scholarly journals Boundary conditions for the formation of the Moon

2015 ◽  
Vol 95 (2) ◽  
pp. 131-139 ◽  
Author(s):  
M. Reuver ◽  
R.J. de Meijer ◽  
I.L. ten Kate ◽  
W. van Westrenen
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Total Angular Momentum ◽  
Nuclear Explosion ◽  
Moment Of Inertia ◽  
The Moon ◽  
Moon System ◽  
Giant Impact ◽  
The Earth ◽  
The Impact

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.

scholarly journals On the Initial Distance of the Moon Forming in the Circumterrestrial Swarm

1972 ◽  
Vol 47 ◽  
pp. 402-404
Author(s):  
E. L. Ruskol
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Outer Boundary ◽  
The Sun ◽  
The Moon ◽  
Present Value ◽  
Primitive Earth ◽  
Moon System ◽  
Initial Distance ◽  
The Earth

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.

scholarly journals Isotopes as tracers of the sources of the lunar material and processes of lunar origin

2014 ◽  
Vol 372 (2024) ◽  
pp. 20130257 ◽  
Author(s):  
Kaveh Pahlevan
Keyword(s):  
Theoretical Calculations ◽  
The Moon ◽  
Isotopic Tracers ◽  
Moon System ◽  
Giant Impact ◽  
Lunar Material ◽  
The Earth ◽  
Post Impact ◽  
The Right ◽  
Mass Dependent

Ever since the Apollo programme, isotopic abundances have been used as tracers to study lunar formation, in particular to study the sources of the lunar material. In the past decade, increasingly precise isotopic data have been reported that give strong indications that the Moon and the Earth's mantle have a common heritage. To reconcile these observations with the origin of the Moon via the collision of two distinct planetary bodies, it has been proposed (i) that the Earth–Moon system underwent convective mixing into a single isotopic reservoir during the approximately 10 3 year molten disc epoch after the giant impact but before lunar accretion, or (ii) that a high angular momentum impact injected a silicate disc into orbit sourced directly from the mantle of the proto-Earth and the impacting planet in the right proportions to match the isotopic observations. Recently, it has also become recognized that liquid–vapour fractionation in the energetic aftermath of the giant impact is capable of generating measurable mass-dependent isotopic offsets between the silicate Earth and Moon, rendering isotopic measurements sensitive not only to the sources of the lunar material, but also to the processes accompanying lunar origin. Here, we review the isotopic evidence that the silicate–Earth–Moon system represents a single planetary reservoir. We then discuss the development of new isotopic tracers sensitive to processes in the melt–vapour lunar disc and how theoretical calculations of their behaviour and sample observations can constrain scenarios of post-impact evolution in the earliest history of the Earth–Moon system.

scholarly journals Vertical angular momentum constraint on lunar formation and orbital history

2020 ◽  
Vol 117 (27) ◽  
pp. 15460-15464 ◽  
Author(s):  
ZhenLiang Tian ◽  
Jack Wisdom
Keyword(s):  
Angular Momentum ◽  
Orbital Plane ◽  
Orbital Evolution ◽  
The Moon ◽  
Moon System ◽  
Left Behind ◽  
System A ◽  
The Earth ◽  
Momentum Constraint ◽  
Fast Rotating

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.

Formation of the Earth-Moon system

2018 ◽  
Vol 14 (S345) ◽  
pp. 148-151
Author(s):  
Sergei I. Ipatov
Keyword(s):  
Angular Momentum ◽  
Total Mass ◽  
The Moon ◽  
Moon System ◽  
Satellite Systems ◽  
Angular Momenta ◽  
The Earth ◽  
Order Of Magnitude ◽  
Rarefied Condensations

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.

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

scholarly journals Isotopic evidence for the formation of the Moon in a canonical giant impact

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sune G. Nielsen ◽  
David V. Bekaert ◽  
Maureen Auro
Keyword(s):  
Solar System ◽  
Isotope Fractionation ◽  
Main Stage ◽  
The Moon ◽  
Giant Impact ◽  
Bulk Silicate Earth ◽  
The Earth ◽  
The Standard Model ◽  
Isotopic Measurements ◽  
Origin Of The Moon

AbstractIsotopic measurements of lunar and terrestrial rocks have revealed that, unlike any other body in the solar system, the Moon is indistinguishable from the Earth for nearly every isotopic system. This observation, however, contradicts predictions by the standard model for the origin of the Moon, the canonical giant impact. Here we show that the vanadium isotopic composition of the Moon is offset from that of the bulk silicate Earth by 0.18 ± 0.04 parts per thousand towards the chondritic value. This offset most likely results from isotope fractionation on proto-Earth during the main stage of terrestrial core formation (pre-giant impact), followed by a canonical giant impact where ~80% of the Moon originates from the impactor of chondritic composition. Our data refute the possibility of post-giant impact equilibration between the Earth and Moon, and implies that the impactor and proto-Earth mainly accreted from a common isotopic reservoir in the inner solar system.

VI. The nature of the Moon’s surface - The lunar surface and the U. S. Ranger programme

1967 ◽  
Vol 296 (1446) ◽  
pp. 399-417 ◽  
Keyword(s):  
The Moon ◽  
Martian Surface ◽  
Mountain Ranges ◽  
The Earth ◽  
Time Dependencies ◽  
The Alps ◽  
Mare Serenitatis ◽  
The Impact ◽  
Characteristic Colour ◽  
Lunar Maria

The unaided eye can see roundish dark spots on the Moon set in a brighter back­ground. Telescopic observation of these dark spots, called maria (plural of mare , sea) reveals that they are nearly level terrain sparsely covered with craters. The brighter surroundings or terrae are from shadow measurements found to be higher, some 1 to 3 km above the maria. The terra elevations scatter widely, reaching several kilometres in the mountain ranges. The most prominent of these ranges occur as peripheral mountain chains around the near-circular maria. Examples are the Apennines, the Alps, the Carpathians, and the Altai Scarp. These arcuate chains surround the maria as the crater walls surround crater floors, an analogy that can be carried further and implies, apart from scale, a similar origin. This origin is almost certainly impact by massive objects. In the case of the impact maria and pre-mare craters, the source of the objects appear to have been a satellite ring around the Earth through which the Moon swept very early in its history, in its outward journey from its position of origin very near the Earth (Kuiper 1954, 1965). The post-mare craters are presumably mostly asteroidal (and partly comet­ary) in origin and related to the craters observed by Mariner IV on Mars. The estimated time dependencies of these two crater-forming processes are shown schematically in figure 1. A fuller discussion of this problem has been given else­where (Kuiper, Strom & Poole 1966; Kuiper 1966). The higher asteroidal impact rate on Mars, by a factor of about 15, as derived from the Mariner IV records, is interpreted as being due to the greater proximity to the asteroid ring. The num­erical factor approximately agrees with theory. Mars apparently lacks the equiva­lent of the initial excessively intense bombardment of the Moon (attributed to impacts by circumterrestrial bodies); unless, of course, the entire Martian surface has been molten and is directly comparable to the lunar maria. This does not seem probable but can at present not be ruled out; if true, the earliest surface history would have been erased. The nature of the mare surface has, during the past decade, been an object of much, perhaps too much, speculation. With the several recent successful lunar reconnaissance missions completed, the older interpretation of the maria as lava beds, based on telescopic observation, has been abundantly confirmed. Four options discussed in recent literature are analysed in Kuiper (1965, §§A, B, pp. 12–39). Among the most potent arguments for the lava cover of the maria are the prominent lava flows observed on Mare Imbrium and Mare Serenitatis, each having a characteristic colour. A map of some Mare Imbrium flows is found in figure 2.

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