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1.
The planets with a radius < 4 R⊕ observed by the Kepler mission exhibit a unique feature, and propose a challenge for current planetary formation models. The tidal effect between a planet and its host star plays an essential role in reconfiguring the final orbits of the short-period planets. In this work, based on various initial Rayleigh distributions of the orbital elements, the final semi-major axis distributions of the planets with a radius < 4 R⊕ after suffering tidal evolutions are investigated. Our simulations have qualitatively revealed some statistical properties: the semi-major axis and its peak value all increase with the increase of the initial semi-major axis and eccentricity. For the case that the initial mean semi-major axis is less than 0.1 au and the mean eccentricity is larger than 0.25, the results of numerical simulation are approximately consistent with the observation. In addition, the effects of other parameters, such as the tidal dissipation coefficient, stellar mass and planetary mass, etc., on the final semi-major axis distribution after tidal evolution are all relatively small. Based on the simulation results, we have tried to find some clues for the formation mechanism of low-mass planets. We speculate that these low-mass planets probably form in the far place of protoplanetary disk with a moderate eccentricity via the type I migration, and it is also possible to form in situ.  相似文献   

2.
We investigate a new dynamical mechanism for producing Halley-type comets from the scattered disk of comets. Levison and Duncan [Levison, H., Duncan, M., 1997. Icarus 127, 13-32] and Duncan and Levison [Duncan, M., Levison, H., 1997. Science 276, 1670-1672] showed that a significant number of objects leave the scattered disk by evolving to semi-major axes greater than 1000 AU. We find that once these objects reach semi-major axes on the order of 104 AU, a significant fraction immediately have their perihelia driven inward by the galactic tides. Approximately 0.01% of the objects that reach 104 AU then evolve onto orbits similar to the observed Halley-like comets due to gravitational interactions with the giant planets. The orbital element distribution resulting from this process is statistically consistent with observations. We discuss the implications of this model for the number of objects in the scattered disk in the text. The model predicts a temporal variation in the influx of HTCs with a period of ∼118 Myr. At the peak, the model predicts that there should be roughly 10 times as many HTCs as currently observed (i.e., there should be weak HTC showers). However, the model may inflate the importance of these showers because it does not include the effects of passing stars and giant molecular clouds.  相似文献   

3.
We explore the origin and orbital evolution of the Kuiper belt in the framework of a recent model of the dynamical evolution of the giant planets, sometimes known as the Nice model. This model is characterized by a short, but violent, instability phase, during which the planets were on large eccentricity orbits. It successfully explains, for the first time, the current orbital architecture of the giant planets [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461], the existence of the Trojans populations of Jupiter and Neptune [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465], and the origin of the late heavy bombardment of the terrestrial planets [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469]. One characteristic of this model is that the proto-planetary disk must have been truncated at roughly 30 to 35 AU so that Neptune would stop migrating at its currently observed location. As a result, the Kuiper belt would have initially been empty. In this paper we present a new dynamical mechanism which can deliver objects from the region interior to ∼35 AU to the Kuiper belt without excessive inclination excitation. In particular, we show that during the phase when Neptune's eccentricity is large, the region interior to its 1:2 mean motion resonance becomes unstable and disk particles can diffuse into this area. In addition, we perform numerical simulations where the planets are forced to evolve using fictitious analytic forces, in a way consistent with the direct N-body simulations of the Nice model. Assuming that the last encounter with Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of ∼27 AU and an eccentricity of ∼0.3, and that subsequently Neptune's eccentricity damped in ∼1 My, our simulations reproduce the main observed properties of the Kuiper belt at an unprecedented level. In particular, our results explain, at least qualitatively: (1) the co-existence of resonant and non-resonant populations, (2) the eccentricity-inclination distribution of the Plutinos, (3) the peculiar semi-major axis—eccentricity distribution in the classical belt, (4) the outer edge at the 1:2 mean motion resonance with Neptune, (5) the bi-modal inclination distribution of the classical population, (6) the correlations between inclination and physical properties in the classical Kuiper belt, and (7) the existence of the so-called extended scattered disk. Nevertheless, we observe in the simulations a deficit of nearly-circular objects in the classical Kuiper belt.  相似文献   

4.
David Morrison 《Icarus》1977,31(2):185-220
The radiometric method of determining diameters of asteroids is reviewed, and a synthesis of radiometric and polarimetric measurements of the diameters and geometric albedos of a total of 187 asteroids is presented. All asteroids with diameters greater than 250 km are identified, and statistical studies can be carried out of the size distributions of different albedo classes down to 80-km diameter for the entire main asteroid belt (2.0–3.5 AU). The distribution of albedos is strongly bimodal, with mean albedos for the C and S groups of 0.035 and 0.15, respectively. The C asteroids outnumber the S at all sizes and all values of semi-major axis, increasing from a little over half the population inside 2.5 AU to more than 95% beyond 3.0 AU; for all objects with D > 70 km, the ratio C/(C+S) is 0.88 ± 0.04. More than half of all asteroids in this size range have a > 3.0 AU. The M asteroids constitute about 5% of the population for a < 3.0 AU, but no members of of this class have been identified in the outer belt. There are no significant differences between the distributions of C, S, and M asteroids for the largest asteroids (D > 200 km) and for those of intermediate size (200–270 km). The total mass in the belt, down to 70-km size, but excluding Ceres, is about 2 × 1024 g. Evidence is presented that several large asteroids rotate in a prograde sense, and that a real difference existsbetween the bulk densities of Ceres and Vesta.  相似文献   

5.
We simulate the formation of the Oort cloud (OC) till the age of 2 Gyr starting from an initial disc of planetesimals made by 10 038 test particles. The results on the outer part of the distant comet reservoir are reported by Neslu?an et al. (this issue). Here we deal with the evolution of the population and structure at 2 Gyr of the complementary inner part of the Oort cloud. The dynamical evolution of the massless test particles was followed via the numerical integration of their orbits. We considered the perturbations produced by four giant planets assuming they have their current orbits and masses, as well as the perturbations caused by the Galactic tide and passing stars. The efficiency of the formation of inner OC is found to be very low: only about 1.1% of all considered particles ended in this part of the OC. At 2 Gyr, the dynamics of the inner cloud is mainly governed by the dominant z-term of the Galactic tide. The number density of the bodies is proportional to the heliocentric distance, r, as r ?3.53. The directional distribution of orbits is still strongly inhomogeneous. There are large empty regions in the space angles around the Galactic Equator points with the galactic longitude 90 and 270° (non-rotating frame), or there are only few bodies having the ecliptical latitude higher than +60° or lower than 60°. A strong concentration of objects at the Ecliptic is apparent up to ≈1,000 AU, with a possible—but still not proved—extension to ≈1,500 AU. Beyond r ≈ 6,000 AU, bodies directly above and below the Sun, with respect to the Ecliptic, are absent.  相似文献   

6.
We have attempted to reconstruct the orbit of the Farmington L5 chondrite which fell in Kansas in 1890. Because its radiation age is uniquely short (25 000 years), its orbit should still closely resemble that of its parent body. A search of 280 contemporary newspapers and other sources turned up more than 60 useable eyewitness reports from 32 localities, which led to the following estimate of the apparent radiant: height 60°, azimuth 20°, with an uncertainty of about 10°. Orbital elements were determined for this radiant for four plausible preatmospheric velocities: 13, 16, 19, and 22 km/sec. The results show quite definitely that Farmington had a small orbit of low inclination: semimajor axis 1–1.9 AU, perihelion ? 0.4 AU, aphelion ? 3.0 AU, inclination ? 16°. Because of the short radiation age, the parent body of Farmington must already have been in an Earth-crossing orbit when the meteorite was ejected from it by an impact. Of the 11 known Earth-crossing asteroids with encounter velocities below 22 km/sec, 1862 Apollo, Hermes, and 1865 Cerberus are passable matches, while 1620 Geographos and 1685 Toro are more marginal possibilities. Apparently Earth-crossing asteroids are the immediate parent bodies of at least some meteorites. Their ultimate source must be the ultimate source of most stony meteorites.  相似文献   

7.
We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20°). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to various situations in the HD 11964, HD 80606, and HD 98800 systems.  相似文献   

8.
We present Monte Carlo simulations of the dynamical evolution of the Oort cloud over the age of the Solar System, using an initial sample of one million test comets without any cloning. Our model includes perturbations due to the Galactic tide (radial and vertical) and passing stars. We present the first detailed analysis of the injection mechanism into observable orbits by comparing the complete model with separate models for tidal and stellar perturbations alone. We find that a fundamental role for injecting comets from the region outside the loss cone (perihelion distance q > 15 AU) into observable orbits (q < 5 AU) is played by stellar perturbations. These act in synergy with the tide such that the total injection rate is significantly larger than the sum of the two separate rates. This synergy is as important during comet showers as during quiescent periods and concerns comets with both small and large semi-major axes. We propose different dynamical mechanisms to explain the synergies in the inner and outer parts of the Oort Cloud. We find that the filling of the observable part of the loss cone under normal conditions in the present-day Solar System rises from <1% for a < 20 000 AU to about 100% for a ? 100 000 AU.  相似文献   

9.
We analyze the polarization effects of the radiation scattered in conical optically thin plasma envelopes. The density of free electrons in the envelope is assumed to decrease in inverse proportion to the square of the distance from the radiation source. The magnetic field, radial or azimuthal, is also assumed to vary in inverse proportion to the square of the distance from the center of the system. We take into account the fact that the scattered radiation near the surface of a star or a quasar is virtually unpolarized (the model of a nonpoint star). The spectra of linear polarization and its position angle are given for conical-envelope opening half-angles of 7.5°, 15°, and 30°. The inclination of the cone axis with respect to the observer’s direction took on values of 30°, 45°, 60°, 90°, 120°, 135°, and 150°. We allowed for the fact that part of the envelope is screened from the observer by the star itself. We also give polarization spectra for the radiation scattered in two mutually opposite conical envelopes. We use the results of our theoretical calculations to analyze the polarimetric observations of relativistic jets in cosmic gamma-ray bursts and active galactic nuclei. As a result, we estimated the magnetic fields in these objects. The constraint on the density of relativistic electrons is <107 cm?3.  相似文献   

10.
We study the transfer process from the scattered disk (SD) to the high-perihelion scattered disk (HPSD) (defined as the population with perihelion distances q > 40 AU and semimajor axes a>50 AU) by means of two different models. One model (Model 1) assumes that SD objects (SDOs) were formed closer to the Sun and driven outwards by resonant coupling with the accreting Neptune during the stage of outward migration (Gomes 2003b, Earth, Moon, Planets 92, 29–42.). The other model (Model 2) considers the observed population of SDOs plus clones that try to compensate for observational discovery bias (Fernández et al. 2004, Icarus , in press). We find that the Kozai mechanism (coupling between the argument of perihelion, eccentricity, and inclination), associated with a mean motion resonance (MMR), is the main responsible for raising both the perihelion distance and the inclination of SDOs. The highest perihelion distance for a body of our samples was found to be q = 69.2 AU. This shows that bodies can be temporarily detached from the planetary region by dynamical interactions with the planets. This phenomenon is temporary since the same coupling of Kozai with a MMR will at some point bring the bodies back to states of lower-q values. However, the dynamical time scale in high-q states may be very long, up to several Gyr. For Model 1, about 10% of the bodies driven away by Neptune get trapped into the HPSD when the resonant coupling Kozai-MMR is disrupted by Neptune’s migration. Therefore, Model 1 also supplies a fossil HPSD, whose bodies remain in non-resonant orbits and thus stable for the age of the solar system, in addition to the HPSD formed by temporary captures of SDOs after the giant planets reached their current orbits. We find that about 12 – 15% of the surviving bodies of our samples are incorporated into the HPSD after about 4 – 5 Gyr, and that a large fraction of the captures occur for up to the 1:8 MMR (a ⋍ 120 AU), although we record captures up to the 1:24 MMR (a ≃ 260 AU). Because of the Kozai mechanism, HPSD objects have on average inclinations about 25°–50°, which are higher than those of the classical Edgeworth–Kuiper (EK) belt or the SD. Our results suggest that Sedna belongs to a dynamically distinct population from the HPSD, possibly being a member of the inner core of the Oort cloud. As regards to 2000 CR105 , it is marginally within the region occupied by HPSD objects in the parametric planes (q,a) and (a,i), so it is not ruled out that it might be a member of the HPSD, though it might as well belong to the inner core.  相似文献   

11.
We report on the coronal hole (CH) influence on the 54 magnetic cloud (MC) and non-MC associated coronal mass ejections (CMEs) selected for studies during the Coordinated Data Analysis Workshops (CDAWs) focusing on the question if all CMEs are flux ropes. All selected CMEs originated from source regions located between longitudes 15E?–?15W. Xie, Gopalswamy, and St. Cyr (2013, Solar Phys., doi: 10.1007/s11207-012-0209-0 ) found that these MC and non-MC associated CMEs are on average deflected towards and away from the Sun–Earth line, respectively. We used a CH influence parameter (CHIP) that depends on the CH area, average magnetic field strength, and distance from the CME source region to describe the influence of all on-disk CHs on the erupting CME. We found that for CHIP values larger than 2.6 G the MC and non-MC events separate into two distinct groups where MCs (non-MCs) are deflected towards (away) from the disk center. Division into two groups was also observed when the distance to the nearest CH was less than 3.2×105 km. At CHIP values less than 2.6 G or at distances of the nearest CH larger than 3.2×105 km the deflection distributions of the MC and non-MCs started to overlap, indicating diminishing CH influence. These results give support to the idea that all CMEs are flux ropes, but those observed to be non-MCs at 1 AU could be deflected away from the Sun–Earth line by nearby CHs, making their flux rope structure unobservable at 1 AU.  相似文献   

12.
Trojan asteroids undergo very large perturbations because of their resonance with Jupiter. Fortunately the secular evolution of quasi circular orbits remains simple—if we neglect the small short period perturbations. That study is done in the approximation of the three dimensional circular restricted three-body problem, with a small mass ratio μ—that is about 0.001 in the Sun Jupiter case. The Trojan asteroids can be defined as celestial bodies that have a “mean longitude”, M + ω + Ω, always different from that of Jupiter. In the vicinity of any circular Trojan orbit exists a set of “quasi-circular orbits” with the following properties: (A) Orbits of that set remain in that set with an eccentricity that remains of the order of the mass ratio μ. (B) The relative variations of the semi-major axis and the inclination remain of the order of ${\sqrt{\mu}}$ . (C) There exist corresponding “quasi integrals” the main terms of which have long-term relative variations of the order of μ only. For instance the product c(1 – cos i) where c is the modulus of the angular momentum and i the inclination. (D) The large perturbations affect essentially the difference “mean longitude of the Trojan asteroid minus mean longitude of Jupiter”. That difference can have very large perturbations that are characteristics of the “horseshoes orbit”. For small inclinations it is well known that this difference has two stable points near ±60° (Lagange equilibrium points L4 and L5) and an unstable point at 180° (L3). The stable longitude differences are function of the inclination and reach 180° for an inclination of 145°41′. Beyond that inclination only one equilibrium remains: a stable difference at 180°.  相似文献   

13.
We present a surface photometry of M 82 of medium spatial resolution. Special attention was paid to good systematic photometric accuracy. The results are discussed in terms of the distribution of intensity, colour, reddening free parameteer Q and colour excess b -V. The bright elongated body of the galaxy consists of a moderately old stellar population (1 – 3 · 109a) and is only slightly reddned with the exception of the central absorption lane and the southern central region. The chaotic fan-like disturbance south of the center shows the colours of a very young (106 – 107a) highly reddened group of stars; according to polarimetric data from the literature we see their light scattered by dust. The population index Q of the inner halo is bluer than that of the disc everywhere (with the possible exception of the extreme western part). Two sources must be responsible for the illumination of the halo; one of them is responsible for the light from the great disturbances near the minor axis. Both may be located near center but must be partly shadowed. A major contribution of the disc to the illumination is less probable because the population index is different in most places of the halo from that of the disc. In addition to the dusty halo, obscuring dust is probably located to the south of the galaxy. This can be interpreted as part of a thick disc of dust embedding the stellar disc or as beeing connected to a proposed strip of B stars at the southern boundary of the visible disc. Both these interpretations lead to opposite results concerning the direction of the inclination of the disc. The inclination itself is estimated to lie between 80° and 90°.  相似文献   

14.
We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g 5 are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (a S  ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4.  相似文献   

15.
W.-H. Ip 《Icarus》1977,32(3):378-381
Collision of asteroids with the main-belt asteroid population is considered with the effect of the impact kinetic energy taken into account. It is found that objects in eccentric orbits have a larger probability of destructive collision as compared to objects in orbits with mean values of eccentricity (e = 0.15) and inclination (i = 10°); also orbits with small semimajor axes (a ≈ 2.3 AU) are found to have peak values of the probability of destructive collision.  相似文献   

16.
Cosmos 378 rocket, 1970-97B, entered orbit on 17 November 1970, with orbital inclination 74.0°, period 105 min and perigee height 230 km, and decayed on 30 September 1972 after 683 days in orbit. The RAE computer program PROP was used, with more than 1900 observations from 64 stations, to determine the orbit at 39 epochs between February 1971 and September 1972.The main aim of the analysis was to determine the atmospheric rotation rate from the decrease in orbital inclination, which was determined with a mean standard deviation of 0.0010° and a best standard deviation of 0.0003°. After removal of relevant perturbations, analysis of the variation in inclination between July 1971 and April 1972 yields the surprisingly low average atmospheric rotation rate of 0.75 ± 0.05 rev/day, at a mean height of 250 km. The local time at perigee is however strongly biassed towards daytime values (07–16 hr), so the results lend support to the picture of east-to-west winds by day and west-to-east winds by night.Values of scale height are obtained by analysis of the change in perigee height.  相似文献   

17.
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18.
We consider constraints on the planetesimal population residing in the discs of AU Microscopii (AU Mic), β Pictoris (β Pic) and Fomalhaut taking into account their observed thicknesses and normal disc opacities. We estimate that bodies of radius 5, 180 and 70 km are responsible for initiating the collisional cascade accounting for the dust production for AU Mic, β Pic and Fomalhaut's discs, respectively, at break radii from the star where their surface brightness profiles change slope. Larger bodies, of radius 1000 km and with surface density of the order of 0.01 g cm−2, are required to explain the thickness of these discs assuming that they are heated by gravitational stirring. A comparison between the densities of the two sizes suggests the size distribution in the largest bodies is flatter than that observed in the Kuiper belt. AU Mic's disc requires the shallowest size distribution for bodies with radius greater than 10 km suggesting that the disc contains planetary embryos experiencing a stage of runaway growth.  相似文献   

19.
It has previously been suggested that the solar wind might terminate at distances of 5 AU to 20 AU from the Sun, and that the solar wind might be drastically slowed down by charge exchange and photoionization of interstellar hydrogen atoms which approach the Sun. However, recent satellite measurements of resonantly scattered Lyman alpha radiation, together with pulsar dispersion and Faraday rotation measures, imply very small values for the interstellar hydrogen density (0.05 cm−3) and magnetic field strength (3 μG). As a result, the solar wind is not expected to be slowed down by more than about 30% inside the termination distance, which is expected to be about 100 AU.  相似文献   

20.
Classical trans-Neptunian objects (TNOs) are believed to represent the most dynamically pristine population in the trans-Neptunian belt (TNB) offering unprecedented clues about the formation of our Solar System. The long term dynamical evolution of classical TNOs was investigated using extensive simulations. We followed the evolution of more than 17000 particles with a wide range of initial conditions taking into account the perturbations from the four giant planets for 4 Gyr. The evolution of objects in the classical region is dependent on both their inclination and semimajor axes, with the inner (a<45 AU) and outer regions (a>45 AU) evolving differently. The reason is the influence of overlapping secular resonances with Uranus and Neptune (40–42 AU) and the 5:3 (a∼ ∼42.3 AU), 7:4 (a∼ ∼43.7 AU), 9:5 (a∼ ∼44.5 AU) and 11:6 (a∼ ∼ 45.0 AU) mean motion resonances strongly sculpting the inner region, while in the outer region only the 2:1 mean motion resonance (a∼ ∼47.7 AU) causes important perturbations. In particular, we found: (a) A substantial erosion of low-i bodies (i<10°) in the inner region caused by the secular resonances, except those objects that remained protected inside mean motion resonances which survived for billion of years; (b) An optimal stable region located at 45 AU<a<47 AU, q>40 AU and i>5° free of major perturbations; (c) Better defined boundaries for the classical region: 42–47.5 AU (q>38 AU) for cold classical TNOs and 40–47.5 AU (q>35 AU) for hot ones, with i=4.5° as the best threshold to distinguish between both populations; (d) The high inclination TNOs seen in the 40–42 AU region reflect their initial conditions. Therefore they should be classified as hot classical TNOs. Lastly, we report a good match between our results and observations, indicating that the former can provide explanations and predictions for the orbital structure in the classical region.  相似文献   

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