Insight-building models for lunar range and range rate

The analysis of range or Doppler data between sites on the Earth and Moon requires an accurate computation of the lunar orbit and detailed models of the orientation of the Earth and Moon. Models constructed to understand range and range rate can lack detail, but if they include the largest lunar orbit variations, tracking stations on a rotating Earth, and lunar sites on a synchronously rotating Moon, then they will display the largest effects for orbit elements, Earth orientation, tracking station locations, and lunar site coordinates. The range and range rate are expanded into periodic series. To understand accurate solutions, the largest periodic terms that are sensitive to various solution parameters indicate the sensitivity of data to solution parameters and the time spans needed for their determination. Conclusions include: cylindrical coordinates work well for sites on the rapidly rotating Earth, but Cartesian coordinates are more natural for the synchronously rotating Moon since the series for the three coordinate projections are distinct. For range and range rate data, daily, semimonthly, monthly, and longer periods are present. For Doppler data, the daily periods may be stronger and more useful than the long periods, particularly for terms associated with the terrestrial tracking station. Doppler data do not determine the lander coordinate toward the Earth well. Observational strategies for range and Doppler data are not identical. For all data types, one wishes a variety of hour angles, lunar declinations, times of month, and longer periods. A long span of high-quality range data can improve the lunar orbit, orientation of the Earth’s equator, and physical librations. The locations of new lunar sites or new tracking stations can be determined from shorter spans of data.     

A Model of Relation between Fluctuation of Double Differential Total Ionospheric Electron Content and Angular Distance of the Two Satellites Observed by Same-beam VLBI

Time delay and phase fluctuation are produced when the signals of a spacecraft are transmitted through the ionosphere of the earth, which give rise to a great influence on the measurement precision of VLBI (Very Long Baseline Interferometry). Using the 1-year same-beam VLBI data of 2 satellites (Rstar and Vstar) in the Japanese lunar exploration project SELENE, we obtained a model of the relation between the fluctuation of double differential total electron content in the ionosphere and the angular distance of the two satellites. For the 6 baselines, the root mean square r of fluctuation (in units of TECU) and the angular distance of the two satellites θ (in units of ^°) has a relation of r = 0.773θ + 0.562, and for the 4 VLBI stations, the relation is r = 0.554θ + 0.399 from the baselines inversion. The results can serve as a reference for the derivation of differential phase delay and for the occultation observation and study of planetary ionospheres.     

火星电离层无线电掩星探测仿真研究

对中俄联合火星星-星电离层掩星技术体制进行了分析和介绍,采用三维射线追踪方法对电离层掩星事件的电波观测值进行了模拟计算,并利用模拟的掩星观测数据进行了电子密度廓线反演,结果说明仿真算法可靠.利用仿真的方法,分别对掩星电波相位观测误差和卫星轨道误差等带来的反演误差进行了个例计算和分析,结果得到:5%周的相位测量误差对白天电离层掩星探测结果的影响可以忽略,而夜间电子密度测量的绝对误差小于4×108 m-3;卫星轨道误差对掩星的主要影响是导致电离层高度抬升或下降.结果表明,中俄联合火星电离层掩星探测技术体制先进,可望获得高精度的电子密度廓线;其技术体制也可以用于月球电离层环境的探测.     

Response of the Total Electron Content of Terrestrial Ionosphere to GRB041227

At 21:30 UT on 2004 December 27 an extremely strong gamma-ray burst swept across the earth and caused the part of the terrestrial upper atmosphere exposed to it to produce extra ionization. Sudden ionospheric disturbance (SID) events were simultaneously observed at many of the very low frequency (VLF) electric wave observing stations. Analyses of the X-ray data of the GOES satellite as well as the solar wind and interplanetary data of the ACE satellite with the relevant theories show that the observed SID event observed was indeed caused by GRB041227. We calculated the response of the total electron content (TEC) of the terrestrial ionosphere to this γ-ray burst using the observed data provided by the international GPS service network (IGS) and the data processing method of coherent summation. The result indicates that the GRB041227 produced by the SGR1806-20 had an evident effect on the terrestrial ionosphere: in the course of the burst the average ionospheric TEC increased, to a maximum size of about 0.04 TECU (1 TECU = 10¹⁶ el/m²), equivalent to a solar flare with importance of C or lower. The calculated result demonstrates once again that a remote celestial body can also affect the terrestrial space environment to some extent.     

The lunar dust environment

Each year the Moon is bombarded by about 10⁶ kg of interplanetary micrometeoroids of cometary and asteroidal origin. Most of these projectiles range from 10 nm to about 1 mm in size and impact the Moon at 10–72 km/s speed. They excavate lunar soil about 1000 times their own mass. These impacts leave a crater record on the surface from which the micrometeoroid size distribution has been deciphered. Much of the excavated mass returns to the lunar surface and blankets the lunar crust with a highly pulverized and “impact gardened” regolith of about 10 m thickness. Micron and sub-micron sized secondary particles that are ejected at speeds up to the escape speed of 2300 m/s form a perpetual dust cloud around the Moon and, upon re-impact, leave a record in the microcrater distribution. Such tenuous clouds have been observed by the Galileo spacecraft around all lunar-sized Galilean satellites at Jupiter. The highly sensitive Lunar Dust Experiment (LDEX) onboard the LADEE mission will shed new light on the lunar dust environment. LADEE is expected to be launched in early 2013.Another dust related phenomenon is the possible electrostatic mobilization of lunar dust. Images taken by the television cameras on Surveyors 5, 6, and 7 showed a distinct glow just above the lunar horizon referred to as horizon glow (HG). This light was interpreted to be forward-scattered sunlight from a cloud of dust particles above the surface near the terminator. A photometer onboard the Lunokhod-2 rover also reported excess brightness, most likely due to HG. From the lunar orbit during sunrise the Apollo astronauts reported bright streamers high above the lunar surface, which were interpreted as dust phenomena. The Lunar Ejecta and Meteorites (LEAM) Experiment was deployed on the lunar surface by the Apollo 17 astronauts in order to characterize the lunar dust environment. Instead of the expected low impact rate from interplanetary and interstellar dust, LEAM registered hundreds of signals associated with the passage of the terminator, which swamped any signature of primary impactors of interplanetary origin. It was suggested that the LEAM events are consistent with the sunrise/sunset-triggered levitation and transport of charged lunar dust particles. Currently no theoretical model explains the formation of a dust cloud above the lunar surface but recent laboratory experiments indicate that the interaction of dust on the lunar surface with solar UV and plasma is more complex than previously thought.     

Coordinate systems and lunar observing station positions

Satellite geodesy has yielded the locations of more than fifty stations in a single coordinate system referred to the Earth's center of mass with accuracies in the five to ten meter range. The following different methods have been used at Goddard to accomplish this.Dynamical solutions have been obtained for the locations of some fifty key stations using data from the GEOS satellite program. The distribution of observations about the stations is illustrated in terms of the data obtained for a typical station such as the one at Edinburg, Texas. Geopotential coefficients were held fixed in these solutions. The results of these dynamical determinations implied geodetic datum shifts which were then used to arrive at positions for some two hundred additional stations.Another approach involved the adjustment of the coordinates of seventeen stations on the basis of observations of short arcs of GEOS satellite orbits. These results were found to be consistent with those obtained through ground surveys to about five meters rms in each coordinate.Simultaneous solutions for station locations and geopotential coefficients have also yielded values for positions of some sixty stations, again in a coordinate system defined in terms of the Earth's center of mass.Lunar laser ranging and lunar occultation observing programs involve knowledge of the positions of the observing sites. In some cases the lunar observing program itself yields station coordinate information. In other cases greater reliance is placed upon independent determinations of site locations. The location of an occultation observation site at Olifantsfontein, for example, has been obtained in a center-of-mass system in both the dynamical and simultaneous satellite solutions. It is anticipated that a dynamical satellite solution will be extended in 1973 to obtain center-of-mass coordinates for a station in New Zealand. This will make it possible to tie an occultation site in that region to a dynamically determined coordinate system referred to the mass center. Coordinates for stations at Organ Pass, New Mexico, determined in both the dynamical and simultaneous solutions, and Edinburg, Texas, found in both the dynamical and short-arc adjustments, provide the basis for referring the location of a facility such as the McDonald Observatory to a center-of-mass system either through accurate ground surveying techniques or by means of a satellite geodesty tie. The latter approach has already been used, for example, to fix the position of an isolated site on Madagascar relative to a reference point in Africa and, in turn, to a center-of-mass coordinate system.Estimates of the accuracies of the satellite determinations are discussed.Theoretical aspects of coordinate systems associated with the Earth and the Moon are also considered.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.     

Moonquakes and lunar tectonism

With the succesful installation of a geophysical station at Hadley Rille, on July 31, 1971, on the Apollo 15 mission, and the continued operation of stations 12 and 14 approximately 1100 km SW, the Apollo program for the first time achieved a network of seismic stations on the lunar surface. A network of at least three stations is essential for the location of natural events on the Moon. Thus, the establishment of this network was one of the most important milestones in the geophysical exploration of the Moon. The major discoveries that have resulted to date from the analysis of seismic data from this network can be summarized as follows:

1. Lunar seismic signals differ greatly from typical terrestrial seismic signals. It now appears that this can be explained almost entirely by the presence of a thin dry, heterogeneous layer which blankets the Moon to a probable depth of few km with a maximum possible depth of about 20 km. Seismic waves are highly scattered in this zone. Seismic wave propagation within the lunar interior, below the scattering zone, is highly efficient. As a result, it is probable that meteoroid impact signals are being received from the entire lunar surface.
2. The Moon possesses a crust and a mantle, at least in the region of the Apollo 12 and 14 stations. The thickness of the crust is between 55 and 70 km and may consist of two layers. The contrast in elastic properties of the rocks which comprise these major structural units is at least as great as that which exists between the crust and mantle of the earth. (See Toks?zet al., p. 490, for further discussion of seismic evidence of a lunar crust.)
3. Natural lunar events detected by the Apollo seismic network are moonquakes and meteoroid impacts. The average rate of release of seismic energy from moonquakes is far below that of the Earth. Although present data do not permit a completely unambiguous interpretation, the best solution obtainable places the most active moonquake focus at a depth of 800 km; slightly deeper than any known earthquake. These moonquakes occur in monthly cycles; triggered by lunar tides. There are at least 10 zones within which the repeating moonquakes originate.
4. In addition to the repeating moonquakes, moonquake ‘swarms’ have been discovered. During periods of swarm activity, events may occur as frequently as one event every two hours over intervals lasting several days. The source of these swarms is unknown at present. The occurrence of moonquake swarms also appears to be related to lunar tides; although, it is too soon to be certain of this point.

These findings have been discussed in eight previous papers (Lathamet al., 1969, 1970, 1971) The instrument has been described by Lathamet al. (1969) and Sutton and Latham (1964). The locations of the seismic stations are shown in Figure 1.     

A 3D hybrid simulation study of the electromagnetic field distributions in the lunar wake

A three-dimensional hybrid code is used to study the electromagnetic disturbances in the solar wind that arise due to the absorption effect of the Moon. Due to the nearly insulating nature of the Moon, interplanetary magnetic fields (IMFs) can move through the interior without hindrance. However, the near-vacuum created in the wake region due to the lunar absorption effect will lead to enhancement of the strength of the magnetic field by a factor of about 1.4 in the middle of the lunar wake and lead to depletions at two sides. The situations arising from different orientations of the interplanetary magnetic fields relative to the radial direction are compared. Asymmetries of the inward diffusions both along and perpendicular to the field lines are also observed. The electric field formed from the plasma convection could reach a magnitude of 0.2–0.8 mV/m at the border of the wake. The role of the electric field on the inward accelerations is important to the geometry of the lunar wake.     

Optimization of lunar occultations for determining the positions of point-like X-ray sources

In view of the scheduled satellite mission EXOSAT (European X-Ray Observatory Satellite) of ESA (European Space Agency) the lunar occultation technique to determine the position of point-like X-ray sources is investigated. An error analysis for the source coordinates resulting from this technique is presented and an occultation strategy is proposed to achieve optimum lunar occultations. The analysis takes into account the errors of the space coordinates of the satellite and the Moon, the unevenness of the lunar surface, the intensities of source and background, the apparent angular velocity of the Moon as seen from the satellite, the finite sizes of the preoccultation position error boxes of the X-ray sources and the inaccuracies in the satellite orbit correction manoeuvres necessary to achieve the occultations.     

Design of lunar landing trajectory under constraints

The design of a lunar landing trajectory which satisfies certain constraints is considered and discussed. The constraints are of two kinds, kinetic constraints, which deal with the relative positions among the Sun, the Moon, the Earth, the spacecraft and tracking stations, and dynamic constraints, which deal with the orbital motion of the spacecraft. After a discussion of the characteristics of lunar flight trajectory, a method of designing standard flight trajectory is suggested that satisfies the constraints. This method is applied to the Chinese lunar landing flight and to the pre-design of the orbit of a lunar satellite.     

An Emulation Research on the Radio Occultation Exploration of Martian Ionosphere

The technical system of the Sino-Russian joint satellite-to-satellite Mars ionosphere occultation is analyzed and introduced. The analogue computation of the observed values of the radio waves of the ionosphere occultation event is carried out by adopting the three-dimensional ray tracking method and the electron density profile inversion is conducted by means of the simulated occultation observational data, with the result showing that the emulation algorithm is reliable. By taking advantage of the emulation method the case computation and analysis of the inversion errors caused by the observational error of the occultation radio wave phase and the satellite orbital error are respectively carried out, and it is obtained from the result that the effect of the phase measuring error of the 5% circle on the result of the daytime ionosphere occultation exploration may be neglected, while the absolute error of the night electron density measurement is less than 4 × 108 m^?3, and the main effect of the satellite orbital error on the occultation leads to the lifting or falling of the ionospheric height. The result shows that the technical system of the Sino-Russian joint Mars ionosphere occultation exploration is advanced. It can be expected that the high accuracy electron density profile is obtained and the technical system can be applied to the exploration of the lunar ionospheric environment.     

A theory for the interpretation of lunar surface magnetometer data

The solution to the problem of the motion of the Moon relative to spatial irregularities in the interplanetary magnetic field is found. The lunar electrical conductivity is modeled by a two-layer conductivity profile. For the interaction of the Moon with the corotating sector structure of the interplanetary magnetic field it is found that the magnetic field in the lunar shell is the superposition of an oscillatory uniform field, an oscillatory dipole field and anoscillatory field that is toroidal about the axis of the motional electric field. With various lunar conductivity models and the theory of this paper, lunar surface magnetometer data can be quantitatively interpreted to yield information on the conductivity and consequently the temperature of the lunar core.Presently visiting the Max-Planck-Institut für Physik und Astrophysik, München, Germany.     

The improvement of the lunar ephemeris

At present the fundamental lunar ephemeris is based on Brown's theory of the motion of the Moon with improvements based on the bypassing of Brown's Tables, the removal of the great empirical term, the substitution of the relevant constants of the IAU system of astronomical constants and the retransformation of Brown's series in rectangular coordinates to spherical coordinates. Even so this ephemeris does not represent adequately the recent range and range-rate radio observations, and it will be inadequate for use in the analysis of laser observations of corner reflectors on the Moon. Numerical integrations for these purposes have already been made at the Jet Propulsion Laboratory, but improved theoretical developments are also required; new solutions of the main problem are in hand elsewhere. Work at H.M. Nautical Almanac Office is aimed at obtaining improved values of the constants of the lunar orbit by a rediscussion of occultation observations made since 1943 and at the redevelopment of the series for the planetary perturbations using more precise theories of the motion of the Sun and planets. The techniques and preliminary results of exploratory numerical integrations were briefly described.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, 17–23 August, 1969.     

Seismoacoustic lunar fields and lunar electromagnetic (nonthermal) emission

For better insight into lunar radio emissions, observations of the Moon were made during the maximal Geminids meteor shower and during the lunar eclipse without external effects. Statistical processing of the obtained data was carried out. It was found that the lunar endogenous and exogenous processes are displayed in both the seismic-emission fields and lunar nonthermal electromagnetic emissions. Both types of signals demonstrate good correlation. The seismic and electromagnetic emission processes have common periodicities, some of which determine the internal structure of the Moon. Similar regularities are expected for other bodies of the Solar System.     

The Experiment and Analysis on VLBI Observations of Space Passive Hydrogen Maser

China plans to establish a lunar orbital VLBI (Very Long Baseline Interferometer) station around 2025, which will carry a space passive hydrogen maser as the time and frequency reference. Since it is the first time to use a space passive hydrogen maser for VLBI observation, its feasibility needs to be studied and verified. Therefore, we carried out VLBI observations using the space passive hydrogen maser as the frequency reference. In the experiment, the active hydrogen atomic clock and space passive hydrogen maser were used as the frequency standard, and the alternate VLBI observations of China’s Mars probe TW1 (Tianwen 1) were carried out using the 25 m radio telescope at Sheshan, Shanghai, and other VLBI stations. The results of data processing and analysis show that the standard deviation of VLBI residual group delay based on both active hydrogen atomic clock and space passive hydrogen maser are within 0.5 ns, which indicates that the space passive hydrogen maser can meet the accuracy requirements of VLBI measurement for deep space exploration, and verify its feasibility as the frequency standard of lunar orbital VLBI stations.     

日本SELENE月球探测计划和卫星间多普勒跟踪的数学模型

日本月球探测计划（SELENE）定于2004年夏季利用HIIa火箭发射一组共3颗绕月人造卫星。他们是主卫星、跟踪中断卫星和空间VLBI电波源。其主要科学目标之一是利用对绕月卫星的多普勒跟踪数据精确测定月球重力场,研究月球的起源与演化。SELENE计划中实现这个科学目标的关键技术是引入中继卫星,目的在于当处于低轨道的主卫星飞行到月球背面地面观测站无法观测时,采用卫星间跟踪方法（SST）,建立地面站与主卫星之间的联系,以得到月球背面重力场的直接测量数据。介绍了几种典型的四程卫星间多普勒跟踪模式和相应的数学模型,并针对SELENE计划中采用的特殊四程多普勒跟踪模式建立了卫星相对观测站速度与跟踪信号多普勒频移之间的转换关系。提出了利用GEODYNⅡ定轨分析软件处理SELENE多普勒跟踪数据的流程。     

星载氢钟VLBI观测实验及分析

中国计划于2025年左右建立月球轨道VLBI (Very Long Baseline Interferometer)测站,将会搭载被动型星载氢钟作为时间频率标准.由于是首次在VLBI观测中使用星载氢钟,需要研究和验证其可行性.因此,利用星载氢钟作为频率基准开展了VLBI观测.实验时,分别使用主动型地面氢钟和被动型星载氢钟作为频率基准,利用上海天文台佘山25 m射电望远镜和其他测站对我国火星探测器天问一号进行了交替VLBI观测.数据处理分析结果表明,基于地面氢钟与星载氢钟的VLBI残余群时延标准差均在0.5 ns以内,表明星载氢钟可满足深空探测VLBI测定轨的精度要求,验证了其作为月球VLBI测站频率基准的可行性.     

Comparison of lunar ultraviolet reflectivity with that of terrestrial rock samples

The ultraviolet and visible albedos of a number of terrestrial basalts, gabbros and anorthosites have been investigated over the wavelength range 800 Å to 8000 Å and compared with previously reported measurements of the lunar albedo. For most of the terrestrial samples the albedo changed only slightly between visible and middle ultraviolet wavelengths in striking contrast to the Moon where the ultraviolet albedo is about a factor of five or ten less than it is in the visible. Some of the lighter coloured terrestrial anorthositic samples were however found to have albedo curves that fairly closely approximate the ultraviolet darkening of the Moon. The general shape of the lunar ultraviolet albedo may be caused by a layer of anorthositic fragments on the Moon such as have been found to be a very abundant component of the Apollo ‘coarse-fines’.     

New views of the lunar plasma environment

A rich set of new measurements has greatly expanded our understanding of the Moon–plasma interaction over the last sixteen years, and helped demonstrate the fundamentally kinetic nature of many aspects thereof. Photon and charged particle impacts act to charge the lunar surface, forming thin Debye-scale plasma sheaths above both sunlit and shadowed hemispheres. These impacts also produce photoelectrons and secondary electrons from the surface, as well as ions from the surface and exosphere, all of which in turn feed back into the plasma environment. The solar wind interacts with sub-ion-inertial-scale crustal magnetic fields to form what may be the smallest magnetospheres in the solar system. Proton gyro-motion, solar wind pickup of protons scattered from the dayside surface, and plasma expansion into vacuum each affect the dynamics and structure of different portions of the lunar plasma wake. The Moon provides us with a basic plasma physics laboratory for the study of fundamental processes, some of which we cannot easily observe elsewhere. At the same time, the Moon provides us with a test bed for the study of processes that also operate at many other solar system bodies. We have learned much about the Moon–plasma interaction, with implications for other space and planetary environments. However, many fundamental problems remain unsolved, including the details of the coupling between various parts of the plasma environment, as well as between plasma and the surface, neutral exosphere, and dust. In this paper, we describe our current understanding of the lunar plasma environment, including illustrative new results from Lunar Prospector and Kaguya, and outstanding unsolved problems.     

电离层掩星反演的正则最大熵法

电离层掩星数据现已成为电离层观测数据的重要来源,对掩星数据的反演研究一直是掩星研究的热点.传统采用的改正TEC(1btal Electron Content)的Abel变换反演法为线性反演法,它会把测量误差带入反演结果中.为改善反演效果受测量误差的影响,引入两种非线性的反演方法一正则化和正则最大熵反演法.随后设计模拟试验,对3种方法进行验证、比较,得到正则最大熵反演法可以很好地减小测量误差的影响.