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1.
In the IERS Standards (1989), for the Moon the adopted value of the tide Love number, k 2, is equal to 0.0222. In this paper using the latest geodetic parameters of the Moon a group of internal structure models are constructed for this celestial body (see Table V), then the dependence of the Moon's core size on calculated value of k 2 is explored. The obtained results indicate that the second degree Love number, k 2 = 0.02664, of the lunar model 91–04 is near its observed value (0.027 ± 0.006). This implies that the Moon may possess an outer core of 660 km radius and of 300 kbar mean rigidity. With the same method the static Love numbers from degree 2 to 30 are computed for the terrestrial planets — Mercury, Venus, and Mars (see Table VII), and the influence of some parameters (such as the rigidity) of the outer core on low degree Love numbers is discussed. Finally, the likely range of the second degree Love numbers is determined for the terrestrial planets (see Table XI). It seems that if low degree Love numbers of a terrestrial planet can be detected in the future space explorations, there is some possibility to improve the planetary internal structure model. For example, as soon as space techniques yield an observed value of k 2 > 0.10 for Mercury, there will be reason to anticipate that a partly melted iron core exists in this planet.  相似文献   

2.
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   

3.
In view of the elastic deformation of the Earth we performed the comparative study for the Earth's models 1066 A and PREM, calculated the static Love numbers from degree 2 to 30, and discussed the relative variations of the second degree Love numbers and their combinations due to the variation of the position of the core-mantle boundary, due to the redistribution of V p, V s, and in the lower mantle, and due to the possible rigidity in the outer core. From the above-mentioned discussions we recommended that the Standard Earth Model (SEM) should include two kinds of models—one is oceanless, and another has an oceanic surface. Finally, we calculated the astronomicgeodetic parameters, which are consistent with the primary constants in the IERS Standards, of the SEM.  相似文献   

4.
IERS1996规范在参考系方面的改进   总被引：2，自引：0，他引：2  
对ＩＥＲＳ１９９６规范中有关参考系方面作了简单而系统的介绍，重点叙述了与ＩＥＲＳ１９９２标准相比ＩＥＲＳ１９９６规范在参考系方面的主要改进：天球参考架中的基本源从５７颗增加到２３６颗；动力学参考架采用ＪＰＬ ＤＥ４０３／ＬＥ４０３历表代替ＤＥ２００／ＬＥ２００历表；采用ＮＵＶＥＬ ＮＮＲ－１Ａ板块运动模型代替ＮＵＶＥＬ ＮＮＲ－１模型；变更了９个基本常数值；给出了天极坐标的观测和理论间差的经验模型  相似文献   

5.
The paper briefly describes the purpose and features of the Japanese project ILOM (In-situ Lunar Orientation Measurement) in which it is planned to install the zenith telescope with a CCD lens on one of the poles of the Moon for the observation of stars in order to determine the physical libration of the Moon (PhLM). The studies presented in this paper are the result of the first stage of the theoretical support of the project:
  1. The compilation of the list of stars within the field of view of the telescope during the precessional motion of the lunar pole.
  2. Modeling and analysis of the behavior of stellar tracks during the observation period.
  3. Simulation and testing of the sensitivity of the measured selenographic star coordinates to changes in the parameters of the dynamic model of the Moon and the elastic parameters of the lunar body.
Direct and inverse PhLM problems are discussed. Within the scope of the direct problem visible “daily parallels” and one-year star tracks are calculated. Their behavioral features when observed from the lunar surface are shown. At this stage of the simulation selenographic star coordinates for the four models of the gravitational field of the Moon have been compared, i.e., the model constructed on the basis of the lunar laser ranging (LLR), GLGM-2, LP150Q, and SGM100h. It is shown that even when comparing modern models LP150Q and SGM100h stellar tracks differ from the arc by more than 10 ms of arc. At the stage of the inverse problem, the manifestation of viscoelastic properties of the Moon in selenographic coordinates has been studied. In the spectrum of the simulated residual differences harmonics have been identified which can serve as indicators to refine parameters, Love number k 2 and the delay time characterizing the viscous properties of the lunar body.  相似文献   

6.
The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970–2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon’s extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission. Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is \(-25.90 {{}^{\prime \prime }}/\mathrm{cy}^2\), and the eccentricity is increasing by \(1.48\times 10^{-11}\) each year.  相似文献   

7.
In the present article we develop the theory of the long period tidal effects in the motion of artificial satellites assuming the variability of elastic parameters of the Earth (Love numbers) across the parallels. The dependence of Love numbers on the longitude produces perturbations of the period of one day or less and hence is neglected in the present theory. In this respect we follow in the footsteps of Kaula (1969). If the deviations ofk 2 andk 3 from pure constants are not taken into consideration, then the perturbations caused by the variability ofk 2 andk 3 across the parallels will be misinterpreted as the perturbations caused byk 4...-terms, and the spurious values ofk 4... will be deduced. It is extremely doubtful, however, that the real effects caused byk 4,k 5,..., are significant enough to be detected. The short period effects with the period of the revolution of the satellite, or less, were removed from the differential equations for the variation of elements of the satellite by the averaging over the orbit of the satellite. These differential equations are in the form convenient for numerical integration over a long interval of time and also suitable for developing the tidal effects into trigonometric series with the arguments ω, Ω of the satellite andl, l′, F, D, Γ of the Moon. The numerical integration can be performed using some simple quadrature formula, without resorting to a predictor-corrector system.  相似文献   

8.
This survey is a general overview of modern optical studies of the Moon and their diagnostic meaning. It includes three united parts: phase photometry, spectrophotometry, and polarimetry. The first one is devoted to the progress in the photometry of the Moon, which includes absolute albedo determination to refine the albedo scale (e.g., to connect lunar observations and the data of lunar sample measurements) and mapping the parameters of a lunar photometric function (e.g., the phase-angle ratios method) with the aim of making qualitative estimates of regolith structure variations. This part also includes observations of the lunar opposition effect as well as photogrammetry and photoclinometry techniques. In particular, available data show that because of the low albedo of the lunar surface, the coherent backscattering enhancement hardly influences the lunar opposition spike, with the exception of the brightest lunar areas measured in the NIR. The second part is devoted to chemical/mineral mapping of the Moon's surface using spectrophotometric measurements. This section also includes analyses related to the detection of water ice or hydroxyl, prognoses of maturity, and helium-3 abundance mapping. In particular, we examine the relationship between superficial OH/H2O compounds spectrally detected recently and bulk “water ice” found earlier by the Lunar Prospector GRS and LRO LEND, assuming that the compounds are delivered to cold traps (permanently shadowed regions) with electrostatically levitated dust saturated by solar wind hydrogen. Significant problems arise with the determination of TiO2 content, as the correlation between this parameter and the color ratio C(750/415 nm) is very non-linear and not universal for different composition types of the lunar surface; a promising way to resolve this problem is to use color ratios in the UV spectral range. The third part is devoted to mapping of polarization parameters of the lunar surface, which enable estimates of the average size of regolith particles and their optical inhomogeneity. This includes considerations of the Umov effect and results of spectropolarimetry, negative polarization imagery, and measurements of other polarimetric parameters, including the third Stokes parameter. Although these three research divisions have not been developed equally and the numbers of proper references are very different, we try to keep a balance between them, depicting a uniform picture. It should be emphasized that many results presented in this review can be applied to other atmosphereless celestial bodies as well.  相似文献   

9.
Doppler tracking data from the Lunar Orbiter series of spacecraft have been used in a more complete analysis of the spherical harmonic coefficients of the lunar gravitational field through thirteenth degree and order. The value obtained for the mass of the Moon,GM = 4902.84 km3 s–2, is in good agreement with previous results and with results obtained by alternate procedures. Acceleration contour plots, derived from the gravitational coefficients, show correlations with surface features on the near side of the Moon, but are of questionable validity for the far side because of the lack of direct tracking data on the far side. Based on the most recent gravitational field data, the current estimate for the polar moment of inertia of the Moon isC/Ma 2 = 0.4019-0.002 +0.004. This value indicates that the interior of the Moon can be homogeneous, but some results presented strongly suggest that the Moon is differentiated, with an excess of mass in the direction toward the Earth.Paper presented at the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September, 1971.  相似文献   

10.
The evolutionary changes that occur in the internal density concentration parameterk 2 (called the apsidal constant for brevity) for a star of given mass and initial composition are examined in detail. The purpose is to ascertain whether or not such an approach leads to a reduction in the differences now noted between the theoretically derived values ofk 2 and the observed values derived from the secular advance of the periastron in close eclipsing binary systems.A series of stellar models of mass 2.0, 5.0, 10.0 and 20.0M were employed, with an initial compositional mixture ofX=0.739,Y=0.24 andZ=0.021. These models cover an evolutionary range from a point in time where the star has just completed the Hayashi phase of its pre-Main Sequence contraction through its entire Main Sequence phase to the point where hydrogen depletion in the core is complete.For each model, a value ofk 2 is determined by numerically integrating Radau's equation and using the values of , the ratio of the star's density at pointa to its mean density, as taken from the models. The result is the time history ofk 2 for each stellar mass over the evolutionary range of interest. The results are then summarized in the (logk 2, logT e) plane which, for the first time, quantitatively indicates the variation ink 2 as a function of the evolutionary state of the star.A comparison between these theoretically derived values ofk 2 and a selected set of observationally determined ones immediately indicates that the secular variation ink 2 plays an extremely important part in any comparison between theory and observation. For most of the cases studied, the difference between the theoretically and observationally determined values ofk 2 can be reconciled in terms of the evolutionary history of the binary system.While tentatively providing a satisfactory explanation for the previously noted differences in the determination ofk 2, there now exists the problem of accurately pinpointing the evolutionary state of the observed binary system.  相似文献   

11.
An analytical theory of lunar physical librations based on its two-layer model consisting of a non-spherical solid mantle and ellipsoidal liquid core is developed. The Moon moves on a high-precision orbit in the gravitational field of the Earth and other celestial bodies. The defined fourth mode of a free libration is caused by the influence of the liquid core, with a long period of 205.7 yr, with amplitude S = 0″0395 and with an initial phase Π0 = ?134° (for the initial epoch 2000.0). Estimates of dynamic (meridional) oblatenesses of a liquid core of the Moon have been estimated: ?D = 4.42 × 10?4, μD = 2.83 × 10?4 (?D + μD = 7.24 × 10?4). These results have been obtained as a result of comparison of the developed analytical theory of physical librations of the Moon with the empirical theory of librations of the Moon constructed on the basis of laser observations.  相似文献   

12.
In this paper the relation between the uncertainty of the Moon's mean moment of inertia (I/Ma 2) and that of the core density c is discussed with a two-layer model of the Moon - a mantle obeying Roche's law of the density distribution and a homogeneous core (Fe-core or Fe-FeS-core). When the uncertainty of I/Ma 2 is 0.0023 (that is the accuracy in present observation), a core with radius of 450 km will be appropriate to the limitation of c about 1 g cm–3. Considering the accuracy obtained in space explorations, and the compressibility and the quasi-homogeneity of the Moon, we suggest that the parameters C 20, , , a, and GM of the Moon should define as primary constants, but C 22 and C/Ma 2 as derived constants. Therefore, the ratio of mass of Moon to that of Earth in the IAU (1976) system of astronomical constants will become a deducible constant.  相似文献   

13.
We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J 2 and C 22 terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the inclination and the argument of pericenter do not remain both constant at the same time, as is the case when only the J 2 term is taken into account. Instead, there exist quasi-critical solutions, for which the argument of pericenter librates around a constant value. These solutions are represented by smooth curves in phase space, which determine the dependence of the quasi-critical inclination on the initial nodal phase. The amplitude of libration of both argument of pericenter and inclination would be quite large for a non-rotating Moon, but is reduced to <0°.1 for both quantities, when a uniform rotation of the Moon is taken into account. The values of J 2, C 22 and the rotation rate strongly affect the quasi-critical inclination and the libration amplitude of the argument of pericenter. Examples for other celestial bodies are given, showing the dependence of the results on J 2, C 22 and rotation rate.  相似文献   

14.
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   

15.
A program of lunar infrared radiometry which uses large area scanning is described. Procedures for atmospheric attenuation correction and data reduction to temperature by relative radiometry are outlined. The scan data of the waning Moon taken during ten evenings in the 10- to 12-µm window are presented as isothermal contour maps of the lunar disc. More than 160 areas of anomalous thermal emission have been found in the lunar darkside data. These are tabulated and are also shown on an accompanying map. An error analysis, derived from accuracy estimates of the independent parameters, is included.  相似文献   

16.
The Halo orbits originating in the vicinities of both,L 1 andL 2 grow larger, but shorter in period, as they shift towards the Moon. There is in each case a narrow band of stable orbits roughly half-way to the Moon. Nearer to the Moon, the orbits are fairly well-approximated by an almost rectilinear analysis. TheL 2 family shrinks in size as it approaches the Moon, becoming stable again shortly before penetrating the lunar surface. TheL 1-family becomes longer and thinner as it approaches the Moon, with a second narrow band of stable orbits with perilune, however, below the lunar surface.  相似文献   

17.
From the observations of the gravitational field and the figure of the Moon, it is known that its center of mass (briefly COM) does not coincide with the center of figure (COF), and the line “COF/COM” is not directed to the center of the Earth, but deviates from it to the South–East. Here we study the deviation of the lunar COM to the East from the mean direction to Earth.At first, we consider the optical libration of a satellite with synchronous rotation around the planet for an observer at a point on second (empty) orbit focus. It is found that the main axis of inertia of the satellite has asymmetric nonlinear oscillations with amplitude proportional to the square of the orbit eccentricity. Given this effect, a mechanism of tidal secular evolution of the Moon’s orbit is offered that explains up to \(20\%\) of the known displacement of the lunar COM to the East. It is concluded that from the alternative—evolution of the Moon’s orbit with a decrease or increase in eccentricity—only the scenario of evolution with a monotonous increase in orbit eccentricity agrees with the displacement of lunar COM to the East. The precise calculations available confirm that now the eccentricity of the lunar orbit is actually increasing and therefore in the past it was less than its modern value, \(e = 0.0549\).To fully explain the displacement of the Moon’s COM to the East was deduced a second mechanism, which is based on the reliable effect of tidal changes in the shape of the Moon. For this purpose the differential equation which governs the process of displacement of the Moon’s COM to the East with inevitable rounding off its form in the tidal increase process of the distance between the Earth and the Moon is derived. The second mechanism not only explains the Moon’s COM displacement to the East, but it also predicts that the elongation of the lunar figure in the early epoch was significant and could reach the value \(\varepsilon\approx0.31\). Applying the theory of tidal equilibrium figures, we can estimate how close to the Earth the Moon could have formed.  相似文献   

18.
Lunar physical librations and laser ranging   总被引：1，自引：0，他引：1  
The analysis of lunar laser ranging data requires very accurate calculations of the lunar physical librations. Libration terms are given which arise from the additive and planetary terms in the lunar theory. The large size of the recently discovered terms due to third degree gravitational harmonics will allow some of these harmonics to be measured, in addition to and, by laser ranging to the Moon. Combining the laser ranging determinations of = 630.6 ± 0.5 × 10–6 and = 226.4 ± 3.0 × 10–6 with lunar orbiter measurements ofC 20 andC 22 givesC/MR 2=0.395 -0.010 +0.006 . Numerical integration promises to be an effective method of calculating librations. Comparison of numerical integrations with analytic series indicates that the calculation of the series due to third and fourth degree harmonics is not yet as accurate as the more extensively developed second degree terms.Communication presented at the Conference on Lunar Dynamics and Observational Coordinate Systems, held January 15–17, 1973, at the Lunar Science Institute, Houston, Tex., U.S.A.  相似文献   

19.
The diagnostic potentialities of the torsional oscillations for probing the structure of the interiors of the Moon are investigated. Models with no core, a liquid core, and a solid core are considered. The profiles of compressional and shear wave velocities V P and V S for the lunar interior estimated by Bills and Ferrari (1977), Goins et al. (1981), and Nakamura (1983) from the Apollo lunar seismic network are used. For all these models, the periods of torsional oscillations for n = 2–100 and four overtones have been calculated. The derivatives of the dimensionless eigenfrequency with respect to the dimensionless shear modulus and density are calculated and tabulated for use. These data can be used to determine corrections to the model density and shear modulus distributions due to their small change. The damping of torsional oscillations is studied. Several trial radial distributions of the dissipative function Q are considered.  相似文献   

20.
The identification of hydrogen in a range of lunar samples and the similarity of its abundance and isotopic composition with terrestrial values suggest that water could have been present in the Moon since its formation. To quantify the effect of water on early lunar differentiation, we present new analyses of a high‐pressure, high‐temperature experimental study designed to model the mineralogical and geochemical evolution of the solidification material equivalent to 700 km deep lunar magma oceans first reported in Lin et al. (2017a). We also performed additional experiments to better quantify water contents in the run products. Water contents in the melt phases in hydrous run products spanning a range of crystallization steps were quantified directly using a secondary ion mass spectrometry (SIMS). Results suggest that a significant but constant proportion (68 ± 5%) of the hydrogen originally added to the experiments was lost from the starting material independent of run conditions and run duration. The volume of plagioclase formed during our crystallization experiments can be combined with the measured water contents and the observed crustal thickness on the Moon to provide an updated lunar interior hygrometer. Our data suggest that at least 45–354 ppm H2O equivalent was present in the Moon at the time of crust formation. These estimates confirm the inference of Lin et al. (2017a) that the Moon was wet during its magma ocean stage, with corrected absolute water contents now comparable to estimates derived from the water content in a range of lunar samples.  相似文献   

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