Formation of the Earth-Moon system

2018 ◽  
Vol 14 (S345) ◽  
pp. 148-151
Author(s):  
Sergei I. Ipatov

AbstractTrans-Neptunian satellite systems and embryos of the Earth-Moon system could be formed as a result of contraction of rarefied condensations. The angular momenta of rarefied condensations needed for such formation could be acquired at collisions of condensations. The angular momentum of the present Earth-Moon system could be acquired at a collision of two rarefied condensations with a total mass not smaller than 0.1ME, where ME is the mass of the Earth. The mass of the condensation that was a parent for the embryos of the Earth and the Moon could be about 0.01ME, if we take into account the growth of the angular momentum of the embryos with growth of their masses. The Moon embryo could get by an order of magnitude more material ejected from the Earth embryo than that fell directly onto the Moon embryo.

2015 ◽  
Vol 95 (2) ◽  
pp. 131-139 ◽  
Author(s):  
M. Reuver ◽  
R.J. de Meijer ◽  
I.L. ten Kate ◽  
W. van Westrenen

AbstractRecent measurements of the chemical and isotopic composition of lunar samples indicate that the Moon's bulk composition shows great similarities with the composition of the silicate Earth. Moon formation models that attempt to explain these similarities make a wide variety of assumptions about the properties of the Earth prior to the formation of the Moon (the proto-Earth), and about the necessity and properties of an impactor colliding with the proto-Earth. This paper investigates the effects of the proto-Earth's mass, oblateness and internal core-mantle differentiation on its moment of inertia. The ratio of angular momentum and moment of inertia determines the stability of the proto-Earth and the binding energy, i.e. the energy needed to make the transition from an initial state in which the system is a rotating single body with a certain angular momentum to a final state with two bodies (Earth and Moon) with the same total angular momentum, redistributed between Earth and Moon. For the initial state two scenarios are being investigated: a homogeneous (undifferentiated) proto-Earth and a proto-Earth differentiated in a central metallic and an outer silicate shell; for both scenarios a range of oblateness values is investigated. Calculations indicate that a differentiated proto-Earth would become unstable at an angular momentum L that exceeds the total angular momentum of the present-day Earth–Moon system (L0) by factors of 2.5–2.9, with the precise maximum dependent on the proto-Earth's oblateness. Further limitations are imposed by the Roche limit and the logical condition that the separated Earth–Moon system should be formed outside the proto-Earth. This further limits the L values of the Earth–Moon system to a maximum of about L/L0 = 1.5, at a minimum oblateness (a/c ratio) of 1.2. These calculations provide boundary conditions for the main classes of Moon-forming models. Our results show that at the high values of L used in recent giant impact models (1.8 < L/L0 < 3.1), the proposed proto-Earths are unstable before (Cuk & Stewart, 2012) or immediately after (Canup, 2012) the impact, even at a high oblateness (the most favourable condition for stability). We conclude that the recent attempts to improve the classic giant impact hypothesis by studying systems with very high values of L are not supported by the boundary condition calculations in this work. In contrast, this work indicates that the nuclear explosion model for Moon formation (De Meijer et al., 2013) fulfills the boundary conditions and requires approximately one order of magnitude less energy than originally estimated. Hence in our view the nuclear explosion model is presently the model that best explains the formation of the Moon from predominantly terrestrial silicate material.


1972 ◽  
Vol 47 ◽  
pp. 402-404
Author(s):  
E. L. Ruskol

According to the Radzievskij-Artemjev hypothesis of the ‘locked’ revolution of the circumplanetary swarms around the Sun, the initial Moon-to-Earth distance and the angular momentum acquired by the Earth through the accretion of the inner part of the swarm can be evaluated. Depending on the concentration of the density to the centre of the swarm we obtain the initial distance for a single protomoon in the range 15–26 Earth radii R and for a system of 3-4 protomoons in the range 3–78 R, if the outer boundary of the swarm equals to the radius of the Hill's sphere (235 R). The total angular momentum acquired by the primitive Earth-Moon system through the accretion of the swarm particles is ½–⅔ of its present value. The rest of it should be acquired from the direct accretion of interplanetary particles by the Earth. The contribution of satellite swarms into the rotation of other planets is relatively less.


2020 ◽  
Vol 117 (27) ◽  
pp. 15460-15464 ◽  
Author(s):  
ZhenLiang Tian ◽  
Jack Wisdom

The Moon likely formed in a giant impact that left behind a fast-rotating Earth, but the details are still uncertain. Here, we examine the implications of a constraint that has not been fully exploited: The component of the Earth–Moon system’s angular momentum that is perpendicular to the Earth’s orbital plane is nearly conserved in Earth–Moon history, except for possible intervals when the lunar orbit is in resonance with the Earth’s motion about the Sun. This condition sharply constrains the postimpact Earth orientation and the subsequent lunar orbital history. In particular, the scenario involving an initial high-obliquity Earth cannot produce the present Earth–Moon system. A low-obliquity postimpact Earth followed by the evection limit cycle in orbital evolution remains a possible pathway for producing the present angular momentum and observed lunar composition.


1972 ◽  
Vol 9 (5) ◽  
pp. 479-485
Author(s):  
Jean-Maurice Chevallier ◽  
André Cailleux

The authors expressed the view in 1952 that tidal friction between the earth and moon could account for many features such as alterations in biological rhythms, or tectonic effects of unequalled amplitude throughout geological times and the remote past. Tests for this theory are: (a) It is remarkable that the loss of angular momentum by the earth since the "original" state almost exactly matches the amount required to bring the moon from the earth's equator to its present orbit; (b) Recent observations of daily growth increments in fossil organisms show, at least for the last 400 m.y., that the order of magnitude of the time-scale previously adopted by the authors is satisfactory, the scale having only to be somewhat shortened and the values—theoretical and observed—of the month-to-day ratio are in good concordance.


2019 ◽  
Vol 64 (8) ◽  
pp. 762-776
Author(s):  
E. M. Galimov

This article discusses some features of geochemistry of the Earth and the Moon, which manifests the specificity of the mechanism of their formation by fragmentation of protoplanetary gas-dust condensation (Galimov & Krivtsov, 2012). The principal difference between this model and other hypotheses of the Earth-Moon system formation, including the megaimpact hypothesis, is that it assumes the existence of a long stage of the dispersed state of matter, starting with the formation of protoplanetary gas-dust condensation, its compression and fragmentation and ending with the final accretion to the formed high-temperature embryos of the Earth and the Moon. The presence of the dispersed state allows a certain way to interpret the observed properties of the Earth-Moon system. Partial evaporation of solid particles due to adiabatic heating of the compressing condensation leads to the loss of volatiles including FeO. Computer simulations show that the final accretion is mainly performed on a larger fragment (the Earth’s embryo) and only slightly increases the mass of the smaller fragment (the Moon embryo).This explains the relative depletion of the Moon in iron and volatile and the increased concentration of refractory components compared to the Earth. The reversible nature of evaporation into the dispersed space, in contrast to the kinetic regime, and the removal of volatiles in the hydrodynamic flow beyond the gas-dust condensation determines the loss of volatiles without the effect of isotopes fractionation. The reversible nature of volatile evaporation also provides, in contrast to the kinetic regime, the preservation of part of the high-volatile components, such as water, in the planetary body, including the Moon. It follows from the essence of the model that at least a significant part of the Earth’s core is formed not by segregation of iron in the silicate-metal melt, but by evaporation and reduction of FeO in a dispersed medium, followed by deposition of clusters of elemental iron to the center of mass. This mechanism of formation of the core explains the observed excess of siderophilic elements in the Earth’s mantle. It also provides a plausible explanation for the observed character of iron isotopes fractionation (in terms of δ57Fe‰) on Earth and on the Moon. It solves the problem of the formation of iron core from initially oxide (FeO) form. The dispersed state of the substance during the period of accretion suggests that the loss of volatiles occurred during the time of accretion. Using the fact that isotopic systems: U–Pb, Rb–Sr, 129J–129Xe, 244Pu–136Xe, contain volatile components, it is possible to estimate the chronology of events in the evolution of the protoplanetary state. As a result, agreed estimates of the time of fragmentation of the primary protoplanetary condensation and formation of the embryos of the Earth and the Moon are obtained: from 10 to 40 million years, and the time of completion of the earth’s accretion and its birth as a planetary body: 110 – 130 million years after the emergence of the solar system. The presented interpretation is consistent with the fact that solid minerals on the Moon have already appeared at least 60 million years after the birth of the solar system (Barboni et al., 2017), and the metal core in the Earth and in the Moon could not have formed before 50 million years from the start of the solar system, as follows from the analysis of the Hf-W system (Kleine et al., 2009). It is shown that the hypothesis of megaimpact does not satisfy many constraints and does not create a basis for the explanation of the geochemistry of the Earth and the Moon.


Author(s):  
L. V. Morrison ◽  
F. R. Stephenson ◽  
C. Y. Hohenkerk ◽  
M. Zawilski

Historical reports of solar eclipses are added to our previous dataset (Stephenson et al. 2016 Proc. R. Soc. A 472 , 20160404 ( doi:10.1098/rspa.2016.0404 )) in order to refine our determination of centennial and longer-term changes since 720 BC in the rate of rotation of the Earth. The revised observed deceleration is −4.59 ± 0.08 × 10 −22  rad s −2 . By comparison the predicted tidal deceleration based on the conservation of angular momentum in the Sun–Earth–Moon system is −6.39 ± 0.03 × 10 −22  rad s −2 . These signify a mean accelerative component of +1.8 ± 0.1 × 10 −22  rad s −2 . There is also evidence of an oscillatory variation in the rate with a period of about 14 centuries.


Author(s):  
J. Salmon ◽  
R. M Canup

Impacts that leave the Earth–Moon system with a large excess in angular momentum have recently been advocated as a means of generating a protolunar disc with a composition that is nearly identical to that of the Earth's mantle. We here investigate the accretion of the Moon from discs generated by such ‘non-canonical’ impacts, which are typically more compact than discs produced by canonical impacts and have a higher fraction of their mass initially located inside the Roche limit. Our model predicts a similar overall accretional history for both canonical and non-canonical discs, with the Moon forming in three consecutive steps over hundreds of years. However, we find that, to yield a lunar-mass Moon, the more compact non-canonical discs must initially be more massive than implied by prior estimates, and only a few of the discs produced by impact simulations to date appear to meet this condition. Non-canonical impacts require that capture of the Moon into the evection resonance with the Sun reduced the Earth–Moon angular momentum by a factor of 2 or more. We find that the Moon's semi-major axis at the end of its accretion is approximately 7 R ⊕ , which is comparable to the location of the evection resonance for a post-impact Earth with a 2.5 h rotation period in the absence of a disc. Thus, the dynamics of the Moon's assembly may directly affect its ability to be captured into the resonance.


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.


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