scholarly journals Some Differences Between Geometrical and Dynamical Figures of the Moon

1972 ◽  
Vol 47 ◽  
pp. 32-34 ◽  
Author(s):  
I. V. Gavrilov
Keyword(s):  
Gravity Field ◽  
Lunar Surface ◽  
Homogeneous Model ◽  
Artificial Satellites ◽  
Geometrical Shape ◽  
The Moon ◽  
Geometrical Figure ◽  
Centre Of Gravity ◽  
The North ◽  
The Earth

The geometrical shape of the Moon is determined from measurements of absolute heights of the lunar surface, while its dynamical shape is described by means of the Moon's gravity field parameters. All these data are derived from observations of the lunar artificial satellites (‘Luna-10’, ‘Orbiters 1-4’) and astronomical measurements.In the paper differences of the lunar geometrical and dynamical figures are analysed. It is shown, that the homogeneous model of the Moon is not capable of explaining these differences. It is found, that the lunar centre of gravity situated about 0.9 km to the north, and 1.1 km nearer to the Earth, than the centre of its geometrical figure.

Automated Determination of the Position of Ships by Satellites

1967 ◽  
Vol 20 (03) ◽  
pp. 281-285
Author(s):  
H. C. Freiesleben
Keyword(s):  
Celestial Body ◽  
World Wide ◽  
Artificial Satellites ◽  
Radio Waves ◽  
The Moon ◽  
Position Determination ◽  
The Earth ◽  
Navigational Aids ◽  
Automated Determination

It has recently been suggested that 24-hour satellites might be used as navigational aids. To what category of position determination aids should these be assigned ? Is a satellite of this kind as it were a landmark, because, at least in theory, it remains fixed over the same point on the Earth's surface, in which case it should be classified under land-based navigation aids ? Is it a celestial body, although only one tenth as far from the Earth as the Moon ? If so, it is an astronomical navigation aid. Or is it a radio aid ? After all, its use for position determination depends on radio waves. In this paper I shall favour this last view. For automation is most feasible when an object of observation can be manipulated. This is easiest with radio aids, but it is, of course, impossible with natural stars.At present artificial satellites have the advantage over all other radio aids of world-wide coverage.

Coverage Analysis of Lunar Communication/Navigation Constellations Based on Halo Orbits and Distant Retrograde Orbits

2020 ◽  
Vol 73 (4) ◽  
pp. 932-952
Author(s):  
Zhao-Yang Gao ◽  
Xi-Yun Hou
Keyword(s):  
Lunar Surface ◽  
Polar Regions ◽  
The Moon ◽  
Halo Orbits ◽  
Satellite Constellation ◽  
The North ◽  
Polar Caps ◽  
Distant Retrograde Orbits ◽  
Distant Retrograde Orbit ◽  
South Polar

AbstractWith more and more missions around the Moon, a communication/navigation constellation around the Moon is necessary. Halo orbits, due to their unique geometry, are extensively studied by researchers for this purpose. A dedicated survey is carried out in this work to analyse the coverage ability of halo orbits. It is found that a two-satellite constellation is enough for continuous one-fold coverage of the north or the south polar regions but never both. A three-satellite constellation is enough for continuous one-fold coverage of both north and south polar regions. A four-satellite constellation can cover nearly 100% of the whole lunar surface. In addition, the coverage ability of another special orbit – distant retrograde orbit (DRO) – is analysed for the first time in this study. It is found that three satellites on DROs can cover 99·8% of the lunar surface, with coverage gaps at polar caps. A four-satellite constellation moving on spatial DROs can cover nearly the whole lunar surface. By combining halo orbits and DROs, we design a five-satellite constellation composed of three halo orbit satellites and two DRO satellites. This constellation can provide 100% continuous one-fold coverage of the whole lunar surface.

scholarly journals The Shape of the Moon

1972 ◽  
Vol 47 ◽  
pp. 22-31 ◽  
Author(s):  
S. K. Runcorn ◽  
S. Hofmann
Keyword(s):  
Lunar Surface ◽  
Major Axis ◽  
Great Depth ◽  
The Moon ◽  
Method Of Least Squares ◽  
Global Shape ◽  
The Earth ◽  
Intrinsic Scatter ◽  
Simple Statistical Analysis

The determination of the heights of points on the lunar surface by Earth based astronomy using the geometrical librations, although individually of low accuracy, still provides our best method of obtaining the global shape of the Moon. The intrinsic scatter of the results arises from the effects of ‘seeing’ and simple statistical analysis is required to derive valid conclusions about the shape. Baldwin's method of fitting ellipsoidal surfaces to the points on the maria and uplands, separately by the method of least squares proves to be a valuable tool.Analyses of the ACIC points and of the Pic du Midi studies of G. A. Mills show that good first descriptions of the global shape of the Moon for both the maria and uplands are triaxial ellipsoids with their long axes within 10° of the Earth direction, the major axis of the maria being about 1.3 km smaller than that of the uplands. Of particular significance is that the ellipticity of these surfaces is about 2½ times greater than the dynamical ellipticity; thus the non-hydrostatic figure of the Moon is not simply the result of distortion from a uniform Moon during its early history. The angular variation in density within the Moon cannot be simply a phenomena within the crust but must extend to a great depth. Convection could provide an explanation.The departures of the lunar surface from the idealised ellipsoids are also of interest. The circular maria are systematically depressed relative to the maria ellipsoid: can the mascons have adjusted isostatically since their formation? Systematic differences in height between the western and eastern southern uplands are also noted.

Evidence from the surface configuration of the Moon on its dynamical evolution

1967 ◽  
Vol 296 (1446) ◽  
pp. 298-303
Keyword(s):  
Lunar Surface ◽  
High Velocity ◽  
Dynamical Evolution ◽  
Great Majority ◽  
Major Axis ◽  
The Moon ◽  
Moon System ◽  
The Past ◽  
The Earth ◽  
High Velocity Impacts

Examination of the Moon through large telescopes reveals a multitude of fine detail down to a scale of 1 km or less. The most prominent feature of the lunar surface is the abundance of circular craters. Many investigators agree that a great majority of these craters have been caused by explosions associated with high velocity impacts. It is further generally assumed that the majority of these high velocity impacts took place during the earliest stages of development of the present Earth-Moon system. The morphology of the Moon surface appears in dynamical considerations in the following way. We know from the work of G. H. Darwin that the Moon has been steadily retreating from the Earth. Dynamical considerations suggest that the period of rotation of the Moon on the average equals its period of revolution about the Earth. Thus when the Moon approaches the Earth, its rotation would be accelerated. Since the Moon, like the Earth, approximates to a fluid body, we should expect that a figure of the Moon would have changed in response to its changing rate of rotation. If the craters formed at a time at which the Moon’s figure was markedly different from the present, then initially circular craters would be deformed and any initially circular depression would tend to change into an elliptically shaped depression, with the major axis of the ellipse along the local meridian. Study of the observed distortions of the craters can give evidence as to the past shape of the Moon, provided the craters formed at a time when the Moon possessed a different surface ellipticity. I should like to examine the limitations the present surface structure places on the past dynamical history of the Moon. I will first review briefly calculations bearing on the dynamical evolution of the Earth-Moon system and the implications these calculations have on the past shape of the lunar surface.

Review Lecture: The dynamical properties and internal structures of the Earth, the Moon and the planets

1972 ◽  
Vol 328 (1574) ◽  
pp. 301-336 ◽  
Keyword(s):  
Internal Structure ◽  
Recent Progress ◽  
High Pressures ◽  
Artificial Satellites ◽  
The Moon ◽  
The Earth ◽  
Internal Structures ◽  
Theoretical Investigations ◽  
Dynamical Properties ◽  
Very High

The aim of this review is to bring together and relate recent progress in three subjects - the internal structure of the Earth, the behaviour of materials at very high pressures and the dynamical properties of the planets. Knowledge of the internal structure of the Earth has been advanced in recent years, particularly by observations of free oscillations of the whole Earth excited by the very largest earthquakes; as a consequence, it is clear that K. E. Bullen’s hypothesis that bulk modulus is a smooth function of pressure irrespective of composition is close to the truth for the Earth. Understanding of the behaviour of materials at very high pressure has increased as a result both of experiments on the propagation of shock waves and of theoretical investigations along a number of lines and it can now be seen that Bullen’s hypothesis is not true irrespective of chemical composition and crystal structure but that it happens to apply to the Earth because of particular circumstances. Studies of the orbits of artificial satellites and space probes have led to better knowledge of the dynamics of the Moon, Mars and Venus, and there have also been recent improvements in the traditional studies of Uranus and Neptune. Our knowledge of the dynamics of the planets is on the whole rather restricted, and Bullen’s hypothesis only applies directly to the Moon (for which the application is trivial) and possibly to Mars; the dynamical properties do none the less set fairly restrictive limits to the models that can be constructed for other planets. It would be possible for all planets to have cores of similar composition to the Earth ’s, surrounded by mantles of different sorts, silicates for the terrestrial planets and mostly hydrogen for Jupiter, Saturn, Uranus and Neptune.

Chemical composition of the Moon's 'primary' crust – a clue at a terrestrial origin

2020 ◽  
Author(s):  
Audrey Vorburger ◽  
Peter Wurz ◽  
Manuel Scherf ◽  
Helmut Lammer ◽  
André Galli ◽  
...  
Keyword(s):  
Lunar Surface ◽  
Major Elements ◽  
The Moon ◽  
Lunar Crust ◽  
Near Surface ◽  
Origin And Evolution ◽  
The Past ◽  
The Earth ◽  
Terrestrial Origin ◽  
In The Beginning

<p>The Moon is one of the best characterized objects in space science, yet its origin still actively researched. Available orbital, geophysical, and geochemical information imposes clear restrictions on the origin and evolution of the Earth-Moon system (e.g., Canup 2008, 2012; Ćuk and Stewart 2012; Young et al. 2016). In regard to geochemical constraints, one of the most puzzling conundrums is posed by the similar isotopic fingerprints of the Earth and the Moon (e.g., Wiechert et al. 2001; Armytage et al. 2012; Zhang et al. 2012; Young et al. 2016; Schiller et al. 2018), together with the apparent lunar depletion in volatile elements (e.g., Ringwood and Kesson 1977; Wanke et al. 1977; Albarède et al. 2015; Taylor 2014). This apparent lunar volatile depletion is most notable in the low K content in comparison to U, a finding based on chemical analyses of samples collected from the lunar surface and lunar meteorites, and on spectroscopic observations of the lunar near-surface, despite both having been heavily processed in the past ~ 4.4 billion years.</p><p>In the past 4.4 billion years, space has been a harsh environment for our Moon, especially in the beginning, when the young Sun was still very active and the young Moon was continuously bombarded by meteorites of varying sizes. Solar wind and micro-meteoritic interactions with the lunar surface led to rapid and intensive processing of the lunar crust. Hence, the K/U depletion trend observable on today's lunar surface does not necessarily reflect a K/U ratio valid for the Moon in its entirety. We model the evolution of the abundances of the major elements over the past 4.3 to 4.4 billion years to derive the composition of the original lunar crust. Accounting for this processing, our model results show that the original crust is much less depleted in volatiles than the surface observable today, exhibiting a K/U ratio compatible with Earth and the other terrestrial planets, which strengthens the theory of a terrestrial origin for the Moon.</p>

scholarly journals Experimental Study of Torque Using a Small Scoop on the Lunar Surface

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Long Xue ◽  
Baichao Chen ◽  
Zhenjia Zhao ◽  
Zhaolong Dang ◽  
Meng Zou
Keyword(s):  
Experimental Study ◽  
Bulk Density ◽  
Lunar Surface ◽  
Great Influence ◽  
Test Results ◽  
The Moon ◽  
Rotating Speed ◽  
Simple Apparatus ◽  
The Earth

Chinese missions to the moon are planned to sample the regolith and return it to the earth. Microscale excavators may be good candidates for these missions, as they would significantly reduce the launch mass. Thus, it is necessary to research the interaction between the scoop and the regolith being sampled. We present the development of a simple apparatus to measure excavation torque. All tests were conducted using TYII-2 regolith simulant with gravels. The test results show that, under loose regolith conditions, the penetrating angle and the bulk density had a great influence on the excavation torque, while the rotating speed had little effect. However, when the bulk density was compact, the rotating speed did influence the excavation torque. The excavation torque increased sharply when the scoop encountered the gravels; actually, some of the parameters will influence the value of the torque such as the diameter, quantity, and position and inbuilt depth of the gravels. When the excavation torque sharply increases, the operation should be immediately stopped and checked.

New Economy in space: Cis-lunar economic circle and analogue simulations in China to the 2061 Horizon

2020 ◽  
Author(s):  
guo linli ◽  
blanc michel ◽  
huang tieqiu ◽  
huang jiangze ◽  
yuan jianping ◽  
...  
Keyword(s):  
International Cooperation ◽  
Lunar Surface ◽  
Space Exploration ◽  
Shaanxi Province ◽  
Lunar Exploration ◽  
Test Field ◽  
The Moon ◽  
Liquid Propellant ◽  
The Earth

<p>    The Moon is sometimes also called the "eighth continent" of the Earth. Determining how to utilize cis-lunar orbital infrastructures and lunar resources to carry out new economic activities extended to the space of the Earth-Moon system is one of the long-term goals of lunar exploration activities around the world. Future long-term human deep-space exploration missions to the Moon, on the Moon surface or using the Moon to serve farther destinations will require the utilization of lunar surface or asteroid resources to produce water, oxygen and other consumables needed to maintain human survival and to produce liquid propellant for the supply of spacecraft on the lunar surface. In complement to exploration activities, Moon tourism in cis-lunar orbit and on the lunar surface will become more and more attractive with the increase of  human spaceflight capacity and the development of commercial space activities. However, the development of a sustainable Earth-Moon ecosystem requires that we solve the following five problems:</p><p>(1)How to design alow-cost cis-lunar space transportation capacity? To find an optimal solution, one must compare direct Earth-Moon flight modes with flights based on the utilization of space stations, and identify the most economical spacecraft architectures.</p><p>(2)How to design an efficient set ofcis-lunar orbital infrastructures combining LEO space stations, Earth-Moon L1/L2 point space stations and Moon bases for commercial tourism, taking into account key issues such as energy, communications and others?</p><p>(3)Significant amounts ofliquid oxygen, water, liquid propellant and structural material will be needed for human bases, crew environmental control and life support systems, spacecraft propulsion systems, Moon surface storage and transportation systems. How to  design in-situ resources utilization (ISRU) of the Moon, including its soil, rocks and polar water ice reservoirs, to produce the needed amounts?</p><p>(4) How to simulate on the Earth surface the different components and key technologies that will enable a future long-term human residence on the Moon surface?</p><p>(5). How to accommodate the co-development of public and commercial space and foster international cooperation? How can space policies and international space law help this co-development?</p><p>    China has made rapid progress in robotic lunar exploration activities in the last 20 years, as illustrated by the recent discoveries provided by the Chang'e-4 lander on the far side of the Moon. By 2061, China will have gone into manned lunar exploration and built Moon bases. In preparation for this new phase of its contribution to space exploration, lunar surface simulation instruments have been built in Beijing, Shenzhen and other places in China. A series of achievements have been made in the field of space life sciences . An ambitious project to establish a large Moon base simulation test field, the Lunar Base Yulin (LBY) project, currently in its design phase in Yulin, Shaanxi Province in China, will allow the verification of key relevant technologies.</p><p>    By the 2061 Horizon, we believe that international cooperation and public-private partnership will be key elements to enable this vision of a new, sustainable cis-lunar space economy.</p>

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