Some qualitative manifestations of the physical libration of the Moon by observing stars from the lunar surface

Targets and problems of the future Japanese project ILOM (In situ Lunar Orientation Measurement), which is planned to be realized as one kind of observations of lunar rotation at the second stage of SELENE-2 mission, are briefly described in the article. Inverse problem of lunar physical libration is formulated and solved. Accuracy of libration angles depending on accuracy of measuring selenographic coordinates is estimated. It is shown that selenographic coordinates of polar stars are insensitive to longitudinal librations τ(t). Comparing coordinates calculated for two models of a rigid and deformable Moon is carried out and components sensitive to Love number k₂ and to anelastic time delay are revealed.     

Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging

Lunar laser ranging (LLR) measurements are crucial for advanced exploration of the laws of fundamental gravitational physics and geophysics as well as for future human and robotic missions to the Moon. The corner-cube reflectors (CCR) currently on the Moon require no power and still work perfectly since their installation during the project Apollo era. Current LLR technology allows us to measure distances to the Moon with a precision approaching 1 mm. As NASA pursues the vision of taking humans back to the Moon, new, more precise laser ranging applications will be demanded, including continuous tracking from more sites on Earth, placing new CCR arrays on the Moon, and possibly installing other devices such as transponders, etc. for multiple scientific and technical purposes. Since this effort involves humans in space, then in all situations the accuracy, fidelity, and robustness of the measurements, their adequate interpretation, and any products based on them, are of utmost importance. Successful achievement of this goal strongly demands further significant improvement of the theoretical model of the orbital and rotational dynamics of the Earth–Moon system. This model should inevitably be based on the theory of general relativity, fully incorporate the relevant geophysical processes, lunar librations, tides, and should rely upon the most recent standards and recommendations of the IAU for data analysis. This paper discusses methods and problems in developing such a mathematical model. The model will take into account all the classical and relativistic effects in the orbital and rotational motion of the Moon and Earth at the sub-centimeter level. The model is supposed to be implemented as a part of the computer code underlying NASA Goddard’s orbital analysis and geophysical parameter estimation package GEODYN and the ephemeris package PMOE 2003 of the Purple Mountain Observatory. The new model will allow us to navigate a spacecraft precisely to a location on the Moon. It will also greatly improve our understanding of the structure of the lunar interior and the nature of the physical interaction at the core–mantle interface layer. The new theory and upcoming millimeter LLR will give us the means to perform one of the most precise fundamental tests of general relativity in the solar system.     

The Japanese lunar mission SELENE: Science goals and present status

The Japanese lunar mission SELENE (SELenological and ENgineering Explorer) has been in development to target launch scheduled 2007 summer by H-IIA rocket. The SELENE is starting final integration test after SAR (System Acceptance Review), SRR (System Reliability Review) and instrument environment test. The SELENE is a remote-sensing mission orbiting 100 km altitude of the Moon for nominal one year and extended some months to collect the data for studying the origin and evolution of the Moon. Fourteen instruments and experiment systems are preparing for studies of the Moon, in the Moon, and from the Moon; global element and mineral compositions, topological structure, gravity field of whole moon, and electromagnetic and particle environment of the Moon. The new data center SOAC (SELENE Operation and data Analysis Center) are completed to construct in JAXA Sagamihara campus, and end-to-end test will be carried out between SOAC and data downlink stations.     

一种小天体旋转参数估计方法

小天体旋转参数是科学数据,也是小天体测绘,着陆导航的基础数据.研究一种在小天体探测接近段过程中使用的基于图像上特征点跟踪和扩展卡尔曼滤波器的小天体旋转参数估计方法.该方法首先建立小天体旋转关系模型,表示小天体在相机坐标系中的姿态变化;然后定义小天体旋转的状态方程,推到了扩展卡尔曼滤波器的计算过程.通过对观测图像序列上的特征点跟踪,利用扩展卡尔曼滤波器方法得到小天体旋转轴指向和自转角速度估计.实验中,在仿真相机与小天体相机100 km距离上,分析了相机坐标系小天体坐标系之间的四元数初值,图像上特征点跟踪精度,相机的观测指向等因素对小天体旋转参数估计精度的影响.实验结果表明,提出的基于图像特征点跟踪和扩展卡尔曼滤波器的小天体旋转参数估计方法能够得到具有较高精度的估计结果.     

Surface temperatures at the nearside of the Moon as a record of the radiation budget of Earth’s climate system

Understanding the balance between incoming radiation from the Sun and outgoing radiation from Earth is of critical importance in the study of climate change on Earth. As the only natural satellite of Earth, the Moon is a unique platform for the study of the disk-wide radiation budget of Earth. There are no complications from atmosphere, hydrosphere, or biosphere on the Moon. The nearside of the Moon allows for a focus on the solar radiation during its daytime, and on terrestrial radiation during its nighttime. Additionally, lunar regolith temperature is an amplifier of the terrestrial radiation signal because lunar temperature is proportional to the fourth square root of radiation as such is much more sensitive to the weak terrestrial radiation in nighttime than the strong solar radiation in daytime. Indeed, the long-term lunar surface temperature time series obtained inadvertently by the Heat Flow Experiment at the Apollo 15 landing site three decades ago may be the first important observation from deep space of both incoming and outgoing radiation of the terrestrial climate system. A revisit of the lunar surface temperature time series reveals distinct characteristics in lunar surface daytime and nighttime temperature variations, governed respectively by solar and terrestrial radiation.     

Project “The Moon – 2012+”: Spin-orbital evolution,geophysics and selenodesy of the Moon

The Russian scientific project “The Moon – 2012+” is directed at solving fundamental problems of celestial mechanics, selenodesy and geophysics of the Moon through the pursuance of theoretical research and computer simulations of the following fields.     

月球表面元素含量的定量分析方法

综合了月球元素定量研究在探测手段和定量方法等方面取得的最新进展。在探测手段方面,介绍了美国最近发射的克莱门汀和月球勘探者探测器使用的多谱段成像仪、中子探测仪以及γ谱仪的主要性能,在定量方法方面,讨论Fe、Ti以及稀土元素等在定量方法上的进展。     

Autonomous navigation for lunar final approach based on gravity gradient measurements

Lunar final approach navigation is critical for pin-point lunar landing in future missions. This study investigates the use of lunar gravity gradient measurements for autonomous navigation of a lunar probe during the final approach phase. As the spacecraft approaches the Moon, the strength of gravity gradient signals improves. A spaceborne gravity gradiometer can precisely measure local gravity gradients, and the latest lunar gravity model GL1500E is used to provide reference values. The employed truncation degree and order of the gravity model are increased stepwise considering the decreasing altitude of the spacecraft in order to reach a compromise between computational costs and model accuracy. An iterative Kalman filter is developed for coupled orbit and attitude estimation using gravity gradient measurements and attitude quaternions obtained from star sensors. A simulated spacecraft with a gradiometer noise level of 0.01 E is considered. Simulation results show that the spacecraft’s position converges rapidly and achieves an accuracy of less than 100 m at the last epoch.     

Hipparchus vs. Ptolemy and the Antikythera Mechanism: Pin–Slot device models lunar motions

The ancient Greek astronomical calculator known as the Antikythera Mechanism has been analyzed using geometrical, calculus, trigonometric and complex variable methods. This analysis demonstrates that the Mechanism modeled the variations in the Moon’s angular velocity as seen from the Earth, to better than 1 part in 200. A major implication of this analysis is that the Antikythera Mechanism of the 2nd century BCE modeled the anomalistic motion of the Moon more accurately than Ptolemy’s account of Hipparchus’s theory of the 2nd century CE. In the present work, mathematics, astronomy, history and methodology of the sciences combine in the study of a unique artifact, preserved for posterity in an ancient ship that sank in the Mediterranean 2100 years ago and recovered by Greek sponge divers at the dawn of the 20th century.     

月球探测器发射机会分析

发射月球探测器实际上是使探测器与月球交会的问题,由于月球位置的变化,选择不同的交会日期相应的地月转移轨道是不相同的。文章分析了月球在一个恒星月内位置变化与相应的地月转移轨道升交点赤经和近地点幅角变化的关系,在这个基础上讨论了发射机会和发射窗口问题。     

Reports to COSPAR from the International Lunar Exploration Working Group (ILEWG)

In accordance with its charter, the International Lunar Exploration Working Group (ILEWG) reports to COSPAR, and a summary was given at the Beijing COSPAR 2006 Assembly on ILEWG activities conducted since the previous COSPAR 2004 assembly held in Paris. This included reports from the 6th and 7th ILEWG International Conference on Exploration and Utilization of the Moon, held respectively in Udaipur, India on 22–26 November 2004 (ICEUM6) and in Toronto, Canada on 18–23 September 2005 (ICEUM7). We give in this issue of Advances in Space Research the “lunar declarations” from these ICEUM conferences, as well as for the ICEUM8 conference held in Beijing immediately after the 2006 COSPAR Assembly. One year after the COSPAR Beijing assembly, the 9th ILEWG International Conference on Exploration and Utilization of the Moon (ICEUM9), was held in Sorrento, Italy on 18–23 September 2007. We report also in this issue the “Sorrento Lunar Declaration” in advance of the ILEWG formal report to be given at the COSPAR Assembly to be held in Montreal, Canada in July 2008.     

Cramér-rao lower bound for pulsar rotation parameters estimation with X-ray pulsar observation data

In this paper, the Cramér-Rao Lower Bound (CRLB) for estimating the rotation parameters of pulsars using X-ray pulsar observation data is deduced, and the calculation equation is presented. In order to verify the correctness of the deduced equation, we use the X-ray pulsar observation data to estimate pulsar rotation parameters, and obtain the root mean square error (RMSE) of the estimated pulsar rotation parameters through conducting repeated experiments. The experimental results suggest that when the observation time increases, the RMSE gradually approaches the estimated CRLB, and that when the observation time is 2.4 × 10⁶ s, the error between the RMSE of pulsar frequency estimation and the CRLB stays at 10^?11 order of magnitude. This verifies that the CRLB expression deduced in this paper is the theoretical lower bound for estimating pulsar rotation parameters. The deduced CRLB in this paper helps determine the minimum variance estimator for pulsar rotation parameter estimation using X-ray pulsar data, providing a benchmark for the comparison between the minimum variance estimator and other estimators.     

A lunar cargo mission design strategy using variable low thrust

A design technique for a near optimal, Earth–Moon transfer trajectory using continuous variable low thrust is proposed. For the Earth–Moon transfer trajectory, analytical and numerical methods are combined to formulate the trajectory optimization problem. The basic concept of the proposed technique is to utilize analytically optimized solutions when the spacecraft is flying near a central body where the transfer trajectories are nearly circular shaped, and to use a numerical optimization method to match the spacecraft’s states to establish a final near optimal trajectory. The plasma thruster is considered as the main propulsion system which is currently being developed for crewed/cargo missions for interplanetary flight. The gravitational effects of the 3rd body and geopotential effects are included during the trajectory optimization process. With the proposed design technique, Earth–Moon transfer trajectory is successfully designed with the plasma thruster having a thrust direction sequence of “fixed-varied-fixed” and a thrust acceleration sequence of “constant-variable-constant”. As this strategy has the characteristics of a lesser computational load, little sensitivity to initial conditions, and obtaining solutions quickly, this method can be utilized in the initial scoping studies for mission design and analysis. Additionally, derived near optimal trajectory solution can be used as for initial trajectory solution for further detailed optimization problem. The demonstrated results will give various insights into future lunar cargo trajectories using plasma thrusters with continuous variable low thrust, establishing approximate costs as well as trajectory characteristics.     

我国探月工程技术发展综述

我国的探月工程,在2020年前分“绕、落、回”三步实施。本文以我国探月工程各次任务为脉络,针对目前已经完成的“嫦娥1号”“嫦娥2号”“嫦娥3号”及“嫦娥5号”高速再入试验任务,简述了工程和科学目标,介绍了实施效果,总结了主要技术成就。在此基础上,展望了探月工程未来的发展趋势,给出了月球后续任务的总体思路和框架。     

月球主要构造特征：嫦娥一号月球影像初步研究

月球在31亿年前已基本停止地质活动,从而保留了其形成初期的信息．这些信息对于认识月球、地球乃至太阳系的形成演化具有重要意义．在已有研究成果的基础上,结合嫦娥一号探月卫星CCD影像数据,从月海穹窿、撞击坑、月岭、断裂、月坑链、月溪及月谷等方面介绍了月球主要构造形式的地质特征、形貌特征及遥感影像特征,对其成因以及所隐含的地质意义进行了分析．结果表明,嫦娥一号CCD影像信息丰富,影像清晰,利用其CCD影像数据进一步研究月球的构造现象是可行的．     

Simulation of optical response of retroreflectors for future lunar laser ranging

We numerically examined various retroreflectors as laser ranging targets for future missions to the Moon. The geometric conditions, such as the angle of incidence and velocity aberration, with lunar targets are much more restricted than those with most of the earth-orbiting artificial satellites. The numerical optical response simulation carried out in this study indicates that a single retroreflector with a diameter of 150–250 mm performs similar to the existing Apollo retroreflector arrays. Further, no dihedral angle is required for small retroreflectors with diameters below 150 mm for uncoated ones and below 100 mm for coated and hollow ones. Retroreflectors with larger diameters require dihedral angles of 0.20, 0.25, and 0.35 arcsec for coated, uncoated and hollow types, respectively. The objective of this fundamental study is to underlie the development of future laser ranging targets that are to be placed on the Moon.     

Simulation software for the spiral trajectory of our Moon

At 4.56 Ga, the accretion of the slowly rotating Solar Nebula led to the formation of Sun and its Planets in the plane of disc of accretion. Moon was formed by accretion from a circumterrestrial disk of debris generated by the glancing angle impact of the young Earth by a Mars size planetary embryo at about 4.5 Ga at a distance of 15,000 km. The Moon since then has migrated to the present position of 384,400 km from the center of the Earth. In course of this outward migration it has slowed down the spin rate of Earth and caused the lengthening of diurnal day length from 5 h initially to 24 h presently. The basic mechanics of Earth–Moon System has been worked out and theoretical determination of lengthening of day curve is carried out. This theoretical lengthening of day curve is compared with the observed lengthening of day curve based on paleobotanical evidences, ancient tidalites and Australian Banded Iron Formation. There is a remarkable correspondence between the two curves except for intermittent deviations due to geographical and geophysical factors. Based on the theoretical curve of lengthening of day, an empirical formula for the lunar orbital radius expansion is determined. Based on this empirical formula, simulation software is developed that gives the correct evolution of the semi-major axis (a) of our Moon for any time span from the inception to the time chosen under study. For mathematical simplicity the system is considered to be a two body rotating system throughout its evolutionary history of 4.5 Gyrs. This simulation draws the Moon’s spiral trajectory from its inception to any subsequent epoch. The terminal epoch is an input to the simulation software to arrive at the spiral trajectory of the Moon from the inception to the given epoch. The basic mechanics of Earth–Moon System and this simulation can be generalized to lay the foundation of simulation software for any Planet–Satellite pair or any Sun-Planet pair in our Solar System or Star-Planet pair in any Extra-Solar System. The basic dynamics has been found to be valid for Star–Planet pair also. So this Simulation Methodology can as well be applied to study the migratory evolution of Gas Giants also.     

Chang'E-1 Lunar Mission:An Overview and Primary Science Results

Chang'E-1 is the first lunar mission in China, which was successfully launched on Oct. 24th, 2007. It was guided to crash on the Moon on March 1, 2009, at 52.36oE, 1.50oS, in the north of Mare Fecunditatis. The total mission lasted 495 days, exceeding the designed life-span about four months. 1.37 Terabytes raw data was received from Chang'E-1. It was then processed into 4 Terabytes science data at different levels. A series of science results have been achieved by analyzing and applicating these data, especially "global image of the Moon of China's first lunar exploration mission'. Four scientific goals of Chang'E-1 have been achieved. It provides abundant materials for the research of lunar sciences and cosmochemistry. Meanwhile these results will serve for China's future lunar missions.      

一种改进的巡视器惯性/视觉组合导航模型

在传统的以惯性与视觉相对运动参数差为观测量的惯性/视觉组合导航模型中,为了得到简单的观测矩阵,惯性相对旋转四元数与平台失准角之间的函数关系往往通过近似处理得到。但当航向角较大时,该近似处理的误差很大,不可忽略。为解决该问题,文章提出了一种不需该近似处理的改进的观测量误差分析方法,并建立了改进的观测模型。该方法利用含误差的惯性姿态已知的特点,得到了更精确的惯性相对旋转四元数误差表达式,减少了Kalman滤波中惯性与视觉相对旋转差的状态模型预测误差。月面仿真和地面试验表明该改进方法相比传统方法可实现更高的导航精度,其中位置精度提高达68%。     

极月轨道上太阳电池阵外热流规律分析

准确的月球表面温度分布模型对于开展月球探测具有重要意义. 目前有关月球表面温 度模型还缺乏对完整月球表面温度分布的计算方法研究. 本文建立了一套计算完整月球表面温度的方法, 其中月球阳面温度采用Racca模型直接计算得到; 对于月球阴面, 将其沿纬度方向划分为若干区域, 每个区域的地表土壤采用一维非稳态热传导模型, 根据嫦娥三号着陆器太阳电池阵在轨环月阶段的温度数据, 修正得到月球表面土壤导热系数、密度及比热容, 通过数值计算求解一维非稳态热传导方程, 得出任意时刻月球阴面表面温度随时间的变化. 嫦娥三号着陆器太阳电池阵环月阶段热分析结果与在轨温度符合较好, 初步说明本文建立的完整月球表面温度计算方法正确可行. 基于本文方法计算得到整个月球表面温度分布, 进一步研究了极月轨道太阳电池阵外热流变化规律.