Imaging and power generation strategies for chandrayaan-1

The Chandrayaan-1 mission proposes to put a 550 kg lunarcraft into Geostationary Transfer Orbit (GTO) using the Polar Satellite Launch Vehicle (PSLV) which will subsequently be transferred into a 100 km circular lunar polar orbit for imaging purposes. In this paper, we describe certain aspects of mission strategies which will allow optimum power generation and imaging of the lunar surface. The lunar orbit considered is circular and polar and therefore nearly perpendicular to the ecliptic plane. Unlike an Earth orbiting remote sensing satellite, the orbit plane of lunar orbiter is inertially fixed as a consequence of the very small oblateness of the Moon. The Earth rotates around the Sun once a year, resulting in an apparent motion of Sun around this orbit in a year. Two extreme situations can be identified concerning the solar illumination of the lunar orbit, noon/midnight orbit, where the Sun vector is parallel to the spacecraft orbit plane and dawn/dusk orbit, where the Sun vector is perpendicular to the spacecraft orbit plane. This scenario directly affects the solar panel configuration. In case the solar panels are not canted, during the noon/midnight orbit, 100% power is generated, whereas during the dawn/dusk orbit, zero power is generated. Hence for optimum power generation, canting of the panels is essential. Detailed analysis was carried out to fix optimum canting and also determine a strategy to maintain optimum power generation throughout the year. The analysis led to the strategy of 180‡ yaw rotation at noon/midnight orbits and flipping the solar panel by 180‡ at dawn/dusk orbits. This also resulted in the negative pitch face of the lunarcraft to be an anti-sun panel, which is very useful for thermal design, and further to meet cooling requirements of the spectrometers. In principle the Moon’s surface can be imaged in 28 days, because the orbit chosen and the payload swath provide adequate overlap. However, in reality it is not possible to complete the imaging in 28 days due to various mission constraints like maximum duration of imaging allowed keeping in view the SSR sizing and payloads data input rate, time required for downlinking the payload data, data compression requirements and visibility of the lunarcraft for the Bangalore DSN. In each cycle, all the latitudes are swept. Due to the constraints mentioned, only 60‡ latitude arc coverage is possible in each orbit. As Bangalore DSN is the only station, half of the orbits in a day are not available. The longitudinal gaps because of non-visibility are covered in the next cycle by Bangalore DSN. Hence, in the firstprime imaging season, only 25% of the prime imaging zones are covered, and an additional threeprime imaging seasons are required for a full coverage of the Moon in two years. Strategy is also planned to cover X-ray payload coverage considering swath and orbit shift.     

Launch strategy for Indian lunar mission and precision injection to the Moon using genetic algorithm

The Indian lunar mission Chandrayaan-1 will have a mass of 523 kg in a 100 km circular polar orbit around the Moon. The main factors that dictate the design of the Indian Moon mission are to use the present capability of launch vehicles and to achieve the scientific objectives in the minimum development time and cost. The detailed mission planning involves trade-off studies in payload optimization and the transfer trajectory determination that accomplishes these requirements. Recent studies indicate that for an optimal use of the existing launch vehicle and space-craft systems, highly elliptical inclined orbits are preferable. This indeed is true for the Indian Moon mission Chandrayaan-1. The proposed launch scenario of the Indian Moon mission program and capabilities of this mission are described in this paper, highlighting the design challenges and innovations. Further, to reach the target accurately, appropriate initial transfer trajectory characteristics must be chosen. A numerical search for the initial conditions combined with numerical integration produces the near accurate solution for this problem. The design of such transfer trajectories is discussed in this paper.     

SMART-1 after lunar capture: First results and perspectives

SMART-1 is a technology demonstration mission for deep space solar electrical propulsion and technologies for the future. SMART-1 is Europe’s first lunar mission and will contribute to developing an international program of lunar exploration. The spacecraft was launched on 27th September 2003, as an auxiliary passenger to GTO on Ariane 5, to reach the Moon after a 15-month cruise, with lunar capture on 15th November 2004, just a week before the International Lunar Conference in Udaipur. SMART-1 carries seven experiments, including three remote sensing instruments used during the mission’s nominal six months and one year extension in lunar science orbit. These instruments will contribute to key planetary scientific questions, related to theories of lunar origin and evolution, the global and local crustal composition, the search for cold traps at the lunar poles and the mapping of potential lunar resources     

Transition regions between stable periodic solutions of the general three-body problem

The behavior of triple systems in the transition zones located between regions of stability is studied in the framework of the general three-body problem with equal masses and zero angular momentum. It is well known that there are exist three stable periodic orbits, namely, the Schubart orbit for the rectilinear problem, the Broucke orbit for the isosceles problem, and the Moore eight-figure orbit. In the space of the initial conditions, these orbits are surrounded by sets of points where bounded motions are observed over substantial time intervals. The transition zones between the Schubart and Moore orbits and the Moore and Broucke orbits are studied. It is shown that the boundaries of the regions of stability can be either smooth and sharp or diffuse. Beyond these boundary regions, the dynamical evolution of triple systems results in a distant ejection of one of the components, or the decay of the system. The distribution of the times when the stability is lost is constructed, and obeys a power law for long time intervals. Three stages in the evolution of an unstable triple system are identified.     

人造卫星轨道要素的计算

本文阐述了人造卫星的轨道计算方法。内容包括轨道的形成、分类与要素以及椭圆轨道与圆轨道的设计计算方法。     

The changing iconography of Japanese political geography

Our world is very fluid, very complex, constantly moving, made up of a great number of interdependent components. Therefore, the locus and the orbit of a particular area play an important role in geography and in politics. The purpose of this study is to examine the iconography of orbit and freedom of movement through an analysis of the transformation of the international politico-economic structure and its impact on Japan and to make clear the footsteps of Jean Gottmann on political geography. Due to its locus being on the crossroad of international power struggles, Japan had accepted different iconographies of orbits every time she faced great mutation in her history. This, in turn, accelerated the synchronism, synergism and synthesis of different iconographies that came to converge at the crossroad. The integration of imported cultures with the Japanese traditional culture promoted the transformation of Japanese society and community to emphasize the freedom of movements. The flexibility of Japanese society and the unifying iconography of Japanese community have enabled Japan to adapt and readapt to changing politico-economic phases. Interested in the relationship between freedom of movement and iconography, Jean Gottmann spent a considerable portion of his academic life inquiring into the changing dynamics of Japanese iconography on the global scene. After a quarter-century pursuit, he contributed to the establishment of political geography in Japan.     

The Deviation of the Lunar Center of Mass to the East of the Direction Toward the Earth. A Mechanism Based on Orbital Evolution

It is known from observations of the gravitational field and figure of the Moon that its center of mass (COM) does not coincide with its geometric center, with the line connecting these two points deviating to the Southeast of the direction toward the center of the Earth. The deviation of the lunar COM to the South was explained earlier. Here, the deviation of the lunar COMto the East of the direction toward the Earth is considered. The theory of the optical libration of a satellite orbiting synchronously about a planet for an observer at the secondary (free) focus of the orbit is first refined. It is shown that the main axis of inertia of the satellite undergoes asymmetric, non-linear oscillations whose amplitude is proportional to the square of the orbital eccentricity. A mechanism for the evolution of the orbit has been developed, taking into account the preferred direction of the axis of inertia of the Moon toward the empty focus. Of two alternative scenarios—evolution of the lunar orbit with decreasing or increasing eccentricity—only the latter scenario is consistent with the observed eastward shift of the lunar COM. This mechanism predicts that the lunar orbit had a lower eccentricity in the past than it does today. This conclusion is consistent with the results of observations and also with the fact that the eccentricity of the Moon’s orbit is indeed currently increasing, indicating that it was lower in the past than its current value, e = 0.0549. It is shown by averaging themotion over a rapid variable that thismechanismfor the orbital evolution can explain about 18% of the currently known eastward shift of the lunar COM. The results obtained refine the theory of the tidal evolution of the Moon.     

Statistical characteristics of barotropic atmospeheric system and its unstable periodic solutions

This paper is devoted to the problem of approximating an invariant measure and statistical characteristics of barotropic atmospheric model with the help of its periodic trajectories. In this procedure orbits are taken into account according to their weights defined by the orbit instability characteristics. The method comes from the dynamical systems theory where in several specific case (for hyperbolic systems in particular) unstable periodic orbits define the system invariant measure. In our study we show that the system PDF could be reconstructed with the error less than 10% provided that the optimal orbit weight function is chosen.     

Insolation and glacials

Climatic changes result from variables in planetary orbits which modulate solar energy emission and change seasonal and latitudinal distribution of heat received by the Earth. Small insolation changes are multiplied by the albedo effect of the winter snow fields of the Northern Hemisphere, by ocean-atmosphere feedbacks, and, probably, by the stratospheric ozone layer. The role of volcanic explosions and other aperiodic phenomena is secondary. The immediate climate response to insolation trends permits astronomic dating of Pleistocene events. A new glacial insolation regime, expected to last 8000 years, began just recently. Mean global temperatures may eventually drop about 1^oC in the next hundred years. A refinement of the Milankovitch theory in terms of the lunar orbit and more data on solar periodicities are needed for reliable long range predictions.     

月球形成演化与月球地质图编研

按照大碰撞假说,月球形成于一次大碰撞事件,抛射出的高能量物质留在绕地轨道上,最后吸积形成月球。月球核幔在早期迅速发生分离,并出现全球性的岩浆熔融,形成了岩浆圈层（岩浆洋）。岩浆洋的结晶分异和固化导致了月壳的形成。随着月壳与月幔发生持续分异,形成了固化的月壳。而在月球后期的演化历史中,撞击作用是最重要的地质作用,形成了多尺度、多期次的撞击盆地和撞击坑,而大型撞击盆地多形成于月球演化的早期。月球地质图是开展月球形成与演化研究的重要手段,从20世纪60年代起,到70年代末止,通过对阿波罗时代探月成果的系统总结,完成了第一轮月球地质图的研制。但尽管从20世纪90年代以来国际月球探测和月球科学的研究进入一个新的高潮,获得了大量有关月球形成和演化的新认识,但还没有正式的新的月球地质图发布,因此开展新一轮月球地质图的编研,系统总结后阿波罗时代的月球探测与研究成果,是非常必要和迫切的。在新一轮月球地质图的编制过程中,需重点关注图件比例尺的选择、月面历史的划分以及月球构造和岩石建造的表达。     

Multifactorial Method of Search for Small Bodies in Close Orbits

The results of the search for Apollo, Amor, and Aten asteroids with the orbits close to those of meteoroids of the δ-Cancrids meteor complex (code DCA), which consists of the northern (code NCC) and southern (code SCC) branches, are presented. The search for small bodies in close orbits was performed on the basis of a multifactorial method of combining several criteria: Drummond orbital similarity criterion, Kholshevnikov metric, and parameters of the dynamic evolution of the orbits using two catalogs of meteor orbits (Japan Meteor Society, SonatoCo, and CAMS Meteoroid Orbit Database v2.0, CAMS) obtained from television observations. Asteroids in close orbits with the meteoroid orbits of the northern NCC and southern SCC branches of the δ-Cancrids are identified only in the Apollo group. The following asteroids are common for the NCC and SCC branches: 2015 PU228, 2014 YQ34, 2017 YO4 (according to the CAMS orbit catalog); Hephaistos 1978 SB, 2003 RW11, 2006 BF56, 2011 SR12, 2014 RS17, 2001 YB5 (SonatoCo catalog). The asteroid 85182 (1991 AQ) is identified only with the northern NCC branch but in two catalogs of meteor orbits.     

The Deviation of the Lunar Center of Mass to the East of the Direction toward the Earth. A Mechanism Based on Rounding of the Figure of the Moon

It is known that the center of mass (CM) of the Moon does not coincide with its geometrical center of figure (CF), and that the CF–CMline deviates to the Southeast of the direction toward the center of the Earth. An investigation of this phenomenon, which has remained incompletely understood, has been carried out in two stages. One mechanism can explain part of the eastward shift of the lunar CM as being due to tidal evolution of the lunar orbit. A second mechanism is considered here, which relates this shift of the lunar CM with evolution of the shape of the Moon. A differential equation describing the shift of the lunar CMto the East in the course of the physically inevitable rounding of its shape as it moves away from the Earth is derived and solved. This mechanism not only explains the eastward shift of the lunar CM, but also predicts that the oblateness of the Moon could have been appreciable at earlier epochs, reaching values ε ≈ 0.31. The theory of figures of equilibrium in a tidal gravitational field is used to determine how close to the Earth the Moon could have formed.     

月表构造与深部构造的关系

地球和月球很可能是通过大撞击形成的。在行星地质学中,研究月球的地质-构造现象,对了解月球、地球乃至太阳系的形成与演化历史都有很大帮助。月球的构造分为深部构造与月表构造,寻找它们在分布或成因上的关系,可以为月球甚至地月系的起源和演化历史提供重要参考。利用LROC的宽视角影像数据以及LOLA数据提取解译月表构造,结合深大断裂进行观察分析,并对月球的撞击盆地进行统计,最后以静海地区为例分析构造分布特征,发现月球的质量瘤盆地中具有环状分布的月岭,外侧具有近环状分布的深大断裂,自前酒海纪至酒海纪,具备上述特征的质量瘤盆地占总撞击盆地的比例突然有一个很大的提升,且静海地区西部具有该构造分布特征。推测该特征与撞击、月海沉降等有关,且在酒海纪与雨海纪期间月球有较多的月海玄武岩分布,由此判断静海西部存在质量瘤,发生过撞击与月海沉降。     

SST-ll重力卫星轨道运动对K波段测距系统的影响

给出了物体作近圆椭圆轨道运动的近似运动学方程,并结合GRACE重力卫星的轨道参数,在没有考虑摄动效应的前提下,计算了双星的距离、相对速度以及双星连线的倾角,并讨论了这些量对K波段测距系统的影响。同时分析表明,2倍轨道频率的效应可望用于K波段测距和测速的在轨性能检验,这对于K波段研究具有一定指导意义。     

Decimation and Spectrum Correlation Analysis of Gravity Solid Tide Signal Based on Surface-Simplex Swarm Evolution Optimization Algorithm

In order to reveal the correlation between the harmonic components in the earth's solid tidal wave and the non-correlation superposition relationship, and based on these relations, the tidal harmonic implicit in the gravitational solid tidal signal was analyzed. According to the position relationship among the Earth, the moon and the sun's rotating orbit, an orthogonal decomposition model of tidal force was established. Furthermore, on the orthogonal decomposition model of gravity solid tidal wave based on the independent component analysis of the improved SSSE intelligent optimization algorithm, the spectral correlation method was used to analyze the independent components of gravity solid tidal wave. Thus, the multiplicative demodulation after the orthogonal decomposition of the conformal wave was completely realized. Finally, the above model and algorithm were used to compare and analyze the actual observation data and the theoretical signal as reference background. The results show that the proposed model and method can effectively achieve the orthogonal decomposition of tidal harmonics, highlight the weak energy of the long period harmonics component, and reflect the change of tidal harmonic modulation relationship from the spectral correlation map.     

Long-Period Variations in Oscillations of the Earth’s Pole due to Lunar Perturbations

A numerical–analytical approach is used to investigate irregular effects in oscillations of the Earth’s pole related to variations in the Chandler and annual components. An approach to studying oscillations in the motion of the Earth’s pole based on a joint analysis of the Chandler and annual components of this motion is proposed. A transformation to a new coordinate system in which the motion of the pole is synchronous with the precession of the lunar orbit can be found in this approach. Estimates of the precision of predictions of the coordinates of the Earth’s pole taking into account additional terms due to lunar perturbations are presented.

     

Research on the inversion of elemental abundances from Chang’E-2 X-ray spectrometry data

The elemental abundances of lunar surface are the important clues to study the formation and evolution history of the Moon. In 2010, China＇s Chang＇E-2 （CE-2） lunar orbiter carried a set of X-ray spectrometer （XRS） to investigate the elemental abundances of the lunar surface. During CE-2＇s life span around the Moon, the XRS ex- perienced several events of solar flare. The X-ray solar monitor onboard recorded the spectra of solar X-rays at the same time. In this paper, we introduced the XRS instrument and data product. We analyzed the characteristics of the XRS data. Using the data obtained during an M solar flare event which had occurred on Feb. 16, 201 l, we derived the elemental abundances ofMg, A1, Si, Ca and Fe of the lunar surface in the Oceanus Procellarum. Finally, we dis- cussed the factors that influence the accuracy of the inversion.     

Lunar-A mission: Outline and current status

The scientific objective of the Lunar-A, Japanese Penetrator Mission, is to explore the lunar interior by seismic and heat-flow experiments. Two penetrators containing two seismometers (horizontal and vertical components) and heat-flow probes will be deployed from a spacecraft onto the lunar surface, one on the near-side and the other on the far-side of the moon. The data obtained by the penetrators will be transmitted to the earth station via the Lunar-A mother spacecraft orbiting at an altitude of about 200 km. The spacecraft of a cylindrical shape, 2.2 m in maximum diameter and 1.7 m in height, is designed to be spin-stabilized. The spacecraft will be inserted into an elliptic lunar orbit, after about a half-year cruise during which complex manoeuvering is made using the lunar-solar gravity assist. After lunar orbit insertion, two penetrators will be separated from the spacecraft near perilune, one by one, and will be landed on the lunar surface. The final impact velocity of the penetrator will be about 285 m/sec; it will encounter a shock of about 8000 G at impact on the lunar surface. According to numerous experimental impact tests using model penetrators and a lunar-regolith analog target, each penetrator is predicted to penetrate to a depth between l and 3 m, depending on the hardness and/or particle-size distribution of the lunar regolith. The penetration depth is important for ensuring the temperature stability of the instruments in the penetrator and heat flow measurements. According to the results of the Apollo heat flow experiment, an insulating regolith blanket of only 30 cm is sufficient to dampen out about 280 K lunar surface temperature fluctuation to < 3 K variation. The seismic observations are expected to provide key data on the size of the lunar core, as well as data on deep lunar mantle structure. The heat flow measurements at two penetrator-landing sites will also provide important data on the thermal structure and bulk concentrations of heat-generating elements in the Moon. These data will provide much stronger geophysical constraints on the origin and evolution of the Moon than has been obtained so far. Currently, the Lunar-A system is being reviewed and a more robust system for communication between the penetrators and spacecraft is being implemented according to the lessons learned from Beagle-2 and DS-2 failures. More impact tests for penetrators onto a lunar regolith analogue target will be undertaken before its launch.     

Correlations between global features of terrestrial fields

Studies of correlation coefficients between different sets of global geophysical data may lead to useful inferences concerning their relationship or independence. If one data set is allowed to rotate with respect to another, the statistical theory is complicated and extra care is required before one can conclude that there is any statistical significance to a maximized correlation coefficient. If, for some relative rotation, two spherical harmonic fields are significantly correlated, then their individual degree component harmonics of dominant power must also be significantly correlated. Rotations can be found that result in high correlations between the dominant low-degree spherical harmonics of the geomagnetic and tertestrial gravity field potentials, but rotations can also be found that result in equally high, yet meaningless, correlations if the lunar gravity field is substituted for the geomagnetic field. To explain such high correlations, the theoretical correlation distribution function between normally distributed component harmonics is derived and then verified for lowdegree harmonics by using a Monte Carlo technique which takes into account the three-dimensional rotation group. Some curious properties surface: (1)the correlation distribution function for all possible relative orientations is almost the same between identical and uncorrelated fields; and (2)a system for determining the correlation distribution function from randomly selected fields or from randomly rotated fields is almost ergodic.     

基于单形进化优化算法的重力固体潮信号解混及谱相关分析

为了揭示地球固体潮中谐波成分间的相关乘性调制关系与非相关叠加关系,并根据这些关系来分析重力固体潮信号中隐含的潮汐谐波。根据地球、月球与太阳旋转轨道的位置关系,建立了一个引潮力的正交分解模型。进一步,基于改进单形进化智能优化算法的独立分量分析的重力固体潮正交分解模型上,利用谱相关方法,对重力固体潮的独立成分进行谱相关分析,从而完整实现了潮汐谐波加性正交分解之后的乘性解调。最后,结合实际观测数据,并引入理论信号作为参考背景,利用以上模型与算法进行对比处理和分析。研究表明,所提出的模型与方法可以有效地实现潮汐谐波的正交分解,凸显能量较弱的长周期谐波分量,并从谱相关图谱中反映潮汐谐波调制关系的变化。