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1.
We calculate the Love numbers kn for n = 2 to 10, and determine the “gravitational noise” from tides. The new values k2 for Jupiter, Saturn, and Uranus yield new estimates for the planetary dissipation functions: , . 相似文献
2.
A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ～3 × 107 years in Jupiter's zone and ～2 × 108 years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ～1028 g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ～10 m⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m1 ≈ 50 m⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding (m = m2 ≈ 130 m⊕), the width of the exhausted zone being of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 105?106 years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m1 > m2 ≈ 30 m⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m⊕, when the luminosity of the planet reaches 3 × 10?3 L⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000?2400° K (at m ≈ 20?25 m⊕) and a luminosity up to 10?4 L⊙. 相似文献
3.
Joseph A. Burns 《Icarus》1981,45(1):1-3
The Galilean satellites Io, Europa, and Ganymede interact through several stable orbital resonances where and λ1 ? 3λ2 + 2λ3 = 180°, with λi being the mean longitude of the ith satellite and the longitude of the pericenter. The last relation involving all three bodies is known as the Laplace relation. A theory of origin and subsequent evolution of these resonances outlined earlier (C. F. Yoder, 1979b, Nature279, 747–770) is described in detail. From an initially quasi-random distribution of the orbits the resonances are assembled through differential tidal expansion of the orbits. Io is driven out most rapidly and the first two resonance variables above are captured into libration about 0 and 180° respectively with unit probability. The orbits of Io and Europa expand together maintaining the 2:1 orbital commensurability and Europa's mean angular velocity approaches a value which is twice that of Ganymede. The third resonance variable and simultaneously the Laplace angle are captured into libration with probability ～0.9. The tidal dissipation in Io is vital for the rapid damping of the libration amplitudes and for the establishment of a quasi-stationary orbital configuration. Here the eccentricity of Io's orbit is determined by a balance between the effects of tidal dissipation in Io and that in Jupiter, and its measured value leads to the relation with the k's being Love numbers, the Q's dissipation factors, and f a factor to account for a molten core in Io. This relation and an upper bound on Q1 deduced from Io's observed thermal activity establishes the bounds 6 × 104 < QJ < 2 × 106, where the lower bound follows from the limited expansion of the satellite orbits. The damping time for the Laplace libration and therefore a minimum lifetime of the resonance is 1600 QJ years. Passage of the system through nearby three-body resonances excites free eccentricities. The remnant free eccentricity of Europa leads to the relation for rigidity μ2 = 5 × 1011 dynes/cm2. Probable capture into any of several stable 3:1 two-body resonances implies that the ratio of the orbital mean motions of any adjacent pair of satellites was never this large.A generalized Hamiltonian theory of the resonances in which third-order terms in eccentricity are retained is developed to evaluate the hypothesis that the resonances were of primordial origin. The Laplace relation is unstable for values of Io's eccentricity e1 > 0.012 showing that the theory which retains only the linear terms in e1 is not valid for values of e1 larger than about twice the current value. Processes by which the resonances can be established at the time of satellite formation are undefined, but even if primordial formation is conjectured, the bounds established above for QJ cannot be relaxed. Electromagnetic torques on Io are also not sufficient to relax the bounds on QJ. Some ideas on processes for the dissipation of ideal energy in Jupiter yield values of QJ within the dynamical bounds, but no theory has produced a QJ small enough to be compatible with the measurements of heat flow from Io given the above relation between Q1 and QJ. Tentative observational bounds on the secular acceleration of Io's mean motion are also shown not to be consistent with such low values of QJ. Io's heat flow may therefore be episodic. QJ may actually be determined from improved analysis of 300 years of eclipse data. 相似文献
4.
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
5.
Previous studies based on radio scintillation measurements of the atmosphere of Venus have identified two regions of small-scale temperature fluctuations located in the vicinity of 45 and 60 km. A global study of the fluctuations near 60 km, which are consistent with wind-shear-generated turbulence, was conducted using the Pioneer Venus measurements. The structure constants of refractive index fluctuations cn2 and temperature fluctuations cT2 increase poleward, peak near 70° latitude, and decrease over the pole; cn2 varies from 2 × 10?15 to 1.5 × 10?14m and cT2 from 4 × 10?3 to 7 × 10?2°K2m. These results indicate greater turbulent activity at the higher latitudes. In the region near 45 km the refractive index fluctuations and the corresponding temperature fluctuations are substantially lower. Based on the analysis of one representative occultation measurement, in the 45-km region. The fluctuations in this region also appear to be consistent with wind-shear-generated turbulence. The turbulence level is considerably weaker than that at 60 km; the energy dissipation rate ε is 4.9 × 10?5m2sec?3 and the small-scale eddy diffusion coefficient K is 2 × 103 cm2 sec?1. 相似文献
6.
7.
The motion of fragments following a catastrophic destruction by either a normal or an oblique impact at 2.5–2.9 km sec?1 into cubic and spherical basalt targets was studied with a high-speed framing camera. Velocities at the antipodes of the targets vary as (E/M)0.75 (E = impact energy; M = target mass) and are lower than 200 m sec?1 at E/M ? 109 ergs g?1. Excluding fine-grained particles from the impact site, 70 to 80% by mass fraction of the fragments have velocities lower than twice the antipodal velocity. Comminution and ejection energies wasted in this mass fraction were a few percent of the impact energy at E/M ? 5 × 107 ergs g?1. During a catastrophic impact into asteroids some of the fragmented bodies can be reconcentrated by mutual gravitation. 相似文献
8.
Allen S. Grossman James B. Pollack Ray T. Reynolds Audrey L. Summers Harold C. Graboske 《Icarus》1980,42(3):358-379
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
9.
Robert L. Younkin 《Icarus》1974,21(3):219-229
The irradiance of Titan has been measured from 0.50 to 1.08μ in 30 Å band-passes spaced 0.01–0.02μ apart. Geometric albedos have been computed at the wavelenghts of measurement using a standard solar flux distribution after Labs and Neckel. The maximum value of pλ(0) is 0.37 at 0.68, 0.75, and 0.834μ, the minimum value, in the centers of the strongest methane absorption bands, is 0.10 at 0.887 and 1.012μ.The brightness of Titan at the time of the present measurements has been compared with that of previous modern photoelectric measurements. Within the apparent consistency of the different photoelectric systems, the brightness of Titan appears to undergo changes with time.A provisional curve of the geometric albedo from 0.30 to 4.0μ has been made by combining the present results with those of other authors, i.e., relative measurements of Titan from 0.30 to 0.50μ, and measurements of Jupiter and Saturn from 1.08 to 4.00μ. The latter are used to estimate the strengths of the methane absorption bands of Titan in that spectral range. The bolometric geometric albedo, , is computed to be 0.21. A variety of current measurements of Titan indicate a substantial atmosphere, suggesting a value of the phase integral . The bolometric Bond albedo, , is then 0.27 ± 0.04, giving an effective radiative temperature Te= 84 ± 2°K.The absorption band contours of Titan have been compared with those of Jupiter and Saturn at the same resolution. The bands of the planets are known to be due primarily to methane, and they show a very regular relationship, with those of Saturn being consistently deeper and wider. For Titan, the strengths of the bands are equal or less than those of Jupiter in the band centers, while the wings are stronger than those of Saturn.Previous photoelectric and photographic spectra have been examined for evidence of temporal variation of the methane path length in the atmosphere of Titan. Differences in measurement techniques prohibit detection of small differences. The only potential differences beyond experimental uncertainties are those of Kuiper (1944) and Harris (mid-fifties). Taking Kuiper's results at face value, Titan appears to have a shorter methane path length in 1972. Harris's results can be reconciled only by the doubtful hypothesis of an almost complete absence of methane at that time. 相似文献
10.
The UCSD X-ray telescope on OSO-3 scanned Jupiter for 33 days during February and March 1968. We have searched the data for a steady Jovian flux, and for a burst component at times of decametric radio bursts. Neither component was detected at a sensitivity of ～0.1 photon (cm2sec)?1 for hv > 7.7 keV. At 4.4AU, the 3σ upper limits correspond to X-ray luminosities of 7.4 × 1019 ergs sec?1 for the steady component, and 2 × 1020 ergs sec?1 for the burst component. The observations occurred during a period of high solar activity, during which three sudden-commencement magnetic storms were observed at Earth. We compare the upper limits with several different calculations of the expected flux levels, and conclude that major improvements in X-ray detection techniques will be required before Jovian X rays can be detected with near-Earth observations. 相似文献
11.
Observations of Uranus during the 1975, 1976, and 1978 apparitions reveal a weak absorption at the wavelength of the R5(1) line of HD with equivalent width . The ratio in Uranus' atmosphere implied by this line and other published spectra is (4.8 ± 1.5) × 10?5, and may not be significantly different from that in the atmospheres of Jupiter and Saturn. In addition, the spectra exhibit two weak absorption at which we were unable to identify. No trace of absorption is visible near these wavelengths or near the HD wavelength in a laboratory spectrum of 4.92 km-am CH4 which we obtained in an attempt to identify these absorption features and to verify that the HD feature does not arise from CH4. 相似文献
12.
We have performed N-body simulations on final accretion stage of terrestrial planets, including the eccentricity and inclination damping effect due to tidal interaction with a gas disk. We investigated the dependence on a depletion time scale of the disk, and the effect of secular perturbations by Jupiter and Saturn. In the final stage, terrestrial planets are formed through coagulation of protoplanets of about the size of Mars. They would collide and grow in a decaying gas disk. Kominami and Ida [Icarus 157 (2002) 43-56] showed that it is plausible that Earth-sized, low-eccentricity planets are formed in a mostly depleted gas disk. In this paper, we investigate the formation of planets in a decaying gas disk with various depletion time scales, assuming disk surface density of gas component decays exponentially with time scale of τgas. Fifteen protoplanets with are initially distributed in the terrestrial planet regions. We found that Earth-sized planets with low eccentricities are formed, independent of initial gas surface density, when the condition (τcross+τgrowth)/2?τgas?τcross is satisfied, where τcross is the time scale for initial protoplanets to start orbit crossing in a gas-free case and τgrowth is the time scale for Earth-sized planets to accrete during the orbit crossing stage. In the cases satisfying the above condition, the final masses and eccentricities of the largest planets are consistent with those of Earth and Venus. However, four or five protoplanets with the initial mass remain. In the final stage of terrestrial planetary formation, it is likely that Jupiter and Saturn have already been formed. When Jupiter and Saturn are included, their secular perturbations pump up eccentricities of protoplanets and tend to reduce the number of final planets in the terrestrial planet regions. However, we found that the reduction is not significant. The perturbations also shorten τcross. If the eccentricities of Jupiter and Saturn are comparable to or larger than present values (∼0.05), τcross become too short to satisfy the above condition. As a result, eccentricities of the planets cannot be damped to the observed value of Earth and Venus. Hence, for the formation of terrestrial planets, it is preferable that the secular perturbations from Jupiter and Saturn do not have significant effect upon the evolution. Such situation may be reproduced by Jupiter and Saturn not being fully grown, or their eccentricities being smaller than the present values during the terrestrial planets' formation. However, in such cases, we need some other mechanism to eliminate the problem that numerous Mars-sized planets remain uncollided. 相似文献
13.
The depletion of an initially uniform distribution of asteroids extending form Mars to Saturn, caused by the gravitational perturbations of Jupiter and Saturn, is calculated by numerical integration of the asteroid orbits. Almost all (about 85%) the asteroids between Jupiter and Saturn are ejected in the first 6000 years Most of the asteroids between the Jupiter resonance (4.0 A.U.) and Jupiter are ejected in the first 2400 years with the exception of the stable librators (e.g., the Hilda group). Interior to the resonance the depletion was small, and interior to the resonance (3.3 A.U.) no asteroids were ejected in the first 2400 years. 相似文献
14.
Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 MSaturn to 10 MJupiter. Giant protoplanets with masses of 5 MJupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼0.25 M⊕ and ∼0.5 M⊕, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M⊕. Saturn's core mass is found to be ∼8 M⊕. 相似文献
15.
Paolo Farinella Andrea Milani Anna M. Nobili Paolo Paolicchi Vincenzo Zappalà 《Icarus》1983,54(2):353-360
Hyperion is an irregularly shaped object of about 285 km in mean diameter, which appears as the likely remmant of a catastrophic collisional evolution. Since the peculiar orbit of this satellite (in resonance locking with Titan) provides an effective mechanism to prevent any reaccretion of secondary fragments originated in a breakup event, the present Hyperion is probably the “core” of a disrupted precursor. This contrasts with the other, regularly shaped small satellites of Saturn, which, according to B.A. Smith et al. [Science215, 504–537 (1982)], were disrupted several times but could reaccrete from narrow rings of collisional fragments. The numerical experiments performed to explore the region of the phase space surrounding the present orbit show that most fragments ejected with a relative velocity rapidly attain chaotic-type orbits, having repeated close encounters with Titan. Ejection velocities of this order of magnitude are indeed expected for a collision at a velocity of ～ 10 km/sec with a projectile-to-target mass ratio of the order of 10?3; similar effects could be produced by less energetic but nearly grazing collisions. Such events are not likely to displace the largest remnant (i.e., the present Hyperion) outside the stable region of the phase space associated with the resonance, but could be responsible for the large amplitude of the observed orbital libration. 相似文献
16.
The rates and altitudes for the dissociation of atmospheric constituents of Titan are calculated for solar UV, solar wind protons, interplanetary electrons, Saturn magnetospheric particles, and cosmic rays. The resulting integrated synthesis rates of organic products range from 102–103 g cm?2 over 4.5 × 109 years for high-energy particle sources to 1.3 × 104 g cm?2 for UV at , and to 5.0 × 105 g cm?2 if (acting primarily on C2H2, C2H4, and C4H2) is included. The production rate curves show no localized maxima corresponding to observed altitudes of Titan's hazes and clouds. For simple to moderately complex organic gases in the Titanian atmosphere, condensation occurs below the top of the main cloud deck at 2825 km. Such condensates comprise the principal cloud mass, with molecules of greater complexity condensing at higher altitudes. The scattering optical depths of the condensates of molecules produced in the Titanian mesosphere are as great as ～ 102/(particulate radius, μm) if column densities of condensed and gas phases are comparable. Visible condensation hazes of more complex organic compounds may occur at altitudes up to ～ 3060 km provided only that the abundance of organic products declines with molecular mass no faster than laboratory experiments indicate. Typical organics condensing at 2900 km have molecular masses = 100–150 Da. At current rates of production the integrated depth of precipitated organic liquids, ices, and tholins produced over 4.5 × 109 years ranges from a minimum ～ 100 m to kilometers if UV at is important. The organic nitrogen content of this layer is expected to be ～ 10?1?10?3 by mass. 相似文献
17.
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
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19.
Both hypervelocity impact and dynamic spall experiments were carried out on a series of well-indurated samples of gabbro to examine the relation between spall strength and maximum spall ejecta thickness. The impact experiments carried out with 0.04- to 0.2-g, 5- to 6-km/sec projectiles produced decimeter- to centimeter-sized craters and demonstrated crater efficiencies of 6 × 10?9 g/erg, an order of magnitude greater than in metal and some two to three times that of previous experiments on less strong igneous rocks. Most of the crater volume (some 60 to 80%) is due to spall failure. Distribution of cumulative fragment number, as a function of mass of fragments with masses greater than 0.1 g yield values of b = d(log Nf)/d log(m) ?0.5 ?0.6, where N is the cumulative number of fragments and m is the mass of fragments. These values are in agreement or slightly higher than those obtained for less strong rocks and indicate that a large fraction of the ejecta resides in a few large fragments. The large fragments are plate-like with mean values of B/A and C/A 0.8 0.2, respectively (A = long, B = termediate, and C = short fragment axes). The small equant-dimensioned fragments (with mass < 0.1 g and B ～ 0.1 mm) represent material which has been subjected to shear failure. The dynamic tensile strenght of San Marcos gabbro was determined at strain rates of 104 to 105 sec?1 to be 147 ± 9 MPa. This is 3 to 10 times greater than inferred from quasi-static (strain rate 100 sec?1) loading experiments. Utilizing these parameters in a continuum fracture model predicts a tensile strenght of , where ε is strain rate. It is suggested that the high spall strenght of basic igneous rocks gives rise to enhanced cratering efficiencies due to spall in the <102-m crater diamter strength-dominated regime. Although the impact spall mechanism can enhance cratering efficiencies it is unclear that resulting spall fragments achieve sufficient velocities such that fragments of basic rocks can escape from the surfaces of planets such as the Moon or Mars. 相似文献
20.
The S(1) line of the pressure-induced fundamental band of H2 was identified and measured in the spectra of Saturn and Jupiter. This broad line at 4750 cm?1 lies in a region free from telluric and planetary absorptions. It is about 99% absorbing in the core; the high-frequency wing extends to at least 5100 cm?1. We compare the obseved line shape to the predictions of both a reflecting-layer model (RLM) and a homogeneous scattering model (HSM). The RLM provides a good fit to the Saturn line profile for temperatures near 150K; the derived base-level density is 0.52 (+0.26, ?0.17) amagat and the H2 abundance is 25 (+10, ?9) km-amagat, assuming a scale height of 48 km. The Jupiter line profile is fit by both the RLM and HSM, but for widely differing temperatures, neither of which seems probable. The precise fitting of the observed S(1) line profile to computed models depends critically on the determination of the true continuum level; difficulties encountered in finding the continuum, especially for Jupiter, are discussed. Derived RLM densities and abundances for both planets are substantially lower than those derived from RLM analyses of the H2 quadrupole lines, the 3ν3 band of CH4, and from other sources. 相似文献