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1.
Infrared observations of the moon and their interpretation   总被引：3，自引：0，他引：3  
The lunar spectrum, resulting from both the directly scattered solar radiation and the Moon's intrinsic thermal radiation, is described. The variations of the thermal component with latitude and phase, and during eclipse conditions, are described and compared with a plane homogeneous model of temperature-independent thermal constants. A review is given of that data appropriate to the lunar crust which may be obtained, both from comparison of this model with observation and from those modifications of the model, which explain otherwise anomalous measurements. Finally, a discussion of the various methods of determining the vertical temperature gradient at the surface leads to a mean value of about 2Km–1, although the heat flux associated with these results is much less than the recent direct measurement.  相似文献   

2.
Wenzhe Fa 《Icarus》2010,207(2):605-615
In China’s first lunar exploration project, Chang-E 1 (CE-1), a multi-channel microwave radiometer was aboard the satellite, with the purpose of measuring microwave brightness temperature (Tb) from lunar surface and surveying the global distribution of lunar regolith layer thickness. In this paper, the primary 621 tracks of swath data measured by CE-1 microwave radiometer from November 2007 to February 2008 are collected and analyzed. Using the nearest neighbor interpolation to collect the Tb data under the same Sun illumination, global distributions of microwave brightness temperature from lunar surface at lunar daytime and nighttime are constructed. Based on the three-layer media modeling (the top dust-soil, regolith and underlying rock media) for microwave thermal emission of lunar surface, the CE-1 measured Tb and its dependence upon latitude, frequency and FeO + TiO2 content, etc. are discussed. The CE-1 Tb data at Apollo landing sites are especially chosen for validation and calibration on the basis of available ground measurements. Using the empirical dependence of physical temperature upon the latitude verified by the CE-1 multi-channel Tb data at Apollo landing sites, the global distribution of regolith layer thickness is further inverted from the CE-1 brightness temperature data at 3 GHz channel. Those inversions at Apollo landing sites and the characteristics of regolith layer thickness for lunar maria are well compared with the Apollo in situ measurements and the regolith thickness derived from the Earth-based radar data. Finally, the statistical distribution of regolith thickness is analyzed and discussed.  相似文献   

3.
We numerically calculate the probability and area of permanent shadowing as a function of the selenographic latitude as well as the total area of the permanently shadowed surface for various hierarchical models of the lunar surface. The permanently shadowed area is shown to rapidly increase with increasing number of hierarchical surface levels. For a two-level model of the lunar relief, where the surface of craters is complicated by a random small-scale relief with a Gaussian distribution of heights and slopes, the area of the doubly shadowed regions of the lunar surface is approximately an order of magnitude smaller than the area of the singly shadowed regions. A comparison of the permanently shadowed area calculated by using averaged statistical relations and data on the actual distribution of craters near the lunar poles shows almost complete agreement.  相似文献   

4.
P. Vernazza  F. DeMeo  M. Birlan  S. Erard 《Icarus》2010,209(1):125-114
We present resolved near-infrared spectra of Mercury scanning 70% of the surface in latitude and longitude from three separate observations, allowing us to perform a compositional investigation of its surface. By scanning the surface we find that all spectra in our sample are remarkably similar suggesting overall compositional homogeneity. We do, however, observe a slope difference between the spectra. These slope changes are most likely due to differences in the emission angle over different parts of the surface. We confirm the presence of a 1.1 μm feature that had been previously detected (Warell, J. et al. [2006]. Icarus 180, 281-291) and attributed to Ca-rich clinopyroxene. Finally, we investigated Mercury’s surface composition by comparing its spectrum with ground-based lunar spectra, lunar soil spectra collected in the laboratory, and analysis with a simple linear mixing model using various minerals as end-members. The result of this compositional investigation reveals that Mercury’s surface composition is likely to be quite different from the Moon’s. While low-Ca iron-rich pyroxenes are main surface components on the Moon (abundance varying from ∼5% to ∼35%), their abundance on Mercury may not exceed 5%. We also find that a Ca-rich clinopyroxene (in the hedenbergite-diopside series) is likely to be a main component of Mercury’s surface whereas this mineral is almost absent on the Moon. Our analysis also suggests the possible presence of olivine. We find that Mercury’s slope is less red than that of the Moon, in agreement with results from MESSENGER (McClintock, W.E., and 12 colleagues [2008]. Science 321, 62-65), and composition rather than variation of space weathering is likely the cause of this difference.  相似文献   

5.
Estimation of solar illumination on the Moon: A theoretical model   总被引：2，自引：0，他引：2  
The solar illumination conditions on the lunar surface represent a key resource with respect to returning to the Moon. As a supplement to mapping the solar illumination by exploring data, lighting simulations using high-resolution topography could produce quantitative illumination maps. In this study, a theoretical model is proposed for estimating the solar illumination conditions. It depends only on the solar altitude and topographical factors. Besides the selenographic longitude and latitude, the former is determined by the selenographic longitude and latitude at the subsolar site, the geocentric ecliptical latitude, and the dimensionless distance of the Sun–Moon relative to 1 AU, which are function of time. The latter is determined by comparing the elevations in solar irradiance direction within 210 km in which the topography might shadow the behind sites to the critical elevations determining whether the behind sites are shadowed or not. Compared to Zuber's model, the model proposed in this study is simpler and easier for computing. It is parameterized with selenographic coordinates, elevations, and time. With high-resolution topography data, the solar illumination conditions at any selenographic coordination could be estimated by this model at any date and time. The lunar surface is illuminated when the solar altitude is non-zero and all the elevations within 210 km in solar irradiance direction are lower than the critical elevations. Otherwise it would be shadowed.  相似文献   

6.
The lunar photometric function, which describes the dependency of the observed radiance on the observation geometry, is used for photometric correction of lunar visible/near-infrared data. A precise photometric correction parameter set is crucial for many applications including mineral identification and reflectance map mosaics. We present, for the first time, spectrally continuous photometric correction parameters for both sides of the Moon for wavelengths in the range 0.5-1.6 μm and solar phase angles between 5° and 85°, derived from Kaguya (SELENE) Spectral Profiler (SP) data. Since the measured radiance also depends on the surface albedo, we developed a statistical method for selecting areas with relatively uniform albedos from a nearly 7000-orbit SP data set. Using the selected data set, we obtained empirical photometric correction parameter sets for three albedo groups (high, medium, and low). We did this because the photometric function depends on the albedo, especially at phase angles below about 20° for which the shadow hiding opposition effect is appreciable. We determined the parameters in 160 bands and discovered a small variation in the opposition effect due to the albedo variation of mafic mineral absorption. The consistency of the photometric correction was checked by comparing observations made at different times of the same area on the lunar surface. Variations in the spectra obtained were lower than 2%, except for the large phase angle data in mare. Lastly, we developed a correction method for low solar elevation data, which is required for high latitude regions. By investigating low solar elevation data, we introduced an additional correction method. We used the new photometric correction to generate a 1° mesh global lunar reflectance map cube in a wavelength range of 0.5-1.6 μm. Surprisingly, these maps reveal that high latitude (?75°) regions in both the north and south have much lower spectral continuum slopes (color ratio r1547.7nm/r752.8nm ? 1.8) than the low and medium latitude regions, which implies lower degrees of space weathering.  相似文献   

7.
It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L 2 of the Earth–Moon system within the framework of the Circular Restricted Three-Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four-Body Problem. In the former case, as main outcome, we observe a more relevant bombardment at the apex of the lunar surface, and a percentage of impact which is almost constant and whose value depends on the assumed Earth–Moon distance dEM. In the latter, it seems that the Earth–Moon and Earth–Moon–Sun relative distances and the initial phase of the Sun θ 0 play a crucial role on the impact distribution. The leading side focusing becomes more and more evident as dEM decreases and there seems to exist values of θ 0 more favorable to produce impacts with the Moon. Moreover, the presence of the Sun makes some trajectories to collide with the Earth. The corresponding quantity floats between 1 and 5 percent. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth–Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering.  相似文献   

8.
We present the results of computer simulation of the shadowing effect for three types of surface: (1) cratered, (2) formed by a random profile with Gaussian statistical height and slope distributions, and (3) a two-scale surface representing a cratered area that is complicated by small-scale random relief. The calculations are based on data on the distribution of lunar craters derived from the diameter/depth ratio and on the assumption of the equilibrium distribution of the crater population in the circumpolar areas of the lunar surface. We determined the characteristics of perpetually shaded areas of the lunar surface: the probability of the constant shadowing of an arbitrary surface point, the fraction of the perpetually shaded area as a function of selenographic latitude, the latitudinal dependence of the perpetually shaded area, and the total area of the perpetually shaded surface. The calculations showed that the presence of structural features of different scale on the lunar surface can considerably increase the estimate of the fraction of the perpetually shaded area compared to existing estimates.  相似文献   

9.
We discuss observations of the Moon at a wavelength of 49.3 cm made with the Owens Valley Radio Observatory Interferometer. These observations have been fit to models in order to estimate the lunar dielectric constant, the equatorial subsurface temperature, the latitude dependence of the subsurface temperature, and the subsurface temperature gradient. The models are most consistent with a dielectric constant of 2.52 ± 0.01 (formal errors), an equatorial subsurface temperature of 249?5+8K, and a change in the subsurface temperature with latitude (ψ), which is proportional to cos0.38ψ. Since the temperature of the Moon has been measured by the Apollo Lunar Heat Flow Experiment, we have been able to use our determination of the equatorial temperature to estimate the error in the flux density calibration scale at 49.3cm (608 MHz). This results in a correction factor of 1.03 ± 0.04, which must be applied to the flux density scale. This factor is much different from 1.21 ± 0.09 estimated by Muhleman et al. (1973) from the brightness temperature of Venus and apparently indicates that the observed decrease in the brightness temperature of Venus at long wavelengths is a real effect.The estimates of the temperature gradient, which are based on the measurement of limb darkening, are small and negative (temperature decreases with depth) and may be insignificantly different from zero since they are only as large as their formal errors. We estimate that a temperature gradient in excess of 0.6K/m at 10m depth would have been observed. Thus, a temperature gradient like that measured in situ at the Apollo 15 and 17 landing sites in the upper 2m of the regolith is not typical of the entire lunar frontside at the 10m depths where the 49.3 cm wavelength emission originates. This result may indicate that the mean lunar heat flow is lower than that measured at the Apollo landing sites, that the thermal conductivity is greater at 10m depth than it is at 2m depth, or that the radio opacity is greater at 10m depth than at 2m depth. The negative estimates of the temperature gradient indicate that the Moon appeared limb bright and might be explained by scattering of the emission from boulders or an interface with solid rock. The presence of solid rock at 10m depths will probably cause heat flows like those measured by Apollo to be unobservable by our interferometric method at long wavelengths, since it will cause both the thermal conductivity and radio opacity of the regolith to increase. Thus, our data may be most consistent with a change in the physical properties of the regolith to those of solid rock or a mixture of rock and soil at depths of 7 to 16m. Our results show that future radio measurements for heat flow determinations must utilize wavelengths considerably shorter than 50 cm (25 cm or less) to avoid the rock regions below the regolith.  相似文献   

10.
《New Astronomy》2007,12(7):523-532
A 3-D numerical model of comet nuclei is presented. An implicit numerical scheme was developed for the thermal evolution of a spherical nucleus composed of a mixture of ice and dust. The model was tested against analytical solutions, simplified numerical solutions, and 1-D thermal evolution codes. The 3-D code was applied to comet 67P/Churyumov-Gerasimenko; surface temperature maps and the internal thermal structure was obtained as function of depth, longitude and hour angle. The effect of the spin axis tilt on the surface temperature distribution was studied in detail. It was found that for small tilt angles, relatively low temperatures may prevail on near-pole areas, despite lateral heat conduction. A high-resolution run for a comet model of 67P/Churyumov-Gerasimenko with low tilt angle, allowing for crystallization of amorphous ice, showed that the amorphous/crystalline ice boundary varies significantly with depth as a function of cometary latitude.  相似文献   

11.
We have examined several theories that imply the generation of X-rays by the Moon. The X-ray fluxes to be expected at the top of the Earth's atmosphere are estimated and compared. For example, we find that an X-ray flux is to be expected when the Moon is full and Kp high, as a consequence of the configuration of the auroral electrons in space deduced from the long tail model of the magnetosphere. The X-ray photons are caused by energetic electrons in the tail that bombard the lunar surface. Alternatively, Gold has suggested that lunar X-rays are produced by the bombardment by solar-wind electrons; this results in a lunar phase dependence that is different from the long tail model. The background is discussed and we conclude that the lunar X-ray flux may be detectable. Experiments of this kind may provide useful tools for investigating the models.  相似文献   

12.
It is evident that lunar mare basins have been subsiding and one reason for such subsidence was the existence of their mascons and their volcanic fills as loads that flexed the lithosphere. The additional effects of drying up and cooling of internal hot volumes may also have been important, leading to still more compressional mare environment. The remaining relicic thermal pulse-induced dilatation within large areas surrounding the mare basins may be responsible for the extensional rille tectonics together with the flexural peripheral bulge due to tensional arching and bending due to differences in internal volume changes. The internal attack against the lunar crust has been quite different above and below the mean surface. Below this level the old crust was more easily attacked by volcanic extrusions, causing thick lava covers and, as a consequence, broken by compressional forces; while above this level the old crust has instead been temporarily and in places attacked by tensional forces in dimensions determined by the internal energy sources and their interaction with the lithospheric roof, thus enabling the internal forces together with flexural bending to dome and fault the upper crustal surface to some extent in respect to mare areas. The rille formation can be characterized by peripheral bulging and bending. The share of asthenosphere-related effects in lunar tectonics must be considered to have been very important. If only lava load and mascons have raised compression within mare areas and tension within the surrounding terra how can be explained those rille graben which do not have any extra mass concentrations nor lavas on their sides and why some major mascon basins have so few tensional rille graben structures around them?  相似文献   

13.
Lunar images acquired at non-zero phase angles show brightness variations caused by both albedo heterogeneities and local topographic slopes of the surface. To distinguish between these two factors, altimetry measurements or photoclinometry data can be used. The distinction is especially important for imagery of phase-function parameters of the Moon. The imagery is a new tool that can be used to study structural anomalies of the lunar surface. To illustrate the removal of the topographic effects from photometric images, we used Earth-based telescopic observations, altimetry measurements carried out with the Kaguya (JAXA) LALT instrument, and a new photoclinometry technique that includes analysis of several images of the same scenes acquired at different phase angles. Using this technique we have mapped the longitudinal component of lunar topography slopes (the component measured along the lines of constant latitude). We have found good correlations when comparing our map with the corresponding data from Kaguya altimetry. The removal of the topographic surface properties allows for the study of the phase-function parameters of the lunar surface, not only for flat mare regions, but for highlands as well.  相似文献   

14.
Laboratory measurements of seismic wave velocities and electrical properties of Apollo lunar samples and similar material of terrestrial origin are discussed in this paper. Measurements of the electrical properties show that in the frequency range above a few hundred Hz the outer region of the Moon may be considered as a low loss dielectric. This observation supports a longstanding speculation that dry, powdered rocks in which the dielectric loss tangent is frequency-independent over a wide range of frequency are present in the uppermost lunar surface layers. The surface layers of the Moon are likely to have an extremely low electrical conductivity. Thus future electromagnetic probing of the Moon to a few hundred kilometer depth is possible in the few kHz frequency range. Based on ultrasonic experiments with pressure as a variable, we next present the elastic constants and equations of state of lunar materials and characteristic dispersion of seismic wave velocities of the Moon. We find thatP andS wave velocities increase sharply within the first 30 km depth and then level off gradually. Combining this observation with lunar seismic and geophone data, we believe that the first 30 km of the Moon may be interpreted as a scattering region. If H2O exists on the Moon, H2O may occur at some shallow depth beneath the outermost surface layer in solid ice interlocking cracks and pores and mineral grains. The rocks in this permafrost state have relatively low seismic velocity and highQ. If permafrost does exist, we would expect a wide range of electrical conductivity and dielectric constant. Future electromagnetic probing of the Moon should yield very usefull information on the physical state of the lunar interior; when this electrical information is combined with the seismic information, we should learn much more about the internal constitution and the state of the Moon than is known today.  相似文献   

15.
We present thermal evolution calculations of inhomogeneous asymmetric initial configurations of a spherical model of Comet 67P/Churyumov-Gerasimenko, using a fully 3-dimensional numerical code. The initial composition is amorphous H2O ice and dust, in a “layered-pile” configuration, where layers differing in ice/dust ratio and thermal properties extend over a fraction of the surface area and about 10 m in depth and may overlap. We analyze the effect of one such layer, as well as the combined effect of many layers, randomly distributed. We find that internal inhomogeneities affect both the surface temperature and the activity pattern of the comet. In particular, they may lead to outbursts at large heliocentric distances and also to activity on the night-side of the nucleus. The rates of ablation and depths of dust mantle and crystalline ice outer layer as functions of longitude and latitude are shown to be affected as well.  相似文献   

16.
The effects of vertical variations in density and dielectric constant on nadir-viewing microwave brightness temperatures are examined. Stratification models as well as models of a continuous increase in density with depth are analyzed. Specific applications address the vertical structure of the lunar frontside regolith, utilizing combined constraints from Apollo data, bistatic radar signatures, and Earth-based measurements of the lunar microwave brightness temperature.Results have been analyzed in terms of the effects on the zeroth and first harmonic of the lunar disk-center brightness temperature variation over a lunation, and their wavelength dependence. Lunation-mean brightness temperatures, which are diagnostic of emissivity and steady-state sub-surface temperatures, are sensitive to both near-surface soil density gradients and single high-impedance dielectric contrasts. Models of the rapid density increase in the upper 5–10 cm of the lunar regolith predict brightness temperature decreases of 2–10°K between λ0 = 3 and 30 cm. The magnitude of this spectral variation depends upon the thickness of a postulated low-density surface coating layer, and the magnitude of the density gradient in the transition soil layer. Comparable decreases in brightness temperature can be produced by a stratified two-layer model of soil overlaying bedrock if the high-density substrate lies within 1–2 m of the surface. Multiple soil layering on a centimeter scale, such as is observed in the Apollo core samples, is not likely to induce spectral variations in mean brightness temperature due to rapid regional variations in layer depths and thicknesses.The fractional variation in disk-center brightness temperature over a lunation (first harmonic) can be altered by vertical-structure effects only for the case in which a larger and abrupt dielectric contrast exists within the upper surface layer where the significant diurnal variations in physical temperature occur. Soil density variations do not cause scattering effects sufficient to significantly alter the microwave emission weighting function within the diurnal layer. For the Moon, this layer consists of the upper 10 cm. Since no widespread rock substrate as shallow as 10 cm exists in the lunar frontside, only volume scattering effects, due to buried shallow rock fragments, can explain the apparent high electrical loss inferred from Earth-based measurements of the amplitude of lunation brightness temperature variations.Representative models of the lunar frontside vertical structure have also been examined for their effects of radar cross-section measurements and resultant inferences of bulk dielectric constant. Models of the near-surface density gradient predict a significant increase in the remotely inferred dielectric constant value from centimeter to meter wavelengths. Such a model is in general agreement with the dielectric constant spectrum inferred from Earth-based brightness temperature polarization measurements, but is difficult to reconcile with the Apollo bistatic radar results at λ0 = 13 and 116 cm.  相似文献   

17.
Making use of Orbiter and Apollo photographs, frequency counts of craters down to 2 km diam as indicators of the relative ages of lunar features, have been made on 264 areas, including 15 terrae, 27 recognized maria, 174 flat-floored craters and 48 lava-covered areas with indefinite boundaries designated as ‘marets’. Analysis of frequency counts on flat-floored craters on the basis of this data and re-assessment of former results, combined with the relatively restricted age range of lunar samples, make it unlikely that the present observations are able to reach back in time to impacts on an assumed primordial floating crust. The range of crater frequencies on the marets, together with their wide distribution over the lunar surface, suggest lava migrations to the surface within autonomous domains each with its own chronology, covering an extensive period of lunar history. The close association of marets with flat-floored craters provides a reasonable origin for the floor material of these latter objects. The lava migrations associated with the marets suggest that internal heating may be a more important factor in the origin of lunar surface features than had formerly been supposed. Kopal's views on the origin of the moon's multiple moments of intertia (1972) are considered to support the concept of autonomous domains. It is considered that the time sequence of separate lava flows represented by the marets may be a reflection of physical processes within the moon responsible for the successive lava flows associated with the larger maria.  相似文献   

18.
A preliminary model of the internal magnetic field of the Moon is developed using a novel, correlative technique on the low-altitude Lunar Prospector magnetic field observations. Subsequent to the removal of a simple model of the external field, an internal dipole model is developed for each pole-to-pole half-orbit. This internal dipole model exploits Lunar Prospector's orbit geometry and incorporates radial and theta vector component data from immediately adjacent passes into the model. These adjacent passes are closely separated in space and time and are thus characteristic of a particular lunar regime (wake, solar wind, magnetotail, magnetosheath) or regimes. Each dipole model thus represents the correlative parts of three adjacent passes, and provides an analytic means of continuing the data to a constant surface of 30 km above the mean lunar radius. The altitude-normalized radial field from the wake and tail regimes is used to build a model in which 99.2% of the 360 by 360 bins covering the lunar surface are filled. This global model of the radial magnetic field is used to construct a degree 178 spherical harmonic model of the field via the Driscoll and Healy sampling theorem. Terms below about degree 150 are robust, and polar regions are considered to be the least reliable. The model resolves additional detail in the low magnetic field regions of the Imbrium and Orientale basins, and also in the four anomaly clusters antipodal to the large lunar basins. The model will be of use in understanding the sources of the internal field, and as a first step in modeling the interaction of the internal field with the solar wind.  相似文献   

19.
Data on thermophysical properties measured on lunar material returned by Apollo missions are reviewed. In particular, the effects of temperature and interstitial gaseous pressure on thermal conductivity and diffusivity have been studied. For crystalline rocks, breccias and fines, the thermal conductivity and diffusivity decrease as the interstitial gaseous pressure decreases from 1 atm to 10–4T. Below 10–4T, these properties become insensitive to the pressure. At a pressure of 10–4T or below, the thermal conductivity of fines is more temperature dependent than that of crystalline rocks and breccias. The bulk density also affects the thermal conductivity of the fines. An empirical relationship between thermal conductivity, bulk density and temperature derived from the study of terrestrial material is shown to be consistent with the data on lunar samples. Measurement of specific heat shows that, regardless of the differences in mineral composition, crystalline rocks and fines have almost identical specific heat in the temperature range between 100 and 340K. The thermal parameter calculated from thermal conductivity, density and specific heat shows that the thermal properties estimated by earth-based observations are those characteristic only of lunar fines and not of crystalline rocks and breccias. The rate of radioactive heat generation calculated from the content of K, Th and U in lunar samples indicates that the surface layer of the lunar highland is more heat-producing than the lunar maria. This may suggest fundamental differences between the two regions.Now at Lamont-Doherty Geological Observatory, Columbia University, Palisades, New York, U.S.A.  相似文献   

20.
Accurate estimation of cratering asymmetry on the Moon is crucial for understanding Moon evolution history. Early studies of cratering asymmetry have omitted the contributions of high lunar obliquity and inclination. Here, we include lunar obliquity and inclination as new controlling variables to derive the cratering rate spatial variation as a function of longitude and latitude. With examining the influence of lunar obliquity and inclination on the asteroids population encountered by the Moon, we then have derived general formulas of the cratering rate spatial variation based on the crater scaling law. Our formulas with addition of lunar obliquity and inclination can reproduce the lunar cratering rate asymmetry at the current Earth-Moon distance and predict the apex/ant-apex ratio and the pole/equator ratio of this lunar cratering rate to be 1.36 and 0.87, respectively. The apex/ant-apex ratio is decreasing as the obliquity and inclination increasing. Combining with the evolution of lunar obliquity and inclination, our model shows that the apex/ant-apex ratio does not monotonically decrease with Earth-Moon distance and hence the influences of obliquity and inclination are not negligible on evolution of apex/ant-apex ratio. This model is generalizable to other planets and moons, especially for different spin-orbit resonances.  相似文献   

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