对月球形状的估算

1799年,Laplace发现月球的3个主惯量矩,与月球的轨道和自转状态并不相符.有些学者认为,这可能是现在的月球仍保留了早期的"化石"形状.大约在三十多亿年前,月球曾经离地球很近并且转得较快,然后月球逐渐迁移远离地球并且转动得慢了下来.在此迁移的较早时期,月球受到了引潮力和自转离心力的作用,成为一个椭球体.并且很快凝固.所幸的是,固态月球的岩石圈较为稳定,使我们现在仍然能够看到很早时期月球的形状.文中利用月球天平动参数以及引力场系数,计算了椭球体3个主向径a,b,c的长度和月球的平衡潮形状,得到如下3个结论:(1)开始时月球离地球是非常近的,大约在三十亿年前月球可能已经冷却和固化,现在的月球基本上保留了凝结时的形状.(2)证明了液态月球的潮汐形变是月球平衡潮高度的1.934倍.因此用月球引力场推算月球形状时,必需考虑到流体勒夫数hf=1.934的影响.(3)根据月球三个主轴a,6,c的长度之差,推算了月球临凝固时的月地距离为1.7455×1O8m,自转周期为3.652 day.从而推算出月球临凝固时的恒星月长度为8.34day.因此在月球凝结时,月球被锁定在与自转速率比为2:1的共振轨道上.     

行星(月球)自转监测望远镜的原理样机地面验证实验

类地行星(月球)自转监测望远镜的科学目标是在行星(月球)表面现场测量行星(月球)自转并研究其内部结构和物理性质.为了验证全新的观测原理和资料处理方法,项目团队设计制造了一套原理样机,在一台商用天文望远镜的光路前端增加3面反射镜组,使其具有同时观测3个视场的能力.自2017年起在地面上开展了观测实验,获得了混合有3视场星象的图像.通过计算星象在前后图像上的位移实现了归属视场识别,使得观测效果与分视场独立观测等同,证明了用一台设备同时观测多视场的可行性.处理图像并通过3个视场中心的指向变化归算地球自转轴的空间指向,与理论值比较偏差平均约1′′,证明了观测原理和数据处理方法有效.对各种观测误差来源进行了分析,包含大气折射、仪器热稳定性和光学分辨能力的影响等,指出采用更长焦距的望远镜可以提高空间分辨率,优化形变控制可以提高观测稳定性.改进多视场同时观测中的光学设计也有助于精度的提高.     

“New” lunar meteorites: Implications for composition of the global lunar surface,lunar crust,and the bulk Moon

Abstract— New data for lunar meteorites and a synthesis of literature data have significant implications for the interpretation of global Th data and for the Moon's bulk composition. As presently calibrated (Prettyman et al. 2002), the Lunar Prospector gamma‐ray data imply that the average global surface Th = 1.58 μg/g. However, that calibration yields implausibly high concentrations for the three most Th‐poor documented sampling sites, it extrapolates to a nonzero Lunar Prospector Th, ?0.7 μg/g, at zero sample Th, and it results in a misfit toward too‐high Th when compared with the global regolith Th spectrum as constrained using mainly lunaite regolith breccias. Another problem is manifested by Th versus K systematics. Ground truth data plot consistently to the high‐Th/K side of the Prospector data trend, offset by a factor of 1.2. A new calibration is proposed that represents a compromise between the Th levels indicated by ground truth constraints and the Prettyman et al. (2002) calibration. Conservatively assuming that the Th versus K issue is mostly a K problem, the average global surface Th is estimated to be ?1.35 μg/g. The Moon's remarkable global asymmetry in KREEP abundance is even more pronounced than previously supposed. The surface Th concentration ratio between the hemisphere antipodal to the Procellarum basin and the hemisphere centered on Procellarum is reduced to 0.24 in the new calibration. This extreme disparity is most simply interpreted as a consequence of Procellarum's origin at a time when the Moon still contained at least a thin residual layer of a global magma ocean. Allowing for diminution of Th with depth, the extrapolated bulk crustal Th is ?0.73 μg/g. Further extrapolation to bulk Moon Th yields ?0.07 μg/g, which is nearly identical to the consensus estimate for Earth's primitive mantle. Assuming chondritic proportionality among refractory lithophile elements implies Al₂O₃ of approximately 3.8 wt%. The Moon's bulk mantle mg ratio is only weakly constrained by seismic and mare‐basaltic data. KREEP‐and mare‐free lunaite regolith samples, other thoroughly polymict lunar meteorites, and a few KREEP‐free Apollo highland samples manifest a remarkable anticorrelation on a plot of Al₂O₃ versus mg. This trend implies that an important component of the Moon is highly magnesian. The bulk Moon is inferred to have an Earth‐like oxide mg ratio of ?87–88 mol%. The close resemblance between the bulk Moon and Earth's primitive mantle extends to moderately volatile elements, most clearly Mn. Unless major proportions of Cr and V are sequestered into deep mantle spinel, remarkably Earth‐like depletions (versus chondrites) are also inferred for bulk Moon Cr and V.     

Fossil figure contribution to the lunar figure

The unusual shape of the Moon given its present rotational and orbital state has been explained as due to a fossil figure preserving a record of remnant rotational and tidal deformation (Jeffreys, H. [1915]. Mem. R. Astron. Soc. 60, 187–217; Lambeck, K., Pullan, S. [1980]. Phys. Earth Planet. Interiors 22, 29–35; Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652–655). However, previous studies assume infinite rigidity and ignore deformation due to changes in the rotational and orbital potentials as the Moon evolves to the present state. We interpret the global lunar figure with a physical model that takes into account this deformation. Although the Moon deforms in response to rotational and orbital changes, a fossil figure capable of explaining the observed figure can be preserved by an elastic lithosphere.     

Analysis of Lunar Terrain Altitudes and Correlation Links between the Terrain and Gravitational Field; Preliminary Conclusions on the Global Density Inhomogeneities of the Lunar Crust

The harmonic and statistical analysis of lunar terrain altitudes has been performed based on the procedure developed by the authors. The explanations for the displacements of the Moon's figure relative to the center of mass and for the shift of the major equatorial axis relative to the earthward direction have been given. The maps have been plotted for the density anomalies in the near-surface layers of the Moon that correspond to mascons (with negative correlation between the field and terrain mainly for N= 10, 11) and other variants of links between the gravitational field and terrain (with positive correlation between the field and terrain). It has been shown that the harmonics of the degree N= 5–9 mainly correspond to the isostatic compensation of the terrain in the near-surface layers of the crust; the low harmonics (N< 5) correspond to the isostatic compensation of the terrain in the deeper layers, while the harmonics of the degrees N > 11 may indicate the presence of tension in the crust generated by small structures of the terrain. Based on the maps, possible locations of deposits of volatile elements (mainly on the far side of the Moon and in the northern cir-cumpolar region) and other natural resources have been determined.

     

The Ground-based Experiment of the Prototype of Planetary (& Lunar) Rotation Monitor Telescope

The scientific objective of the Planetary (& Lunar) Rotation Monitor (PRM) telescope is to study the terrestrial planet's (the Moon's) rotation and its interior structure and physics by in-situ observation. In order to verify the brand new principle of observations and the data processing method, the prototype of the telescope is designed and manufactured. The prototype's optical system consists of a commercial telescope and trihedron mirror set placed at the entrance of its light path to realize the capability of observing three fields of view (FOVs) simultaneously. The ground-based validation observation began in 2017, and the images containing the stars from three FOVs were achieved. Star images from different FOVs are initially mixed together, but they can be classified into the three FOVs respectively by calculating the displacement of star images on the CCD plate between two adjacent exposures, to make the observational effect be identical with three independent observations of the three FOVs respectively. After image processing, from the orientation variation of the three FOVs simultaneously in space due to the Earth's rotation, the direction of the rotation axis of the Earth in space can be derived. Its deviation from the theoretical value is about 1${}^{″}$ in average, indicating that the working principle and data processing method are effective. The main errors in observations are discussed, including the atmospheric refraction, the thermal deformation of the commercial telescope tube, the low optical resolution caused by the short focal length, the optical aberration in the multi-FOV observation, etc. It is indicated that the spatial resolution of the telescope can be enhanced with a longer focal length, and the observational reliability can be improved by optimizing the thermal deformation control. Improving the optical design in the simultaneous observation of multiple FOVs will also be helpful to the accuracy enhancement.     

Extension of Cassini's Laws

We investigate the Cassini's laws which describe the rotational motion in a 1:1 spin-orbit resonance. When this rotational motion follows the conventional Cassini's laws, the figure axis coincides with the angular momentum axis. In this case we underline the differences between the rotational Hamiltonian for a 'slow rotating' body like the Moon and for a 'fast rotating' body like Phobos. Then, we study a more realistic rotational Hamiltonian where the angle J between the figure axis and the angular momentum axis could be different from zero. This Hamiltonian has not been studied before. We have found a new particular solution for this Hamiltonian which could be seen as an extension of the Cassini's laws. In this new solution the angle J is constant, which is not zero, and the precession of the angular momentum plane is equal to the mean motion of the argument of pericenter of the rotating body. This type of rotational motion is only possible when the orbital eccentricity of the rotating body is not zero. This new law enables describing in particular, the Moon mean rotational motion for which the mean value of the angle J is found to be equal to 103.9±0.7 s of arc.     

Tektites - volcanic ejecta from the moon?

The problem of the origin of the enigmatic tektites is still unsolved. The two leading hypotheses - viz., ejecta from terrestrial impacts, and ejecta from lunar volcanoes or lunar impacts, each encounters serious difficulties. The former has ballistic and water content difficulties, while the latter has some compositional difficulties, especially in the trace elements, as determined from the returned samples. It is possible that the latter problem may be met through lunar volcanic ejecta from sites suggesting more differentiation than the majority of the Moon. That such features may exist is suggested from the identity of some granitic material in the returned rocks and soil samples implying fairly sizable source regions on the Moon. The rare terrestrial strewn tektite fields require restrictive ballistic trajectories from the Moon. Calculations reveal that ellipses of varying, decreasing sizes which depend on velocity of vertical ejection from which ejecta will intersect the earth at low-entrance angles occur on the nearside of the Moon. Reasonable velocities were chosen (2.55 to 3.0 km s^?1) and these ellipses circumscribe areas with longitudes between 30 and 50° east and latitudes between 7° north and south of the Moon's equator. These areas were searched for evidence of volcanism. As tektites have compositions ranging from acidic (major tektites) to basic (micro-tektites) contents of silica (SiO₂) both acidic and basic volcanic features were sought. Since tektites range in age from about 30 million to 700000 yr old, they imply recent volcanism. Lunar Transient Phenomena (LTP) and data from various Apollo missions indicate that mild internal activity may still be occurring on the Moon. LTP sites are logical sources to investigate, of which four occur within the above delimited regions. These and their surroundings were examined and a number of possible explosive volcanism sites were found. These sites are identified and discussed after a review of the manifestations found from the various kinds of terrestrial volcanism for which lunar counterparts were sought.     

Planetary and figure-figure effects on the moon's rotational motion

An accurate theory of the rotation of the Moon has been constructed by numerical integration. All direct perturbations on the Moon's rotational motion have been analysed. The requirements of the current observational accuracy are such that some improvements had to be added to the theoretical models. First, the gravitational figure of the Moon has been developed up to the fifth degree harmonics. Second, mutual potential effects between the figure of the Moon and the figure of the Earth have been expanded farther up. The direct action of planets must be taken into account, its effects being very small but not always negligible. The physical librations resulting of planetary effects and Earth-Moon figure-figure interactions are presented in this paper.     

A lunar core and the moon's magnetic field

The suggestion that the Moon's magnetic field is due to adiabatic magnetohydrodynamic convection of a molten core has been made by a number of recent authors. Considerations based on petrology, mass and rotational inertia limit the size of this hypothetical core to a few 100 km at the most. A proposal has been made that this core is either molten iron or iron sulfide. Fortunately, we know the properties of both molten iron and iron-sulfide at lunar core pressures. We can find no way of maintaining circulation in a hypothetical lunar core, as circulation is contingent upon a temperature gradient being greater than the adiabatic gradient, or an internal heat source.     

Petrology and mineralogy of volcanic glass in meteorite Northwest Africa 11801: Implications for their petrogenesis

The study of lunar magma evolution holds significant importance within the scientific community due to its relevance in understanding the Moon's thermal and geological history. However, the intricate task of unraveling the history of early volcanic activity on the Moon is hindered by the high flux of impactors, which have substantially changed the morphology of pristine volcanic constructs. In this study, we focus on a unique volcanic glass found in the lunar meteorite Northwest Africa 11801. This kind of volcanic glass is bead-like in shape and compositionally similar to the Apollo-14 and Apollo-17 very low-Ti glass. Our research approach involves conducting a comprehensive analysis of the petrology and mineralogy of the volcanic glass, coupled with multiple thermodynamic modeling techniques. Through the investigation, we aim to shed light on the petrological characteristics and evolutionary history of the glass. The results indicate that the primitive magma of the glass was created at 1398–1436°C and 8.3–11.9 kbar (166–238 km) from an olivine+orthopyroxene mantle source region. Then, the magma ascended toward the surface along a non-adiabatic path with an ascent rate of ~40 m s⁻¹ or 0.2 MPa s⁻¹. During the magma ascent, only olivine crystallized and the onset of magma eruption occurred at ~1320–1343°C. Finally, the glass cooled rapidly on the lunar surface with a cooling rate ranging between 20 and 200 K min⁻¹. Considerable evidence from petrology, mineralogy, cooling rate, and the eruption rate of the glass beads strongly supports the occurrence of ancient explosive volcanism on the Moon.     

On the deviation of the lunar center of mass to the East. Two possible mechanisms based on evolution of the orbit and rounding off the shape of the Moon

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.     

Lunar heat flow experiments: Science objectives and a strategy for minimizing the effects of lander-induced perturbations

Reliable measurements of the Moon's global heat flow would serve as an important diagnostic test for models of lunar thermal evolution and would also help to constrain the Moon's bulk abundance of radioactive elements and its differentiation history. The two existing measurements of lunar heat flow are unlikely to be representative of the global heat flow. For these reasons, obtaining additional heat flow measurements has been recognized as a high priority lunar science objective. In making such measurements, it is essential that the design and deployment of the heat flow probe and of the parent spacecraft do not inadvertently modify the near-surface thermal structure of the lunar regolith and thus perturb the measured heat flow. One type of spacecraft-related perturbation is the shadow cast by the spacecraft and by thermal blankets on some instruments. The thermal effects of these shadows propagate by conduction both downward and outward from the spacecraft into the lunar regolith. Shadows cast by the spacecraft superstructure move over the surface with time and only perturb the regolith temperature in the upper 0.8 m. Permanent shadows, such as from thermal blankets covering a seismometer or other instruments, can modify the temperature to greater depth. Finite element simulations using measured values of the thermal diffusivity of lunar regolith show that the limiting factor for temperature perturbations is the need to measure the annual thermal wave for 2 or more years to measure the thermal diffusivity. The error induced by permanent spacecraft thermal shadows can be kept below 8% of the annual wave amplitude at 1 m depth if the heat flow probe is deployed at least 2.5 m away from any permanent spacecraft shadow. Deploying the heat flow probe 2 m from permanent shadows permits measuring the annual thermal wave for only one year and should be considered the science floor for a heat flow experiment on the Moon. One way to meet this separation requirement would be to deploy the heat flow and seismology experiments on opposite sides of the spacecraft. This result should be incorporated in the design of future lunar geophysics spacecraft experiments. Differences in the thermal environments of the Moon and Mars result in less restrictive separation requirements for heat flow experiments on Mars.     

Orientation of the moon by numerical integration

The differential equations of rotational motion of the Moon are solved by numerical integration methods. Euler's dynamical equations transformed to a convenient form are treated by techniques analogous to ordinary orbit determination procedures. The proposed method is fully consistent with the ephemeris of the Moon and can utilize a variety of observational material for the solution of the selected parameters. The parameters are grouped into three distinct groups, namely:

--The physical libration angles of the Moon and their time rates at an arbitrary initial epoch.

--Physical constants featuring the principal moments of ineria of the Moon.

--Parameters associated with the particular observational material being used.

Examples are given of comparison between the proposed method and Eckhardt's 1970 model of the physical librations of the Moon. The merits of the new method are discussed in the light of conventional data sources like Earth-based or satellite-based photography as well as newly available data types like Laser ranging to retroreflectors on the Moon.     

Meteoritic material on the moon

Three types of meteoritic material are found on the Moon: micrometeorites, ancien planetesimal debris from the ‘early intense bombardment’, and debris of recent, crater-forming projectiles. Their amounts and compositions have been determined from trace element studies. The micrometeorite component is uniformly distributed over the entire lunar surface, but is seen most clearly in mare soils. It has a primitive, C1-chondrite-like composition, and comprises 1-1.5% of mature soils. Apparently it represents cometary debris. The mean annual influx rate is 2.4 × 10^?9 g cm^?2 yr^?1. It shows no detectable time variation or dependence on selenographic position. The ancient component is seen in highland breccias and soils more than 3.9 AE old. It has a fractionated composition, with volatiles depleted relative to siderophiles. The abundance pattern does not match that of any known meteorite class. At least two varieties exist (LN and DN, with Ir/Au, Re/Au 0.25-0.5 and > 0.5 the C1 value). Both seem to represent the debris of planetesimals that produced the mare basins and highland craters during the first 700 Myr of the Moon's history. It appears that the LN and DN objects impacted at less then 10 km s^?1, had diameters less than 100 km, contained more than 15% Fe, and were not internally differentiated. Both were depleted in volatiles; the LN objects also in refractories (Ir, Re). This makes it unlikely that the LN bodies served as important building blocks of the Moon. The crater-forming component has remained elusive. Only a possible hint of this component has been seen, in ejecta from Dune Crater and Apollo 12 KREEP glasses of Copernican (?) origin.     

Distortions of the Moon's figure due to the Earth

The second zonal and the second sectorial Stokes parameters of the Moon's gravitational field and/or the polar and equatorial flattenings of the lunar triaxial level ellipsoid have been explained by the tidal and rotational distortions due to the Earth. The Epoch at which the Moon's figure formation was finished has been estimated as 1.6 × 10⁹ y B. P. when the Earth-Moon distance was about 168 400 km and the orbital/rotational period of the Moon about 8 days.     

小行星(469219) Kamo`oalewa轨道的确定与误差分析

作为一颗与地球共轨道的小行星,(469219)Kamo'oalewa是一个具有很高研究价值的近地小天体,也是中国首次小行星探测计划的目标天体之一.针对其轨道特性,建立了兼顾太阳、地球和月球非球形引力作用的小行星动力学模型.并在该模型的基础上,利用国际小行星中心(Minor Planet Center,MPC)提供的2004|2018年间的光学观测数据对该小行星的轨道进行确定.拟合后观测残差的均方根误差约为0:2″(与美国喷气推进实验室的Horizons在线历表系统相当),其中2004年期间数据的观测残差有所改进.最后,对小行星(469219)Kamo'oalewa的轨道误差进行了详细分析,并预报了2020-2025年期间该小行星的轨道误差.     

Volatile emission on the moon; Possible sources and release mechanisms

Evidence for very recent emission of volatiles on the Moon is primarily of four types: (1) transient lunar optical events observed by Earth-based astronomers; (2) excursions on Apollo SIDE and mass spectrometer instruments; (3) localized Rn²²²/Po²¹⁰ enhancements on the lunar surface detected by Apollo 15 and 16 orbital alpha spectrometers; (4) presence in lunar fines of retrapped Ar⁴⁰ and other volatiles. Available evidence indicates that the release rate of volatile substances into the lunar atmosphere is not steady, but instead sporadic and episodic. Rn²²²/Po²¹⁰ anomalies are at locations that are among those from which transient events have most often been reported (edges of maria, certain specific craters), and are probably related to them. Volatiles emitted at maria rims may originate in the Moon's fluid core, reaching the surface through deep cylindrical fault systems that ring the maria borders. The sources of volatiles emitted at craters such as Aristarchus or Tsiolkovsky, which possess floors which are cracked or filled with dark lava and possess central peaks, are more likely to be local pockets of magma or trapped gas at shallower depths. The volatiles are produced directly by radioactive decay (He⁴, Ar⁴⁰, Rn) and by heating (other volatiles). The release by heating can occur either during melting or by ‘bakeout’ of unmelted materials. Release of gas into the lunar atmosphere is probably triggered by buildup of its own pressure. This may be assisted by tidal forces exerted on the Moon by the Earth. In addition to independent release, volatile emission is also expected to accompany other lunar activity, such as ash flows, if any lunar volcanism is presently active.

     

A search for lunar sodium

A search of the Moon for traces of sodium vapor similar to that found on Mercury was made with a multiprism spectroscope. The results were negative.