The first new application of the Mathematical Theory of Stochastic Processes to lunar and planetary science: Topography-Profile Diagrams of Mars

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 can be used to investigate physical processes through mathematics. Each model of a stochastic process, according to MTSP, can provide one or more interpretations in the MST domain. A large body of work on impact crater statistics according to MST exists, showing cumulative crater frequency (N km⁻²) as a function of age (years) for some particular crater diameter. However, this is only one possible representation in the MST domain of the bombardment of the planetary surface modeled as a stochastic process according to MTSP. The idea that other representations are possible in the MST domain of the same stochastic process from MTSP has been recently presented. The importance of the approach is that each such mathematical-based interpretation can provide a large amount of new information. Coupled with MOLA data, Topography-Profile Diagrams (TPD) are one of the many examples that can provide a large amount of new information regarding the history of Mars. TPD consists of: (1) Topography-Profile Curve (TPC), which is a representation of the planet’s topography, (2) Density-of-Craters Curve (DCC), which represents density of craters, (3) Filtered-DCC (FDCC), which represents DCC filtered by a low-pass filter, included with the purpose of reducing the noise, and (4) Level-of-Substance-Over-Time Curve (LSOTC), which represents interpretation of the influence on the distribution of craters shown by FDCC. TPC uniquely corresponds to the computation of TPD, whereas DCC depends on algorithms for computing the elevation of each crater according to the topography, center coordinates, and radius of impact crater, and FDCC relies on the architecture of the custom designed low-pass filter for filtering DCC. However, all variations of DCC and FDCC, which includes the various impact crater data sets, showed a correlation among the density of craters and elevation over 70–80% of the planet surface. Additionally, if we assume that the ocean primarily caused the noted correlation, LSOTC offers a mathematical approach for estimating topographic change of the ocean’s extent over time. Accordingly, TPD is the first new practical application of MTSP to lunar and planetary sciences, showing correlation of topography to a physical process.     

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.     

Traverses for the ISECG-GER design reference mission for humans on the lunar surface

This study explores the Design Reference Mission (DRM) architecture developed by Hufenbach et al. (2015) as a prelude to the release of the 2018 Global Exploration Roadmap (GER) developed by the International Space Exploration Coordination Group (ISECG). The focus of this study is the exploration of the south polar region of the Moon, a region that has not been visited by any human missions, yet exhibits a multitude of scientifically important locations – the investigation of which will address long standing questions in lunar research. This DRM architecture involves five landing sites (Malapert massif, South Pole/Shackleton crater, Schrödinger basin, Antoniadi crater, and the South Pole-Aitken basin center), to be visited in sequential years by crew, beginning in 2028. Two Lunar Electric Rovers (LER) are proposed to be tele-robotically operated between sites to rendez-vous with crew at the time of the next landing. With engineering parameters in mind we explore the feasibility of tele-robotic operation of these LERs between lunar landing sites, and identify potential high interest sampling locations en-route. Additionally, in-depth sample collection and return traverses are identified for each individual landing site across key geologic terrains that also detail crew Extra-Vehicular Activity (EVA). Exploration at and between landing sites is designed to address a suite of National Research Council (2007) scientific concepts.     

Journey to the Moon: Recent results,science, future robotic and human exploration

The upcoming fleet of lunar missions, and the announcement of new lunar exploration initiatives, show an exciting “Journey to the Moon”, covering recent results, science, future robotic and human exploration. We review some of the questions, findings and perspectives given in the papers included in this issue of Advances in Space Research.     

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.     

Measuring the economic benefits of a national planetary protection policy to regulate future private space activities between Earth and Mars: Results of a contingent valuation survey in Greece

The emergence of private space actors may soon enable the growth of the novel market segments of space research and exploration, space resources utilization, and human access to space. The interdisciplinary field of Planetary Protection has to keep up with these advances. Planetary Protection is defined as a set of guidelines that aim to prevent the forward contamination of celestial bodies with biological material from Earth and the backward contamination of the terrestrial biosphere with extraterrestrial biological material. As space entrepreneurs acquire and develop the resources and competencies for commercial access to space, significant questions are expected to be raised in the future with respect to potential forward and backward contamination issues, particularly with respect to activities between Earth and Mars. Although such private activities do not seem to pose a serious Planetary Protection threat at the moment, certain preparatory steps need to be taken in order to prudently inform the relevant policy-making procedures. This work describes the application of the Contingent Valuation Method, a useful tool of the environmental economics discipline, with the aim of demonstrating a novel approach to estimate the economic valuation of the external benefits of preventing forward and backward contamination between Earth and Mars. Particularly, via a survey specifically developed for this purpose, a set of questions are used to elicit the perceived economic value that respondents place on the prevention of forward and backward contamination; the survey is administered to a national probability sample in Greece, and the generated data is processed through statistical analysis. The Contingent Valuation Method is a popular and well-established stated preference valuation technique; these techniques are often the more suitable choice for ex-ante valuations of future changes, and are currently the only known approach to capture all the aspects of the economic value of non-market goods. Through an initial proof-of-concept in Greece, the goal of this work is to provide useful insights on the expected external benefits of a national Planetary Protection policy to regulate future private space activities between Earth and Mars, and to encourage a larger-scale application of this tool in other countries around the world.     

空间核动力在深空探测中的应用及发展综述

在概要介绍空间核动力发展历程的基础上,总结了同位素热/电源、核反应堆电源、核推进在深空探测领域的应用情况和相关发展情况,并讨论了空间核动力的安全问题。对未来空间核动力在深空探测中应用面临的技术问题进行了展望。     

Quantitative contribution of climate change and anthropological activities to vegetation carbon storage in the Dongting Lake basin in the last two decades

The Dongting Lake Basin is an important hydrological regulation and flood storage area in the Yangtze River Basin, which plays an important role in maintaining regional ecological security. The watershed vegetation and its carbon sequestration capacity have changed dramatically due to climate change and human activities in the last two decades. In this paper, the monthly and annual vegetation net primary productivity (NPP) of the Dongting Lake basin during 2000 to 2020 was firstly estimated using the improved Carnegie-Ames-Stanford Approach (CASA) model. Then the multi-year NPP change trend and its significance were analyzed based on Theil-Sen median and Mann-Kendall method. Subsequently, the Hurst index was used to simulate the vegetation NPP persistence in the study area. Finally, the driving mechanisms of vegetation NPP changes in the study area were explored using partial correlation coefficients and residual analysis. The results demonstrated that: 1) The annual average NPP in the basin showed a fluctuating and increasing trend from 273.54 to 718.30 g C/m²·yr¹ during 2000 to 2020, and except for autumn, all seasons (spring, summer, winter) and annual NPP series showed an upward trend. The spatial distribution of vegetation NPP is characterized by an asymmetrical horseshoe shape in general, with high values in the west, south and east parts, and low values in the Lake area; 2) During the study years, about 84.38 % of the basin area showed a significant and extremely significant increase of NPP; 3) The future trend of vegetation NPP in the basin shows that the area of decrease (22.79 %) is more than the area of increase (11.35 %). The Chang-Zhu-Tan urban agglomeration will generally show a continuous and extremely significant reduction trend, while parts of Dongting Lake will show a continuous and extremely significant increase trend; 4) The correlation between solar radiation and NPP is stronger than the other two meteorological factors (precipitation and temperature). Temperature has a significant inhibitory effect on NPP, solar radiation has a significant promoting effect on NPP, and the effect of precipitation on NPP was relatively complicated. The relative importance of meteorological factors on vegetation NPP was ranked as follows: solar radiation > precipitation > temperature. The impacts of both climate change and human activities on NPP changes showed great spatial variability, and the positive contributions (89.81 % for climate change and 82.87 % for human activities) were both greater than the negative contributions.     

DDS中相位截断效应分析及其改善方法

分析了在直接数字频率合成（ＤＤＳ）中引起杂散的相位截断效应,针对其引起的杂散特点讨论了一种通过加入伪随机数改善杂散谱分布的方法,并通过计算机仿真进行了验证。