfer ceases at the primary relative mass 10–3 which corresponds to the present Sun-Jupiter system. The total mass of planetoids approximates that of the terrestrial planets. Those are formed through coagulation of the planetoids with the effective radius of capture cross-section as an input parameter in the computer simulation. When the minimum separation between the pair of bodies becomes less than this radius they coalesce into a single body with their masses and momenta summed. If the effective radius value is under a certain limit the computer simulation yields the planetary system like that of terrestrial planets of the present Sun system.Numerical computations reveal the division of the planetoids into 4 groups along their distances from the Sun. Further, each group forms a single planet or a planet and a less massive body at the nearest orbits. The parameters of simulated planet orbits are close to the present ones and the interplanetary spacings are in accord with the Titius-Bode law.  相似文献   

8.
Dynamical relaxation and massive extrasolar planets   总被引：1，自引：0，他引：1  
Following the suggestion of Black that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we investigate a scenario in which 5 N 100 planetary mass objects are assumed to form rapidly through a fragmentation process occuring in a disc or protostellar envelope on a scale of 100 au. These are assumed to have formed rapidly enough through gravitational instability or fragmentation that their orbits can undergo dynamical relaxation on a time-scale of ∼100 orbits.
Under a wide range of initial conditions and assumptions, the relaxation process ends with either (i) one potential 'hot Jupiter' plus up to two 'external' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi-major axis of 10 to 100 times smaller than the outer boundary radius of the inital distribution together with an 'external' companion. Most of the other objects are ejected and could contribute to a population of free-floating planets. Apart from the potential 'hot Jupiters', all the bound objects are on orbits with high eccentricity, and also with a range of inclination with respect to the stellar equatorial plane. We found that, apart from the close orbiters, the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance. This is because of the tendency of the relaxation process to lead to collisions with the central star. The scenario we envision here does not impose any upper limit on the mass of the planets. We discuss the application of these results to some of the more massive extrasolar planets.  相似文献   

9.
Families of nearly circular periodic orbits of the planetary type are studied, close to the 3/1 mean motion resonance of the two planets, considered both with finite masses. Large regions of instability appear, depending on the total mass of the planets and on the ratio of their masses.Also, families of resonant periodic orbits at the 2/1 resonance have been studied, for a planetary system where the total mass of the planets is the 4% of the mass of the sun. In particular, the effect of the ratio of the masses on the stability is studied. It is found that a planetary system at this resonance is unstable if the mass of the outer planet is smaller than the mass of the inner planet.Finally, an application has been made for the stability of the observed extrasolar planetary systems HD82943 and Gliese 876, trapped at the 2/1 resonance.  相似文献   

10.
On the migration of a system of protoplanets   总被引：1，自引：0，他引：1  
The evolution of a system consisting of a protoplanetary disc with two embedded Jupiter-sized planets is studied numerically. The disc is assumed to be flat and non-self-gravitating; this is modelled by the planar (two-dimensional) Navier–Stokes equations. The mutual gravitational interaction of the planets and the star, and the gravitational torques of the disc acting on the planets and the central star are included. The planets have an initial mass of one Jupiter mass M Jup each, and the radial distances from the star are one and two semimajor axes of Jupiter, respectively.
During the evolution a joint wide annular gap is created by the planets. Both planets increase their mass owing to accretion of gas from the disc: after about 2500 orbital periods of the inner planet it has reached a mass of 2.3  M Jup, while the outer planet has reached a mass of 3.2  M Jup. The net gravitational torques exerted by the disc on the planets result in an inward migration of the outer planet on time-scales comparable to the viscous evolution time of the disc. The semimajor axis of the inner planet remains constant as there is very little gas left in its vicinity to induce any migration. When the distance of close approach eventually becomes smaller than the mutual Hill radius, the eccentricities increase strongly and the system may become unstable.
If disc depletion occurs rapidly enough before the planets come too close to each other, a stable system similar to our own Solar system may remain. Otherwise the orbits may become unstable and produce systems like υ And.  相似文献   

11.
Most extrasolar planets discovered to date are more massive than Jupiter, in surprisingly small orbits (semimajor axes less than 3 AU). Many of these have significant orbital eccentricities. Such orbits may be the product of dynamical interactions in multiplanet systems. We examine outcomes of such evolution in systems of three Jupiter-mass planets around a solar-mass star by integration of their orbits in three dimensions. Such systems are unstable for a broad range of initial conditions, with mutual perturbations leading to crossing orbits and close encounters. The time scale for instability to develop depends on the initial orbital spacing; some configurations become chaotic after delays exceeding 108 y. The most common outcome of gravitational scattering by close encounters is hyperbolic ejection of one planet. Of the two survivors, one is moved closer to the star and the other is left in a distant orbit; for systems with equal-mass planets, there is no correlation between initial and final orbital positions. Both survivors may have significant eccentricities, and the mutual inclination of their orbits can be large. The inner survivor's semimajor axis is usually about half that of the innermost starting orbit. Gravitational scattering alone cannot produce the observed excess of “hot Jupiters” in close circular orbits. However, those scattered planets with large eccentricities and small periastron distances may become circularized if tidal dissipation is effective. Most stars with a massive planet in an eccentric orbit should have at least one additional planet of comparable mass in a more distant orbit.  相似文献   

12.
The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

13.
In Sections 1–6, we determine an approximate analytical model for the density and temperature distribution in the protoplanetary could. The rotation of the planets is discussed in Section 7 and we conclude that it cannot be determined from simple energy conservation laws.The velocity of the gas of the protoplanetary cloud is found to be smaller by about 5×103 cm s–1 in comparison to the Keplerian circular velocity. If the radius of the planetesimals is smaller than a certain limitr 1, they move together with the gas. Their vertical and horizontal motion for this case is studied in Sections 8 and 9.As the planetesimals grow by accretion their radius becomes larger thanr 1 and they move in Keplerian orbits. As long as their radius is betweenr 1 and a certain limitr 2 their gravitational interaction is negligible. In Section 10, we study the accretion for this case.In Section 11, we determine the change of the relative velocities due to close gravitational encounters. The principal equations governing the late stages of accretion are deduced in Section 12, In Section 13 there are obtained approximate analytical solutions.The effect of gas drag and of collisions is studied in Sections 14 and 15, respectively. Numerical results and conclusions concerning the last and principal stage of accretion are drawn in Section 16.  相似文献   

14.
One possible origin of the terrestrial planets involves their formation by gravitational accretion of particles originally in Keplerian orbits about the sun. Some implications of this theory are considered. A formal expression for the rate of mass accretion by a planet is developed. The formal singularity of the gravitational collision cross-section for low relative velocities is shown to be without physical significance when the accreting bodies are in heliocentric orbits. The distribution of particle velocities relative to an accreting planet is considered; the mean velocity increases with time. The internal temperature of an accreting planet is shown to depend simply on the accretion rate. A simple and physically reasonable approximate expression for a planetary accretion rate is proposed.  相似文献   

15.
From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiter’s orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth’s embryo, when its mass was smaller than the current mass of the Earth. While the Earth’s embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios. The mass of water delivered to Venus from beyond Jupiter’s orbit was almost the same as that for the Earth, if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was two?three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiter’s orbit could be less than that for the Earth by a factor not more than 20.  相似文献   

16.
Abstract— Here I discuss the series of events that led to the formation and evolution of our planet to examine why the Earth is unique in the solar system. A multitude of factors are involved: These begin with the initial size and angular momentum of the fragment that separated from a molecular cloud; such random factors are crucial in determining whether a planetary system or a double star develops from the resulting nebula. Another requirement is that there must be an adequate concentration of heavy elements to provide the 2% “rock” and “ice” components of the original nebula. An essential step in forming rocky planets in the inner nebula is the loss of gas and depletion of volatile elements, due to early solar activity that is linked to the mass of the central star. The lifetime of the gaseous nebula controls the formation of gas giants. In our system, fine timing was needed to form the gas giant, Jupiter, before the gas in the nebula was depleted. Although Uranus and Neptune eventually formed cores large enough to capture gas, they missed out and ended as ice giants. The early formation of Jupiter is responsible for the existence of the asteroid belt (and our supply of meteorites) and the small size of Mars, whereas the gas giant now acts as a gravitational shield for the terrestrial planets. The Earth and the other inner planets accreted long after the giant planets, from volatile-depleted planetesimals that were probably already differentiated into metallic cores and silicate mantles in a gas-free, inner nebula. The accumulation of the Earth from such planetesimals was essentially a stochastic process, accounting for the differences among the four rocky inner planets—including the startling contrast between those two apparent twins, Earth and Venus. Impact history and accretion of a few more or less planetesimals were apparently crucial. The origin of the Moon by a single massive impact with a body larger than Mars accounts for the obliquity (and its stability) and spin of the Earth, in addition to explaining the angular momentum, orbital characteristics, and unique composition of the Moon. Plate tectonics (unique among the terrestrial planets) led to the development of the continental crust on the Earth, an essential platform for the evolution of Homo sapiens. Random major impacts have punctuated the geological record, accentuating the directionless course of evolution. Thus a massive asteroidal impact terminated the Cretaceous Period, resulted in the extinction of at least 70% of species living at that time, and led to the rise of mammals. This sequence of events that resulted in the formation and evolution of our planet were thus unique within our system. The individual nature of the eight planets is repeated among the 60-odd satellites—no two appear identical. This survey of our solar system raises the question whether the random sequence of events that led to the formation of the Earth are likely to be repeated in detail elsewhere. Preliminary evidence from the “new planets” is not reassuring. The discovery of other planetary systems has removed the previous belief that they would consist of a central star surrounded by an inner zone of rocky planets and an outer zone of giant planets beyond a few astronomical units (AU). Jupiter-sized bodies in close orbits around other stars probably formed in a similar manner to our giant planets at several astronomical units from their parent star and, subsequently, migrated inwards becoming stranded in close but stable orbits as “hot Jupiters”, when the nebula gas was depleted. Such events would prevent the formation of terrestrial-type planets in such systems.  相似文献   

17.
S. Inaba  G.W. Wetherill 《Icarus》2003,166(1):46-62
We have calculated formation of gas giant planets based on the standard core accretion model including effects of fragmentation and planetary envelope. The accretion process is found to proceed as follows. As a result of runaway growth of planetesimals with initial radii of ∼10 km, planetary embryos with a mass of ∼1027 g (∼ Mars mass) are found to form in ∼105 years at Jupiter's position (5.2 AU), assuming a large enough value of the surface density of solid material (25 g/cm2) in the accretion disk at that distance. Strong gravitational perturbations between the runaway planetary embryos and the remaining planetesimals cause the random velocities of the planetesimals to become large enough for collisions between small planetesimals to lead to their catastrophic disruption. This produces a large number of fragments. At the same time, the planetary embryos have envelopes, that reduce energies of fragments by gas drag and capture them. The large radius of the envelope increases the collision rate between them, resulting in rapid growth of the planetary embryos. By the combined effects of fragmentation and planetary envelope, the largest planetary embryo with 21M⊕ forms at 5.2 AU in 3.8×106 years. The planetary embryo is massive enough to start a rapid gas accretion and forms a gas giant planet.  相似文献   

18.
We have accumulated thousands of orbits of test particles in the Solar System from the asteroid belt to beyond the orbit of Neptune. We find that the time for an orbit to make a close encounter with a perturbing planet, T c ,is a function of the Lyapunov time, T ty .The relation is log (T c /T o )= a + b log (T ly T o )where T o is a fiducial period which we have taken as the period of the principal perturber or the period of the asteroid. There are exceptions to this rule interior to the 2/3 resonance with Jupiter. There, at least in the restricted problem, for sufficiently small Jupiter mass, orbits may have a positive Lyapunov exponent and still be blocked from having a close approach to Jupiter by a zero velocity curve. Of more serious concern is whether the relation holds for purely secular resonances, and if it does, how to choose T o .This is the case of interest for the planets in the solar system.  相似文献   

19.
We investigate the possibility of gravitational capture of planetesimals as temporary or permanent satellites of Uranus and Neptune during the process of planetary growth. The capture mechanism is based in the enhancement of the Hill's sphere of action not only due to the mass acquired by the planet, but also by the variation of the planet-Sun distance as a consequence of the scattering of planetesimals by the planets of the outer solar system. Our calculations indicate that satellite capture was very important, specially during the first stages of the accretion process, contributing in a significant way to the planetary growth.  相似文献   

20.
We propose an interpretation of the enrichments in volatiles observed in the four giant planets with respect to the solar abundance. It is based on the assumption that volatiles were trapped in the form of solid clathrate hydrates and incorporated in planetesimals embedded in the feeding zones of each of the four giant planets. The mass of trapped volatiles is then held constant with time. The mass of hydrogen and of not trapped gaseous species continuously decreased with time until the formation of the planet was completed, resulting in an increase in the ratio of the mass of trapped volatiles to the mass of hydrogen (Gautier et al., Astrophys. J. 550 (2001) L227). The efficiency of the clathration depends upon the amount of ice available in the early feeding zone. The quasi-uniform enrichment in Ar, Kr, Xe, C, N, and S observed in Jupiter is reproduced because all volatiles were trapped. The non-uniform enrichment observed in C, N and S in Saturn is due to the fact that CH4, NH3, and H2S were trapped but not CO and N2. The non-uniform enrichment in C, N and S in Uranus and Neptune results from the trapping of CH4, CO, NH3 and H2S, while N2 was not trapped. Our scenario permits us to interpret the strongly oversolar sulfur abundance inferred by various modelers to be present in Saturn, Uranus and Neptune for reproducing the microwave spectra of the three planets. Abundances of Ar, Kr and Xe in these three are also predicted. Only Xe is expected to be substantially oversolar. The large enrichment in oxygen in Neptune with respect to the solar abundance, calculated by Lodders and Fegley (Icarus 112 (1994) 368) from the detection of CO in the upper troposphere of the planet, is consistent with the trapping of volatiles by clathration. The upper limit of CO in Uranus does not exclude that this process also occurred in Uranus.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号