Applying the mathematical theory of stochastic processes to lunar and planetary science: the ancient oceans on Mars case

The Mathematical Statistics Theory (MST) and the Mathematical Theory of Stochastic Processes (MTSP) are different branches of the more general Mathematical Probability Theory (MPT) that represents different aspects of some physical processes we can analyze using mathematics. Each model of a stochastic process according to the MTSP can provide one or more interpretations in the MST domain. The importance of MTSP is that each such interpretation can provide large amount of new information. While large body of work on the impact crater statistics according to MST has already been done, it is yet to be investigated as to how we can model a stochastic process according to MTSP; for example, bombardment of the planetary surface or something else in a Lunar and Planetary Science (LPS) domain. In order to show possible achievements, the possible existence of a Martian ocean was chosen as a query that could be addressed through computations using presumptions according to MTSP, including probability of existence as well as lateral and vertical extent and duration of time. While the presumptions for this particular case will also be addressed in certain degree, this will be done primarily to show complexities of some physical process that can be modeled, rather than to prove correctness of the concrete values computed here. While this in itself can be the objective in some future work toward the formal proof of the probability, extent, and timing of oceans on Mars, the basic idea here is to show the basic principles of MTSP, and its potential for addressing LPS-related phenomena. Here, I attempt to show how this approach can: (1) provide large amounts of previously unknown information about physical processes on the surface of the planet, (2) lead to a better understanding of the processes that have shaped the surface of the planet, and/or (3) help constrain the amount of resurfacing. Coupled with other current methodologies, MTSP can result in a better understanding of the history of Mars, as well as other lunar and planetary bodies.     

Scheme design of the CHANG’E-5T1 extended mission

Flight schemes for the CHANG’E-5T1 extended mission are investigated in this paper. In the flight scheme and trajectory design, the remaining propellant of the CHANG’E-5T1 mission is utilized. The CHANG’E-5T1 mission is firstly introduced with feasible flight goals derived based on the terminal trajectory and satellite status. The flight schemes are designed to include a lunar return and the libration points in the Sun-Earth/Moon and Earth-Moon systems, with an emphasis on the Earth-Moon triangle libration point thus far unexplored. Secondly, three schemes are proposed for the CHANG’E-5T1 extended mission with different flight goals. The direct libration point orbit transfer and injection method is adopted to solve the issue in the transfer trajectory design. Furthermore, an innovative concept is proposed to transfer from the Earth-Moon collinear libration point to the triangle point using the Sun-Earth/Moon libration point. Finally, the merits and drawbacks of the three schemes are discussed in terms of flight time, control energy and frequency, flight distance, and goal value. As a result, the scheme including a lunar return and the Earth-Moon L2 libration point is selected for the CHANG’E-5T1 extended mission. A flight to the Earth-Moon libration point is achieved, replicating the achievement of the ARTEMIS mission.     

Free librations of the two-layer Moon and the possibilities of their detection

Based on the forthcoming second stage of the Japanese Lunar mission ILOM (2013), when an optical telescope will be set on the surface near one of the Lunar poles, the possibility to detect free Lunar modes (Chandler-like wobble and free-core nutation) is considered. The difference between the Lunar Eulerian and Chandler-like wobble is explained. The terms “arbitrary libration” and “free libration” are discussed. The geometrical and physical interpretations of the free polar motion over the Lunar surface are considered from the viewpoints of Lunar surface-based observations and the Lunar Navigation Almanac. The dependencies of the free libration period on the core’s radius, density, and ellipticity are modelled and discussed.     

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.     

Moon surface radiation environment analysis for February 1956 solar event conditions

The radiation environment on the surface of the Moon presents a new source of particles resulting from the interaction of incoming solar protons and galactic cosmic rays with the lunar regolith. Here we present a study of the fluence profile of primary and secondary particles on the top 1 m layer of lunar regolith for the spectrum of one of the hardest spectrum solar event, that of February 1956. Different regolith compositions and their influence in proton and neutron production and backscattering is considered, as well as the nature of the backscattered radiation. Simple geometry Monte Carlo simulations have been used also for calculating regolith shielding properties, and it is shown that a layer of at least 50 cm regolith is needed for significantly reducing the dose levels received by astronauts in a hypothetical lunar habitat.     

嫦娥三号巡视器-着陆器释放分离过程关键力学问题分析

针对嫦娥三号探测器两器释放分离过程几个关键力学问题,给出两器释放分离过程的主要风险点与影响参数,应用ADAMS建立两器释放分离全过程仿真模型,开展了全过程动力学仿真与相关试验。分析得到可适应安全释放分离要求的着陆器最大着陆姿态边界与关键性能参数,为两器释放分离提供了理论支撑与依据。     

月球探测器软着陆机构展开过程的运动学分析

软着陆机构是月球探测器实现软着陆的关键部件。针对一种四腿式软着陆机构方案,论述了该软着陆机构展开的工作原理,分析了机构的奇异性,推导了机构不发生奇异的条件,建立了展开机构的运动学方程组,采用Newton-Raphson法求解了该非线性运动学方程组,获得了主支撑杆运动参数的变化规律。     

月面巡视探测器运动控制方法研究

基于动力学的运动控制是星球探测车研制中的关键技术之一。本文以某多轮驱动、多轮转向的月面巡视探测器运动控制为背景,在建立其三自由度动力学模型的基础上,研究了常规增量式PID和模糊自适应PID控制算法,并进行了仿真比较。典型车轮失效情况下的仿真表明,模糊自适应PID方法能够有效控制月面巡视探测器四轮失效的情况,而常规PID方法能够有效控制探测器三轮失效的情况。模糊自适应PID方法对参数扰动敏感性低,鲁棒性更强,较好地处理了常规控制方法可能产生的小超调与快速性的矛盾。     

求解最优月球软着陆轨道的隐式打靶法

基于间接法思想推导出一种隐式打靶法对月球软着陆轨道优化问题进行了研究。建立月球软着陆轨道归一化系统模型,利用庞特亚金极大值原理将月球软着陆轨道优化问题转化为满足最优必要条件的两点边值问题（TPBVP）,采用一种新的时间变量使两点边值问题的终端时刻固定,同时将终端时刻看作状态变量并引入终端时刻的哈密尔顿函数值作为隐式终端条件,提出一种隐式打靶法对含有隐式终端条件的两点边值问题进行迭代求解,从而得出燃料消耗最优的月球软着陆轨道。仿真结果表明,与直接法和混合法相比,隐式打靶法优化精度高,收敛速度快,实现了月球软着陆过程燃料消耗最优。同时应用隐式打靶法求解不同发动机推力值的最优月球软着陆问题,得到燃料消耗最小的最优推重比,可为月面着陆器下降级发动机选型提供参考。