II. Early history of the Moon - Dynamical capture of the Moon by the Earth

1967 ◽  
Vol 296 (1446) ◽  
pp. 285-292 ◽  
Keyword(s):  
Orbital Motion ◽  
The Body ◽  
Rotational Instability ◽  
The Moon ◽  
Body System ◽  
The Earth ◽  
Geometrical Features ◽  
Planetary Orbits ◽  
History Of ◽  
Three Body

The process of extracting the Moon from the Earth through some mechanism of rotational instability, and one that can also set it into orbital motion round the Earth, has nowadays come to be widely recognized as almost certainly dynamically impossible. Accordingly ideas have turned towards the notion that the Moon originated as a separate planet and was later captured by the Earth. It is reasonable to conjecture beforehand that this could happen in a three-body system consisting of the Sun, Earth, and Moon, but nevertheless it is of interest and importance to establish that such a capture is possible within the laws of dynamics, and moreover we should like to have some numerical indications of the initial dimensions that the lunar orbit would have on the basis of such an origin. Dissipative action may well be operative upon the planetary orbits to a minute extent, and there may have been eras in the history of the solar system when such dissipation was greater than average, but it seems certain that the main geometrical features of the process of capture of a satellite must in the final stages be governed purely by dynamical forces arising only from the mutual attractions of the bodies. Thus the first stage towards demonstrating the possibility of capture will be to study motions under purely conservative dynamical forces. Considerations of a phase-space or ergodic nature suggest that if the moon were captured in such a way it would eventually escape again, but we cannot on such a basis form any notion of the period of time for which the body might remain a satellite before escaping again. Actual numerical instances are needed to determine this.

Early accretional history of the Earth and the Moon-forming event

Lithos ◽  
1993 ◽  
Vol 30 (3-4) ◽  
pp. 207-221 ◽  
Author(s):  
Stuart Ross Taylor
Keyword(s):  
The Moon ◽  
The Earth ◽  
History Of

scholarly journals The Lunar orbit paradox

2013 ◽  
Vol 40 (1) ◽  
pp. 135-146
Author(s):  
Aleksandar Tomic
Keyword(s):  
Inertial Mass ◽  
Lunar Orbit ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Three Body ◽  
Origin Of The Moon ◽  
Force Intensity ◽  
Critical Consideration

Newton's formula for gravity force gives greather force intensity for atraction of the Moon by the Sun than atraction by the Earth. However, central body in lunar (primary) orbit is the Earth. So appeared paradox which were ignored from competent specialist, because the most important problem, determination of lunar orbit, was inmediately solved sufficiently by mathematical ingeniosity - introducing the Sun as dominant body in the three body system by Delaunay, 1860. On this way the lunar orbit paradox were not canceled. Vujicic made a owerview of principles of mechanics in year 1998, in critical consideration. As an example for application of corrected procedure he was obtained gravity law in some different form, which gave possibility to cancel paradox of lunar orbit. The formula of Vujicic, with our small adaptation, content two type of acceleration - related to inertial mass and related to gravity mass. So appears carried information on the origin of the Moon, and paradox cancels.

Science and Exploration of the Moon: Overview

2021 ◽  
Author(s):  
Bradley L. Jolliff
Keyword(s):  
Solar System ◽  
Nearest Neighbor ◽  
Space Environment ◽  
Cold Trap ◽  
The Moon ◽  
Early Solar System ◽  
Geologic History ◽  
The Earth ◽  
History Of ◽  
The Impact

Earth’s moon, hereafter referred to as “the Moon,” has been an object of intense study since before the time of the Apollo and Luna missions to the lunar surface and associated sample returns. As a differentiated rocky body and as Earth’s companion in the solar system, much study has been given to aspects such as the Moon’s surface characteristics, composition, interior, geologic history, origin, and what it records about the early history of the Earth-Moon system and the evolution of differentiated rocky bodies in the solar system. Much of the Apollo and post-Apollo knowledge came from surface geologic exploration, remote sensing, and extensive studies of the lunar samples. After a hiatus of nearly two decades following the end of Apollo and Luna missions, a new era of lunar exploration began with a series of orbital missions, including missions designed to prepare the way for longer duration human use and further exploration of the Moon. Participation in these missions has become international. The more recent missions have provided global context and have investigated composition, mineralogy, topography, gravity, tectonics, thermal evolution of the interior, thermal and radiation environments at the surface, exosphere composition and phenomena, and characteristics of the poles with their permanently shaded cold-trap environments. New samples were recognized as a class of achondrite meteorites, shown through geochemical and mineralogical similarities to have originated on the Moon. New sample-based studies with ever-improving analytical techniques and approaches have also led to significant discoveries such as the determination of volatile contents, including intrinsic H contents of lunar minerals and glasses. The Moon preserves a record of the impact history of the solar system, and new developments in timing of events, sample based and model based, are leading to a new reckoning of planetary chronology and the events that occurred in the early solar system. The new data provide the grist to test models of formation of the Moon and its early differentiation, and its thermal and volcanic evolution. Thought to have been born of a giant impact into early Earth, new data are providing key constraints on timing and process. The new data are also being used to test hypotheses and work out details such as for the magma ocean concept, the possible existence of an early magnetic field generated by a core dynamo, the effects of intense asteroidal and cometary bombardment during the first 500 million–600 million years, sequestration of volatile compounds at the poles, volcanism through time, including new information about the youngest volcanism on the Moon, and the formation and degradation processes of impact craters, so well preserved on the Moon. The Moon is a natural laboratory and cornerstone for understanding many processes operating in the space environment of the Earth and Moon, now and in the past, and of the geologic processes that have affected the planets through time. The Moon is a destination for further human exploration and activity, including use of valuable resources in space. It behooves humanity to learn as much about Earth’s nearest neighbor in space as possible.

Extended Camus Theory and Higher Order Conjugated Curves

2019 ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Stationary Point ◽  
Higher Order ◽  
The Body ◽  
The Other ◽  
Body System ◽  
Straight Line ◽  
Pair Generation ◽  
Curvature Theory ◽  
Three Body ◽  
Two Bodies

Abstract According to Camus’ theorem, for a single DOF 3-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold-Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e. slide along itself), on the line of the instant centers a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotate about a stationary point, the stationary point embedded on the body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of the Camus’ theorem. The Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.

Classification of Swing-By Trajectories Using the Moon

1995 ◽  
Vol 48 (11S) ◽  
pp. S138-S142 ◽  
Author(s):  
Antonio Fernando Bertachini de Almeida Prado ◽  
Roger Broucke
Keyword(s):  
Large Range ◽  
Initial Conditions ◽  
Close Approach ◽  
The Body ◽  
The Moon ◽  
Three Body Problem ◽  
Jacobian Constant ◽  
Three Body ◽  
The Mathematical Model

In the present paper we study and classify the swing-by maneuvers that use the Moon as the body for the close approach. The goal is to simulate a large variety of initial conditions for those orbits and classify them according to the effects caused by the close approach in the orbit of the spacecraft. Special attention is given to identify the regions where the captures and escapes occur. The classical three parameters (Jacobian constant, pericenter distance and angle of approach) used to identify a Swing-By maneuver are varied in large intervals to cover a large range of possibilities for the maneuver. Letter-plots figures are made to show the results obtained in a compact form. The theoretical prediction that for 0° ≤ ψ ≤ 180° the spacecraft losses energy and for 180° ≤ ψ ≤ 360° the spacecraft gains energy is confirmed. Regions containing trajectories that are candidates to generate Belbruno-Miller trajectories are identified. The well-known planar restricted circular three-body problem is used as the mathematical model. The equations are regularized (using Lamaiˆtre’s regularization), so it is possible to avoid the numerical problems that come from the close approach with the Moon.

Constitution of terrestrial planets

1981 ◽  
Vol 303 (1477) ◽  
pp. 287-302 ◽  
Keyword(s):  
Bulk Composition ◽  
Parent Body ◽  
The Moon ◽  
Volatile Elements ◽  
Earth’S Mantle ◽  
The Earth ◽  
History Of ◽  
Relationship Of ◽  
Reduced State

Reliable estimates of the bulk composition are so far restricted to the three planetary objects from which we have samples for laboratory investigation, i.e. the Earth, the Moon and the eucrite parent asteroid. The last, the parent body of the eucrite— diogenite family of meteorites, an object that like Earth and Moon underwent magmatic differentiations, seems to have an almost chondritic composition except for a considerable depletion of all moderately volatile (Na, K, Rb, F, etc.) and highly volatile (Cl, Br, Cd, Pb, etc.) elements. The Moon is also depleted in moderately volatile and volatile elements compared to carbonaceous chondrites of type 1 (Cl) and also compared to the Earth. Again normalized to Cl and Si the Earth’s mantle and the Moon are slightly enriched in refractory lithophile elements and in magnesium. It might be that this enrichment is fictitious and only due to the normalization to Si and that both Earth’s mantle and Moon are depleted in Si, which partly entered the Earth’s core in metallic form. The striking depletion of the Earth’s mantle for the elements V, Cr and Mn can also be explained by their partial removal into the core. The similar abundances of V, Cr and Mn in the Moon and in the Earth’s mantle indicate the strong genetic relationship of Earth and Moon. Apart from their contents of metallic iron, all siderophile elements, moderately volatile and volatile elements, Earth and Moon are chemically very similar. It might well be that, with these exceptions and that of a varying degree of oxidation, all the inner planets have a similar chemistry. The chemical composition of the Earth’s mantle, for which reliable and accurate data have recently been obtained from the study of ultramafic nodules, yields important information about the accretion history of the Earth and that of the inner planets. It seems that accretion started with highly reduced material, with all Fe as metal and even Si and Cr, V and Mn partly in reduced state, followed by the accretion of more and more oxidized matter.

The early history of the Moon and the Earth

Icarus ◽  
1962 ◽  
Vol 1 (1-6) ◽  
pp. 357-363 ◽  
Author(s):  
H. Alfvén
Keyword(s):  
Early History ◽  
The Moon ◽  
The Earth ◽  
History Of

scholarly journals Menelaah Perkembangan Kajian Hisab Rukyah di Indonesia

ELFALAKY ◽  
2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Heri Zulhadi
Keyword(s):  
The Moon ◽  
Start Time ◽  
Naked Eye ◽  
The Earth ◽  
Modern Period ◽  
History Of ◽  
New Moon ◽  
Calculation System

Abstract Hisab and rukyah are two methods of study used by Muslims to determine the start time of prayer, fasting, hajj and so forth. Periodesasi hisab rukyah, at a glance must have imagined what is meant by hisab rukyah. In the discourse about the Hijri calendar known by the term hisab and rukyah. Hisab is a calendar calculation system based on the average circulation of the moon that surrounds the earth and is conventionally defined. This reckoning system began since the establishment of Caliph Umar ibn Khattab ra (17H) as a reference for composing an enduring Islamic calendar. Another opinion says that this calendar system started in 16 H or 18 H, but the more popular is the year 17 H. While Rukyah is seeing the hilal directly with the naked eye or with the help of tools such as telescopes or other tools that support to see the new moon every end of Qamariyah month. The word rukyah is more famous as rukyatul hilalyaitu see moon. In this study, the author will describe a little about the history of hisab and rukyah in the period of prophets, companions, tabi'in, mid to modern period today. In this study, the scope of hisab rukya includes prayer times, Qibla direction, the beginning of Qamariyah month, eclipse and hijri calendar. Keyword: Hisab, Rukyah.

Resonances and chaos in the asteroid belt

1999 ◽  
Vol 173 ◽  
pp. 297-308
Author(s):  
M. Šidlichovský
Keyword(s):  
The Body ◽  
Asteroid Belt ◽  
Orbital Elements ◽  
Orbital Resonance ◽  
Chaotic Diffusion ◽  
Kirkwood Gaps ◽  
History Of ◽  
The Subject ◽  
Basic Facts ◽  
Three Body

AbstractThe present paper reviews the evolution of our understanding of the effect of resonances on the distribution of asteroids in the asteroid belt. The history of this problem goes back to the Kirkwood's discovery (1867) of the Kirkwood gaps located at resonances with Jupiter. We started to understand the mechanism of their origin only in last decades. It seems that only gravitational effects are sufficient for the depletion. It is now clear that the overlap of secular resonances inside the orbital resonance is the most effective mechanism leading to large chaos and variation of orbital elements. This results in the final removal of asteroids from the gaps by collisions with the inner planets. Chaos, however, does not always mean fast removal of the body. The question of the so called stable chaos will be discussed together with the offered explanations (the high order resonances and the so called three-body resonances). Recently it was shown that chaotic diffusion can play an important role for the 2/1 resonance where the aforementioned explanation for other gaps fails. Basic facts will be reviewed but we will not go into this problem as the importance of chaotic diffusion in dynamics of asteroids (and comets) will be the subject of invited lecture at this conference given by Morbidelli and Nesvorný.

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