The question of the Moon’s formation has been pondered since prehistoric times. Early explanations involved supernatural influences. Attempts to scientifically explain the Moon’s origin began 350 years ago and is ongoing (Bush).
Like any scientific investigation, searching for an answer must explain what is observed. In the case of the Moon, there are some very tight constraints on any model. These constraints come from the Apollo program’s observations and material returned from the Moon. The return of these samples was a turning point in developing a theory as it effectively precluded all prior theories of lunar formation. These rocks’ geochemistry and isotopic characteristics are the fingerprints left on the Moon by its formation.
This essay explores the various models of Moon formation. I will first detail the constraints of any model. We will then explore the models proposed before the Apollo program before detailing what is now the cornerstone of our understanding of how the Moon was formed. We will also examine the effect that the Moon has and is having on the Earth. At the end, a summary of the current thinking is provided.
Constraints on Moon Formation Models
Any theory proposed for forming the Moon must account for observational and measured data. Specifically, the model must account for:
The dynamics between of the Earth-Moon system.
The compositional differences and similarities between the Earth and Moon.
The relative depletion of volatiles and isotopic signatures in rocks returned from the Moon.
The moon is quite unusual in the Solar System. At 1% of the mass of the Earth, there are few comparisons in the solar system, with only the Pluto–Charon system being comparable. The largest moons orbiting the other terrestrial planets are about 0.01% of the planets they orbit. This tends to indicate a different mode of formation. However, this uniqueness may result from a small number of examples.
Stevenson points out that the Earth-Moon system may not be so unique. He argues that there are few similar comparisons in the inner Solar System. Mercury and Venus may be too small and are affected by Sun-generated tides. The outer planets are mainly gaseous, and their satellites are from different origins. For example, Jupiter’s satellite Io has a substantial volatile content, while the Moon is depleted in volatiles.
The angular momentum of the Earth-Moon system is comparably very high. If the Moon’s mass were brought to the Earth the planet would rotate in about four hours, which is a much shorter day than any of the other inner planets.
An important feature of the Earth-Moon system is that the tidal bulge in the Earth created by the Moon is 10% ahead on the line joining the Earth and Moon (Freedman and Kaufmann). This results from the Earth rotating faster than the Moon orbits the planet. The misalignment creates a gravitational tug on the moon that lifts it into a higher orbit and increases its sidereal period in accordance with Kepler’s third law. This will be explored in more depth in a later section.
Reflectors placed on the Moon by several Moon missions have provided a method to confirm that the Moon is moving away from the Earth. By continually firing laser light at the reflectors it has been determined that the Moon is spiralling away from Earth at a rate of 3.8cm per year. This rate of distance increase is much higher than other systems in the solar system. It is thought that in the initial stages of the Earth-Moon system, the Moon was 15 times closer to the Earth and that the Moon was inclined at 10o to the Earth’s equatorial plane.
Due to the tidal-induced friction between the oceans and the Earth’s crust, the Earth’s rotation is slowing at a rate of 0.002 seconds per century.
The Apollo missions brought back material from the Moon that provides important clues to the origin of the Moon. These rocks were similar to Earth rocks but with an important difference (Canup). The rocks were found to be depleted of volatile elements (e.g. potassium and sodium). These elements boil at a temperature of 900oC. Furthermore, the Moon rocks are enriched in refractory elements. Refractory minerals (eg calcium and aluminium) boil at temperatures greater than 1400oC. The depletion of volatiles indicates that the matter in Moon rocks has been heated to temperatures greater than the rocks on Earth.
The bulk composition of the Earth and Moon is different. The Moon has a lower iron content and a smaller iron core than the Earth. Surveys conducted by the Clementine spacecraft found that the 12km deep South Pole-Aitken Basin floor has an iron content of 10%.. At the same depth on Earth, the iron concentration is 20 – 30%.
An important feature of the Moon’s composition is that it is close to the Earth’s outer layers (Canup).. The Moon’s average density is similar to that of the Earth’s outer layers at 3344 kgm-3. Furthermore, the oxygen isotopic ratios of Moon rocks are identical to those on Earth (Hartmann and Davis). This may indicate that the Earth and the Moon formed at the same distance from the Sun. However, a process related to the formation of the Moon that caused isotopic equilibrium between materials with different isotopic signatures can not be ruled out (Pahlevan and Stevenson).
Dating the Moon’s Formation
An important consideration in developing a model for the formation of the Moon is when it occurred in the Solar System’s development. A review by Halliday details earlier studies to date on the formation of the Moon.
The studies after the Apollo program returned moon rocks but did not provide an exact date for the moon’s formation. Early Sb-Sr and U-Pb isotopic studies indicated that the Moon had formed 4.45 billion years ago. This was very close to the age of the Earth, as shown by lead isotope studies, indicating that both the Earth and the Moon formed simultaneously.
Later studies using the best anorthosite samples returned from the Moon indicate that the Moon’s age is between 45 and 150 million years after the start of the Solar System. This was achieved by studying three isotopic systems (Sr, Nb and Pb).
Halliday proposed that the Moon formed late at 100 million years after the start of the Solar System. This solved several problems with the earlier isotopic studies and was in total agreement with Earth lead and xenon isotopic ratios. However, others (Jacobsen) maintain that the Moon formed as early as 30 million years after the start of the Solar System.
Larger solid bodies began forming in the solar nebula about 4.56 billion years ago (Canupb) At the same time, the solar wind drove off the hydrogen-rich gas after 1 to 10 million years. With the accretion of smaller bodies, larger proto-planets formed, which developed elliptic orbits due to gravitational interactions. The elliptical orbits allow bodies to collide, and if the conditions are correct, accretion could take place. If the collision velocity were too high, rebound, erosion, or fragmentation would occur. With lower collision velocities, accretion could take place. The larger bodies formed into proto-planets and collected smaller bodies due to their greater gravity. This planet-forming period lasted between ten and several hundred million years.
Towards the end of the planet-forming stage, collisions between lunar and larger-sized objects likely occurred. These giant collisions concentrated matter into fewer bodies, as currently observed in the Solar System. This part of the Solar System’s development may have resulted in spectacular collisions between large bodies.
The isotopic data firmly puts the Moon’s formation in the period when the planets formed from smaller bodies. Furthermore, it appears that the Moon formed at a time when giant collisions were taking place.
Theories of the Formation on the Moon
Capture Theory
The capture theory proposes that the Moon formed within the Solar System and was captured by the Earth (Freedman and Kaufmann). It was envisioned that the Moon was in orbit around the Sun close to the ecliptic plane before being captured by the Earth.
This theory has several unlikely factors that must be just right for capture. The Moon would have to move within 50,000 km of the Earth without hitting the planet. It would also have had to move at a speed that would have placed it near a circular object. Captured bodies elsewhere in the Solar System tend to have eccentric orbits inclined to the planet’s equatorial plane. For example, the outer satellites in the Jupiter system all have eccentric orbits inclined to the planet’s equatorial plane (Freedman and Kaufmann). Furthermore, they tend to have retrograde orbits. Computer modelling has shown that capturing the Moon by the Earth would be difficult, and collisions commonly occur in the event of non-capture (Malcuit, Mehringer and Winters).
The major problem with the dynamics involved in capturing the Moon is the dissipation of the Moon’s kinetic energy. It has been proposed that the energy was dissipated over some time. However, this is deemed unlikely due to the presence of bodies of similar size simultaneously. These tend to disrupt a capture and are more likely to increase velocity than decrease it.
A more likely mechanism has been proposed for a capture theory. It would be easier for the Earth to capture swarms of smaller bodies from the circumsolar disk that collected, accreted and were heated to expel volatile elements. However, this still does not explain the iron depletion in the Moon and is dynamically unlikely. Furthermore, a separate mechanism is required to heat this material to a greater temperature than Earth rocks.
Any capture model struggles to explain the identical oxygen ratios between the Earth and the Moon. A study by Pahlevan and Stevenson found that even a body captured that accreted near the Earth’s orbit should have some difference in the oxygen isotopes. This idea will be covered a little more in a later section.
Co-Creation Theory
The co-creation theory states that the Earth and Moon formed simultaneously but separately (Freedman and Kaufmann). The theory is that matter accumulated and accreted to form the moon as the Earth attracted material during the planet-building stage.
It was proposed that the collision of planetesimals threw debris into orbit when they collided near the Earth (Ruskol). In this model a disk formed in the equatorial plane. The material in the disk was sourced from nearby collisions of up to 100 km wide bodies, resulting in fragmentation. The resultant fragments possessed low levels of kinetic energy, allowing their capture. The different-sized satellites were then collected outside the Roche limit to form the Moon. Ruskol envisioned that the Moon was originally located at between 5 and 10 Earth Radii. However, this theory does not explain the density difference between the two bodies. The Earth may have preferentially collected denser bodies, but this does not explain the lack of volatiles.
The co-creation theory does not account for several factors. The theory fails to describe why the Moon is depleted in iron. Presumably the Earth and Moon would have attracted similar material. It also fails to account for the angular momentum in the Earth-Moon system. The accretion of matter tends to slow rates of rotation. It fails to explain why the rocks were heated to a higher temperature. Furthermore, it fails to explain the inclination of the Moon’s orbit to the equatorial plane without a separate mechanism. Also, since this is an evolutionary process, why is this not evident on other terrestrial planets?
Fission Theory
After deducing that the Moon was moving away from the Earth, George Darwin realised that the Earth must have been rotating at a higher speed than currently. He postulated that the Earth spun so fast that mass tore off the planet to form the Moon. The idea is that the Earth is spinning so fast that a prominent bulge developed on the equator. With time, this bulge split from the Earth to form the Moon. This is known as the fission theory.
This model accounts for the Moon’s lower density (Binder). If the Moon formed from the partly differentiated mantle of the Earth, it would contain a lower iron concentration. However, there are some fundamental problems.
Calculations have shown that the Earth would have to be spinning at such a rate that a day would be 2.5 hours long. No known mechanism can account for such a high rotation rate. As previously stated, the current angular momentum could produce a day of 4 hours. As with the co-creation model, this model can not naturally explain the inclination between the Moon’s orbit and the Earth’s equatorial plane.
Geochemical evidence is also against this model. The Moon is depleted in siderophile elements (elements that have a weak affinity for oxygen and sulphur and dissolve in molten iron) other than iron. If the Moon originated from the still differentiating Earth, the Moon should also contain more nickel and less of other siderophile elements than is present. Also, the Moon contains higher concentrations of refractory elements such as aluminium, uranium and rare earth elements.
To remove some of the problems with this theory, elements of the co-creation model have been used to form a precipitation theory. This theory calls for the formation of a ring structure around the planet. The material in the ring formed from the vaporisation of incoming objects on a 2000oC surface. This produced a thick atmosphere containing abundant hydrogen and carbon dioxide and 10 to 20% volatilised silicates. This material formed a ring structure with volatiles and gasses being swept away by the early solar wind. The result would have been material enriched in refractory elements and depleted in volatiles. The material collected to form the Moon. This variation still did not address the angular momentum in the Earth-Moon system. Also, other planets are expected to have similar large moons.
Recognising that this theory failed in the face of evidence of angular momentum, Wise proposed that the mechanism for fission came from within the Earth. He proposed that the formation of the Earth’s core provided the energy to cause the fission. While the theory received some initial support for the formation of the core, it was demonstrated to be implausible by modelling.
Collisional Ejection Theory
The three models proposed before the return of material from the Moon had significant problems and seemed unlikely. The common problem is that they do not explain high angular momentum in the Earth-Moon system. Further processes were required to explain other characteristics, raising doubts about the validity of the models.
Based on accretion theory modelling, Hartmann and Davis proposed that a large body collided with the proto-Earth towards the end of the planet-forming period. The model was further refined with a study by Cameron and Ward. Together, these now form the cornerstone of our understanding of the formation of the Moon. However, it was not recognised until a thorough comparison of the various theories was undertaken at a conference held in 1984 (Stevenson).
The study by Hartmann and Davis looked at the size distribution of gradually smaller bodies. It showed that bodies progressively grew by sweeping up matter close to their orbit. As the bodies became bigger, they accreted other matter more efficiently. As they grew, the bodies may have been destroyed either by destructive collisions or by being accreted by even larger bodies.
At some point, the Earth would have been the largest body near its orbit, and there may have been at least one other large body in a similar orbit. It was calculated that large bodies had formed close to Earth’s orbit within 107 to 108 years.
As the bodies orbit the Sun, they interact to perturb each other’s orbits. This may cause them to enter an orbit on a collisional course with other large bodies. Another option is that the collision occurred as a failed capture. The study by Hartmann and Davis proposed that a large body hit the Earth, giving rise to the Moon.
As the Earth partly differentiated, its mantle was depleted in iron. It is also thought that the body that struck the Earth had also differentiated. Thus, both bodies’ mantle contributed to the Moon’s material, which is also depleted in iron.
After the collision and formation of the Moon, the remaining smaller bodies gave rise to cratering on the Moon. Similar cratering is evident on other planets. In the case of the Moon, it appears that it was struck by bodies 32 – 95km across during this stage. Mars is like to have been struck by an object 100km in radius.
Cameron and Ward refined Hartmann and Davis’s work. They surmised that the location of the impact is a matter of chance and proposed that a glancing hit rather than a direct hit better explains the result. Both bodies were differentiated and perhaps molten at the time of the collision. Furthermore, the impacting body was Mars-sized.
It is thought that the impact velocity was about 11km/sec. As the impact progressed, the side facing away from the side in contact with the Earth sheared off and was accreted onto the proto-Earth. This part included any iron core present. The mantle material on the impactor interacted with the material in Earth’s mantle. The energy of the collision was sufficient to vaporise silicate minerals but not enough to vaporise the bodies’ cores. When the impact spin was imparted on the Earth, it gave rise to the high angular momentum observed today. The impact also tilted the Earth’s rotation axis with respect to the ecliptic plane. Figure 1 illustrates the formation of the Moon as proposed by Hartmann and Davis and Cameron and Ward.
Figure 1: The formation of the Moon due to an off-centre collision of a Mars-sized object (Freedman and Kaufmann)
The resultant material’s trajectory was initially governed by gas pressure gradients as it expanded into space. It is thought that most material was ejected forward. The hot silicates condensed into centimetre- to metre-sized objects early in the process. At a later stage, the volatiles condensed into thin dust and escaped from the system. This process effectively depleted the material of volatiles and concentrated refractory material.
The enormous number of particles would then interact with each other and form a disk, with most material between 2 and 4 Earth radii. Outside of the Roche limit, gravitational clumping would have taken place. It is thought that the Moon could have formed quite quickly in this fashion.
Cameron and Ward found that this process was only valid for an Earth-sized body. If a similar process occurred with Venus, the resultant satellite would have spiralled into the planet long ago.
Stevenson details the aftermath of the collision. With the formation of the disk containing gas and liquid, a photosphere surrounds both the disk and the proto-Earth. This photosphere was approximately 2000K and radiated infrared radiation. The photosphere above the proto-Earth was underlain by a magma ocean. The disk was up to 350km thick, with proto-moons forming outside the Roche limit (Fig. 2). The resultant Moon was at least partly molten to allow evolution, including differentiation.
The collisional ejection theory has several advantages over the previous theories Hartmann and Davis. As opposed to the fission theory, it provides an energy source and is not evolutionary. As a result, the lack of a similar solar system does not present a problem. It neatly explains iron depletion, refractory enrichment and volatile depletion. Furthermore, it explains the relatively high angular momentum of the Earth-Moon system and explains the tilt of the Earth’s tilt to the ecliptic plane. However, there remain some issues with the theory.
Ringwood details some problems with this model. Due to geochemical signatures, it was thought that a Mars-sized compactor would not contribute any material to the moon. It appears that the material of the Moon was derived from the Earth’s mantle. It was proposed that the impactor did not directly produce the Moon but increased angular momentum. The Earth was thought to be at about 70% of its current size. The material of the Moon was produced by the collision of high velocity 0.001 – 0.01 Earth-mass bodies. The material was injected into orbit without significantly melting the Earth’s mantle.
Another issue with this theory is the similarity of the oxygen isotopes of the Earth and the Moon. If a single body impact results in the moon, then there should be a detectable difference in the isotopes (Pahlevan and Stevenson). They state that the similarity is unexpected. Following the work of Canup Pahlevan and Stevenson refined the model proposed by Ringwood to account for the similarity of the isotopes.
Pahlevan and Stevenson note that the highly similar oxygen isotope ratios between the Earth and the Moon are unlikely. They state that large protoplanets would collect material from a wide zone in the protoplanetary disk. Isotopic differences should be measurable, as indicated by the results of hydrodynamic simulations.
The standard hydrodynamic modelling techniques suggest that the Moon comprises about 80% of the impactor’s material. Due to the high concentration of this material in the Moon, any isotopic differences should be evident. The isotopic influences of the impactor on Earth isotopes are diluted due to the greater mass of the Earth and a smaller amount of material being added to the Earth. They state there is no reason to think this model is incorrect.
To explain the similarity in isotopic ratios, Pahlevan and Stevenson suggest turbulent mixing occurred (fig. 2.) In this model, it was proposed that immediately after the collision of a Mars-sized body, a disk of molten material formed. The surface of the planet was covered with a magma ocean. Both the proto-Earth and disk were encased in a silicate vapour-containing atmosphere. Mixing occurred in the disk before the accretion of Moon matter occurred. At the same time as the mixing, the system radiated away heat. This took place over 100 to 1000 years. This mixing resulted in the exchange of atoms between the gas and liquid phases, leading to the equalisation between the Earth-derived materials and the impactor-derived material.
Pahlevan and Stevenson recognise that the lack of water in Moon rocks presents a problem for this model. They note that water should have been transported into the disk. They suggest that hydrodynamic wind drove the dissociated hydrogen and water out of the disk. The system remained closed for silicate material in the disk.
However, the model is incomplete. With the exchange of matter between the Earth and the disk, there should also be a distribution of angular momentum. The model fails to provide a mechanism for that to occur.
The collision theory fails to explain the current inclination of the Moon’s orbit to the equatorial plane because of the formation of a disk, presumably on the Earth’s equatorial plane.
Figure 2: The aftermath of the collision. A: The off-centre collision resulted in forward-ejected vapour. B: the formation of a magma disk with a common atmosphere with the proto-Earth. Convection in both the disk and the enclosing atmosphere allows the exchange of material to attain isotopic equilibrium. C: the disk spreads, and proto-Moons form outside the Roche limit. (Adapted from Stevenson)
The Development of the Earth-Moon System
As previously stated, the Moon is moving away from the Earth at a rate of 3.8cm per year. We will now examine why this occurs and how it will develop.
With the tidal bulge caused by the Moon being ahead of the Earth-Moon line, angular momentum is transferred from the Earth to the Moon (Arbab). Energy is dissipated due to friction within rocks in the Earth’s crust and friction between the oceans and the underlying material. As a result, the Earth’s rotation is slowing, and the Moon moves into progressively higher orbits. To preserve angular momentum, the Moon’s orbital speed decreases. Conversely, the length of Earth’s day was shorter in the past.
As the tidal bulge the Moon creates in the Earth is ahead of the Moon, a force is applied to it. The force results from the slightly great collection of mass in the bulge, leading to a higher gravitational force (Fig 3). This force tugs on the Moon and transfers angular momentum.
Figure 3: the leading tidal bulge providing the gravitational tug to raise the Moon the progressively higher orbits (AEROweb).
It has been pointed out that the current rate of separation is too high (Finch) and would have been unstable 1.5 million years ago (Arbab). This indicates that the tidal coupling must have been less in the past. However, evidence shows that the separation rate has been constant for 360 million years. One explanation for the changing tidal coupling is the changing nature of the World’s oceans due to factors such as the changing depths of oceans and glacial cycles.
In the same way that the Earth’s rotation slowed after it was formed, so did the Moon’s. As the Moon is smaller than the Earth, its rotation stopped after about 50 million years and is now synchronous. Therefore, the Moon rotates once every time it orbits the Earth, keeping the same face towards Earth.
An effect of the slowing of the Earth’s rotation is the lengthening of the day. Likewise, the length of the lunar month increases. With a decreasing variation between the two periods, the angle between the line joining the Moon and Earth is decreasing. This results in less force on the Moon and less angular momentum transfer. Also, with increased distance, the tidal effect will decrease. At some point, the system will reach equilibrium, and both the Earth and Moon will be in synchronous rotation, and no further evolution can occur. The tidal bulges of each body on the other will align with a line connecting the two. The tidally locked Moon will only be visible from one side of Earth. Earth’s day is believed to be about 55 current days long.
Conclusion
The development of theories proposing how the Moon was formed, explored in this article, began in the early 1900s when George Darwin proposed that it resulted from a fission process. Before the Apollo program, the capture theory and the co-creation theory were also seriously considered. However, all three theories had serious problems with certain observations. After the return of rocks from the Moon, geochemical and isotopic data cast further doubt on the earlier theories.
Today, most accept the collisional ejection theory as the best model. However, some problems remain, and work is still ongoing.
The collisional ejection theory tells us that a Mars-sized body struck the proto-Earth off-centre. This occurred towards the end of the planet-forming period when the planetesimals had collected into relatively few larger bodies. The impactor may have been previously disturbed from its orbit by the Earth and may even have resulted from a failed capture.
The collision imparted an enormous amount of energy onto the Earth, increasing its angular momentum and tilting the axis of rotation to the ecliptic plane. The interaction of the differentiated mantles of the Earth and impactor vaporised material that was injected into Earth’s orbit. This material then interacted and formed a disk of molten material on Earth’s equatorial plane.
The enormous amount of energy imparted on the Earth would have ensured that some of the surface was molten, and a magma ocean may have developed. Enclosing both the Earth and disk, an atmosphere rich in silicates developed. While the system cooled, mixing between the Earth and disk (facilitated by a common atmosphere) allowed isotopic equilibrium to be established. After equilibrium was established, the Moon formed outside the Roche limit.
This model successfully accounts for most of the observations and measurements. However, there are still some problems. The process that develops isotopic equilibrium does not explain why angular momentum was not redistributed simultaneously. Also, the model does not explain the tilt of the Moon’s orbit to the Earth’s equatorial plane.
The video below is a short documentary on the Collisional Ejection Theory for the creating on the Earth’s moon. It features Bill Hartmann and Robin Canup who were important figures in the development of this theory.
After formation the Moon underwent volcanic activity producing interesting features like Lunar Rilles.
I found astronomy while working in dark rural locations. Initially, I explored the night sky and learnt the constellations before purchasing a pair of binoculars to further my knowledge of the sky.
My first telescope was a 200 mm Newtonian reflector on an equatorial mount. I found that this telescope had a steep learning curve but was a rewarding experience.
As time progressed, I became interested in astrophotography. This resulted in purchasing a 110 mm refracting telescope and a dedicated monochrome-cooled astronomical camera. This resulted in another very rewarding steep learning curve that far surpassed the experience with my first telescope.
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