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1.
The temporary capture of the dust grains in the exterior resonances with planets is studied in the frames of the planar circular three-body problem with Poynting-Robertson (PR) drag. For the Earth and particles ~ 10 m the resonances 4/5, 5/6, 6/7, 7/8 are shown to be most effective. The capture is only temporary (of order 105 years) and the position of resonance may be calculated from semi-analytical model using averaged disturbing function. These semi-analytical results are confirmed by numerical integration. For various planet this picture changes as with increasing planetary mass the more exterior resonances become more important. We showed that for Jupiter (at least in the space between Jupiter and Saturn) the resonance 1/2 plays the dominant role. The capture time is here several myr but again eccentricity is evolving to eccentricity e 0 ~ 0.48 of libration point for this resonance.  相似文献   

2.
Orbital resonances tend to force bodies into noncircular orbits. If a body is also under the influence of an eccentricity-reducing medium, it will experience a secular change in semimajor axis which may be positive or negative depending on whether its orbit is exterior or interior to that of the perturbing body. Thus a dissipative medium can promote either a loss or a gain in orbital energy. This process may explain the resonant structure of the asteroid belt and of Saturn's rings. For reasonable early solar system parameters, it would clear a gap near the 2:1 resonance with Jupiter on a time scale of a few thousand years; the gap width would be comparable to the Kirkwood gap presently at the location in the asteroid belt. Similarly, a gap comparable in width to Cassini's division would be cleared in Saturn's rings at the 2:1 resonance with Mimas in ～106 yr. Most of the material from the gap would be deposited at the outer edge of ring B. The process would also affect the radial distribution of preplanetary material. Moreover, it provides an explanation for the large amplitude of the Titan-Hyperion libration. Consideration of the effects of dissipation on orbits near the stable L4 and L5 points of the restricted three-body problem indicates that energy loss causes particles to move away from these points. This results explains the large amplitude of Trojan asteroids about these points and the possible capture of Trojan into orbit about Jupiter.  相似文献   

3.
Tidal evolution of Mimas, Enceladus, and Dione   总被引：2，自引：0，他引：2  
Jennifer Meyer  Jack Wisdom 《Icarus》2008,193(1):213-223
The tidal evolution through several resonances involving Mimas, Enceladus, and/or Dione is studied numerically with an averaged resonance model. We find that, in the Enceladus-Dione 2:1 e-Enceladus type resonance, Enceladus evolves chaotically in the future for some values of k2/Q. Past evolution of the system is marked by temporary capture into the Enceladus-Dione 4:2 ee′-mixed resonance. We find that the free libration of the Enceladus-Dione 2:1 e-Enceladus resonance angle of 1.5° can be explained by a recent passage of the system through a secondary resonance. In simulations with passage through the secondary resonance, the system enters the current Enceladus-Dione resonance close to tidal equilibrium and thus the equilibrium value of tidal heating of 1.1(18,000/QS) GW applies. We find that the current anomalously large eccentricity of Mimas can be explained by passage through several past resonances. In all cases, escape from the resonance occurs by unstable growth of the libration angle, sometimes with the help of a secondary resonance. Explanation of the current eccentricity of Mimas by evolution through these resonances implies that the Q of Saturn is below 100,000. Though the eccentricity of Enceladus can be excited to moderate values by capture in the Mimas-Enceladus 3:2 e-Enceladus resonance, the libration amplitude damps and the system does not escape. Thus past occupancy of this resonance and consequent tidal heating of Enceladus is excluded. The construction of a coherent history places constraints on the allowed values of k2/Q for the satellites.  相似文献   

4.
We investigate the survivability of Trojan-type companions of Neptune during primordial radial migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. We adopt the usual planet migration model in which the migration speed decreases exponentially with a characteristic time scale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus ∼1000 test particle Neptune Trojans with initial distributions of orbital eccentricity, inclination, and libration amplitude similar to those of the known jovian Trojans asteroids. We analyze these simulations to measure the survivability of Neptune's Trojans as a function of migration rate. We find that orbital migration with the characteristic time scale τ=106 years allows about 35% of preexisting Neptune Trojans to survive to 5τ, by which time the giant planets have essentially reached their final orbits. In contrast, slower migration with τ=107 years yields only a ∼5% probability of Neptune Trojans surviving to a time of 5τ. Interestingly, we find that the loss of Neptune Trojans during planetary migration is not a random diffusion process. Rather, losses occur almost exclusively during discrete prolonged episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranus with Neptune. These secondary resonances arise when the circulation frequencies, f, of critical arguments for Uranus-Neptune mean-motion near-resonances (e.g., fUN1:2, fUN4:7) are commensurate with harmonics of the libration frequency of the critical argument for the Neptune-Trojan 1:1 mean-motion resonance (fNT1:1). Trojans trapped in the secondary resonances typically have their libration amplitudes amplified until they escape the 1:1 resonance with Neptune. Trojans with large libration amplitudes are susceptible to loss during sweeping by numerous high-order secondary resonances (e.g., fUN1:2≈11fNT1:1). However, for the slower migration, with τ=107 years, even tightly bound Neptune Trojans with libration amplitudes below 10° can be lost when they become trapped in 1:3 or 1:2 secondary resonances between fUN1:2 and fNT1:1. With τ=107 years the 1:2 secondary resonance was responsible for the single greatest episode of loss, ejecting nearly 75% of existing Neptune Trojans. This episode occurred during the late stages of planetary migration when the remnant planetesimal disk would have been largely dissipated. We speculate that if the number of bodies liberated during this event was sufficiently high they could have caused a spike in the impact rate throughout the Solar System.  相似文献   

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

6.
In a previous publication (Tsiganis et al. 2000, Icarus146, 240-252), we argued that the occurrence of stable chaos in the 12/7 mean motion resonance with Jupiter is related to the fact that there do not exist families of periodic orbits in the planar elliptic restricted problem and in the 3-D circular problem corresponding to this resonance. In the present paper we show that nonexistence of resonant periodic orbits, both for the planar and for the 3-D problem, also occurs in other jovian resonances—namely the 11/4, 22/9, 13/6, and 18/7—where cases of real asteroids on stable-chaotic orbits have been identified. This property may provide a “protection mechanism”, leading to semiconfinement of chaotic orbits and extremely slow migration in the space of proper elements, so that diffusion is practically unrelated to the value of the Lyapunov time, TL, of chaotic orbits. However, we show that, in more complicated dynamical models, the long-term evolution of chaotic orbits initiated in the vicinity of these resonances may also be governed by secular resonances. Finally, we find that stable-chaotic orbits have a characteristic spectrum of autocorrelation times: for the action conjugate to the critical argument the autocorrelation time is of the order of the Lyapunov time, while for the eccentricity- and inclination-related actions the autocorrelation time may be longer than 103TL. This behavior is consistent with the trajectory being sticky around a manifold of lower-than-full dimensionality in phase space (e.g., a 4-D submanifold of the 5-D energy manifold in a three-degrees-of-freedom autonomus Hamiltonian system) and reflects the inability of these “flawed” resonances to modify secular motion significantly, at least for times of the order of 200 Myr.  相似文献   

7.
A number of Jupiter family comets such as Otermaand Gehrels 3make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L 1and L 2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L 1and L 2is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L 1and the other around L 2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold tubes associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.  相似文献   

8.
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   

9.
The periodic orbit representing the motion of the inner three Galilean satellites of Jupiter is constructed in a rotating frame. Stability analysis indicates linear instability; but the repeated Poincaré exponents are associated with time and rotational symmetries, and it is concluded that the system is orbitally stable. Analysis of system frequencies reveals two resonances with the Sun. The rotation rate of the reference frame is close to 8910 the mean motion of Jupiter, and the period of the reference orbit is nearly 1710446 the period of Jupiter. The 8910 resonance is investigated via the method of averaging. The Jovian system currently circulates just outside the capture boundary with a period of about 117000 year, but with rotation rate of the reference frame varying by over an order of magnitude. Including tidal interaction, the system is evolving towards temporary capture in this resonance.  相似文献   

10.
We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15RJ for Jupiter and rCS ∼ 22RS for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (RH), which we choose to be ∼RH/5 (located at ∼150 RJ near the inner irregular satellites for Jupiter, and ∼200RS near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼106 years, Iapetus in 106-107 years, Ganymede in 103-104 years, and Titan in 104-105 years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100RJ. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH3 present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H2O as well as other issues that may help to test our model.  相似文献   

11.
two near-earth-asteroids associated with resonances with Jupiter are studied over a time span of 105 yrs. We found that asteroid (887) is temporary trapped in the 3:1 resonance; thus indicating that this resonance could be a source of short-lived NEAs. We also found that asteroid (3552) with a large eccentricity and a high inclination is wandering about the 1:1 resonant region.  相似文献   

12.
In Wisdom (2017), I presented new simulations of meteorite transport from the chaotic zones associated with major resonances in the asteroid belt: the ν6 secular resonance, the 3:1 mean motion resonance with Jupiter, and the 5:2 mean motion resonance with Jupiter. I found that the observed afternoon excess (the fact that approximately twice as many meteorites fall in the afternoon as in the morning) of the ordinary chondrites is consistent with chaotic transport from the 3:1 resonance, contradicting prior reports. Here I report an additional study of the transport of meteorites from ν6 secular resonance and the 3:1 mean motion resonance. I use an improved integration algorithm, and study the evolution of more particles. I confirm that the afternoon excess of the ordinary chondrites is consistent with transport from the 3:1 resonance.  相似文献   

13.
We have calculated evolutionary and static models of Jupiter and Saturn with homogeneous solar composition mantles and dense cores of material consisting of solar abundances of SiO2, MgO, Fe, and Ni. Evolutionary sequences for Jupiter were calculated with cores of mass 2, 4, 6, and 8% of the Jovian mass. Evolutionary sequences for Saturn were calculated with cores of mass 16, 18, 20, and 22% of total mass. Two envelope mixtures, representative of the solar abundances were used: X (mass fraction of hydrogen) = 0.74, Y (mass fraction of helium) = 0.24 and X = 0.77 and Y = 0.21. For Jupiter, the observations of the temperature at 1 bar pressure (T1bar), radius and internal luminosity were best fit by evolutionary models with a core mass of ～6.5% and chemical composition of X = 0.77, Y = 0.21. The calculated cooling time for Jupiter is approximately 4.9 × 109 years, which is consistent, within our error bars, with the known age of the solar system. For Saturn, the observations of the radius, internal luminosity and T1BAR can be best fit by evolutionary models with a core mass of ～21% and chemical composition of X = 0.77, Y = 0.21. The cooling time calculated for Saturn is approximately 2.6 × 109 years, almost a factor 2 less than the present age of the solar system. Static models of Jupiter and Saturn were calculated for the above chemical compositions in order to investigate the sensitivity of the calculated gravitational moments, J2 and J4, to the mass of the dense core, T1BAR and hydrogen/helium ratio. We find for Jupiter that a model having a core mass of approximately 7% gives values of J2, J4, and T1BAR that are within observational limits, for the mixture X = 0.77, Y = 0.21. The static Jupiter models are completely consistent with the evolutionary results. For Saturn, the quantities J2, J4, and J6 determined from the static models with the most probable T1BAR of 140°K, using modeling procedures which result in consistent models for Jupiter, are considerably below the observed values.  相似文献   

14.
We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus test particle Trojans and quasi-satellites. We find that the libration frequencies of Trojans are similar to those of quasi-satellites. This similarity enables a dynamical exchange of objects back and forth between the Trojan and quasi-satellite resonances during planetary migration. This exchange is facilitated by secondary resonances that arise whenever there is more than one migrating planet. For example, secondary resonances may occur when the circulation frequencies, f, of critical arguments for the Uranus-Neptune 2:1 mean-motion near-resonance are commensurate with harmonics of the libration frequency of the critical argument for the Trojan and quasi-satellite 1:1 mean-motion resonance . Furthermore, under the influence of these secondary resonances quasi-satellites can have their libration amplitudes enlarged until they undergo a close-encounter with their host planet and escape from the resonance. High-resolution simulations of this escape process reveal that ≈80% of jovian quasi-satellites experience one or more close-encounters within Jupiter’s Hill radius (RH) as they are forced out of the quasi-satellite resonance. As many as ≈20% come within RH/4 and ≈2.5% come within RH/10. Close-encounters of escaping quasi-satellites occur near or even below the 2-body escape velocity from the host planet. Finally, the exchange and escape of Trojans and quasi-satellites continues to as late as 6-9τ in some simulations. By this time the dynamical evolution of the planets is strongly dominated by distant gravitational perturbations between the planets rather than the migration force. This suggests that exchange and escape of Trojans and quasi-satellites may be a contemporary process associated with the present-day near-resonant configuration of some of the giant planets in our Solar System.  相似文献   

15.
We investigate the dynamical evolution of trans-neptunian objects (TNOs) in typical scattered disk orbits (scattered TNOs) by performing simulations using several thousand particles lying initially on Neptune-encountering orbits. We explore the role of resonance sticking in the scattered disk, a phenomenon characterized by multiple temporary resonance captures (‘resonances’ refers to external mean motion resonances with Neptune, which can be described in the form r:s, where the arguments r and s are integers). First, all scattered TNOs evolve through intermittent temporary resonance capture events and gravitational scattering by Neptune. Each scattered TNO experiences tens to hundreds of resonance captures over a period of 4 Gyr, which represents about 38% of the object's lifetime (mean value). Second, resonance sticking plays an important role at semimajor axes , where the great majority of such captures occurred. It is noteworthy that the stickiest (i.e., dominant) resonances in the scattered disk are located within this distance range and are those possessing the lowest argument s. This was evinced by r:1, r:2 and r:3 resonances, which played the greatest role during resonance sticking evolution, often leading to captures in several of their neighboring resonances. Finally, the timescales and likelihood of temporary resonance captures are roughly proportional to resonance strength. The dominance of low s resonances is also related to the latter. In sum, resonance sticking has an important impact on the evolution of scattered TNOs, contributing significantly to the longevity of these objects.  相似文献   

16.
Stanley F. Dermott 《Icarus》1979,37(1):310-321
If the orbital resonances in the Jovian and Saturnian satellite systems are the result of orbital evolution due to tidal dissipation then the present rates of energy dissipation (Edot) are >2 × 1020 ergs sec?1 (Jupiter) and ?2 × 1016 ergs sec?1 (Saturn). These values of Edot can be accounted for if the planets have rocky cores with volumes equal to those suggested by current models of the interiors and if the material of these cores is both solid and imperfectly elastic (Qe ～ 34). The calculated values of Qe are not strongly dependent on either the rigidity of the core or the densities of the core and the mantle. Thus, these quantities need not be known precisely. It may be significant that approximately the same value of Qe is needed for all the major planets (Jupiter, Saturn, and Uranus) even though the values of Edot for these planets differ by a factor greater than 104.  相似文献   

17.
Motions of asteroids in mean motion resonances with Jupiter are studied in three-dimensional space. Orbital changes of fictitious asteroids in the Kirkwood gaps are calculated by numerical integrations for 105 – 106 years. The main results are as follows: (1) There are various motions of resonant asteroids, and some of them are very complicated and chaotic and others are regular. (2) The eccentricity of some asteroids becomes very large, and the variation of the inclination is large while the eccentricity is large. (3) In the 3:1 resonance, there is a long periodic change in the variation of the inclination, when (7 : ) is a simple ratio (7: longitude of perihelion, : longitude of node). (4) In the 7:3 resonance, the variation of the inclination of some resonant asteroids is so large that prograde motion becomes retrograde. Some asteroids in the 7:3 resonance can collide with the Sun as well as with the inner planets.  相似文献   

18.
Hilda asteroids and comets are similar from the compositional point of view. The D-taxonomic class prevailing among Hildas has all the characteristics found in cometary spectra. Jupiter Family Comets (JFCs) coming from the trans-neptunian region are under the gravitational control of Jupiter, making them a dynamically unstable population with a mean dynamical lifetime of 104 to 105 years. In contrast, Hilda asteroids residing in the 3:2 mean motion resonance with Jupiter are a very stable population. But once they escape from the resonance, they are dynamically controlled by Jupiter, and in this sense their behavior resembles that of JFC. We performed a numerical simulation to analyze the dynamical evolution that Hildas follow after escaping from the resonance, and their contribution to the JFC population. We found that 8% of the particles leaving the resonance end up impacting Jupiter. 98.7% of the escaped Hildas live at least 1000 years as a JFC, with a mean lifetime of 1.4×106 years. In particular, escaped Hildas stay mainly in the region of perihelion distances greater than 2.5 AU. On the other hand, the number of escaped Hildas reaching the inner Solar System (q<2.5 AU) is negligible. So, there are almost no Hilda asteroids among the NEO population. We also analyzed the possibility that the Shoemaker-Levy 9 were an escaped Hilda asteroid. In this case, it would be possible to give stronger constraints to its pre-capture orbital elements.  相似文献   

19.
Infrared spectral observations of Mars, Jupiter, and Saturn were made from 100 to 470 cm?1 using NASA's G. P. Kuiper Airborne Observatory. Taking Mars as a calibration source, we determined brightness temperatures of Jupiter and Saturn with approximately 5 cm?1 resolution. The data are used to determine the internal luminosities of the giant planets, for which more than 75% of the thermally emitted power is estimated to be in the measured bandpass: for Jupiter LJ = (8.0 ± 2.0) × 10?10L⊙ and for Saturn LS = (3.6 ± 0.9) × 10?10. The ratio R of thermally emitted power to solar power absorbed was estimated to be RJ = 1.6 ± 0.2, and RS = 2.7 ± 0.8 from the observations when both planets were near perihelion. The Jupiter spectrum clearly shows the presence of the rotational ammonia transitions which strongly influence the opacity at frequencies ?250 cm?1. Comparison of the data with spectra predicted from current models of Jupiter and Saturn permits inferences regarding the structure of the planetary atmospheres below the temperature inversion. In particular, an opacity source in addition to gaseous hydrogen and ammonia, such as ammonia ice crystals as suggested by Orton, may be necessary to explain the observed Jupiter spectrum in the vicinity of 250 cm?1.  相似文献   

20.
The stability of an imaginary planet located in the present main asteroid belt is studied with a 7-body model (Sun, Mars, Jupiter, Saturn, Uranus, Neptune and the imaginary planet). The fourth-order Hermite algorithm P(EC)3 is used, which has a very small secular energy error for the integration of periodic orbits with a constant time-step. The evolution of orbits is followed up to 108 years. Our numerical results show that the low-order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper limit of the imaginary planet's mass that can survive in the main belt is around 1025 kg, i.e., about the Earth's mass.  相似文献   

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