Formation of the Moon

[dougettinger]

Why did not other secondary planets occur at other Lagrangian points - especially Jupiter and Saturn? Why have not the asteriods at Jupiter's Lagrangian points been perturbed and collided with Jupiter?

"The 60 degree fore and aft Lagrange points are stable only when the object in it is of insignificant mass. Compared to Jupiter and the Sun, the Trojan asteroids are insignificant."

The giant impact hypothesis predicts an impactor body the mass and size of Mars to possibly create the Moon. Also, time has move onward enough for Earth to differentiate. Mars is not an insignificant mass. What mass located at a Lagrangian point is considered unstable? Also, please tell me what L4 and L5 refer to regarding the Lagrangian points. I presume there are L1, L2, and L3. Please excuse my ignorance.

What was the nature of the perturbation that caused the impactor to move toward and collide with Earth?

"It became too large."

What is too large?

Would not the impactor's glancing blow have knocked Earth away from its orbit as predicted by Bode-Titius Rule?

"Bode's Law is empirical and most likely coincidental. It has little sway in celestial mechanics and no support from extrasolar discoveries. It is also, even if it WERE valid science (which it is not), has no relevance here. It "predicts" nothing."

I am partial to Bode's Law. It did predict the Asteroid Belt and helped to find one of the outer planets. I also personally checked the main satellites of Jupiter and Saturn; these satellites have good agreement with Bode's Law if the initial satellite is chosen correctly. There is not enough complete data from extrasolar discoveries to come to any conclusions about Bode's Law as yet. My contention is that this law predicts the so-called gravity waves which can only be detected by massive bodies that it affects. But I do like your robust answer, Wayne. And, thanks for addressing each of my questions separately.

Why are the bulk composites of the Moon and Earth quite different when they supposely formed from the same region of the solar nebula?

"This is the biggest support of the giant impact hypothesis. When the impactor hit, its dense core merged with Earth's core, giving Earth the over-massive core it has today. The Moon was made from mantle and crust material, lighter silicates which would be blasted off into a stable enough orbit for secondary accretion."

"This is why the Moon is depleted in heavier elements compared to Earth and giant impact is the only theory which can account for it."

You clearly mentioned above that the impactor's dense core merged with Earth's core. Ah, ha. If this is the case then I have to repute the "glancing blow" scenario. And if there was no glancing blow, then the giant impact hypothesis cannot create a Moon. Are you saying that the Earth took a direct hit and the core of the impactor penetrated the Earth's crust and mantle and added much of its mass to the Earth, less the blasted debris? The constraints are beginning to stack up. Too much mass for pre-migrating Lagrangian point and too little mass for a Moon.

[dougettinger]

"It is likely that there were other planets formed early in the development of the Solar System. This was a chaotic environment, with planets perturbing each other, transferring angular momentum, shifting orbital radii, changing position, and being flung out of the Solar System entirely. I think there was plenty of material to allow for collisions like that believed to have created the Moon.

The leading hypothesis is a formation in L4 or L5 of the Earth-Sun system. No chaotic orbits needed. Just a simple case of a body becoming too large to be stable in L4/L5."

Hello Wayne and Chris,

I am enjoying our discussions very much. Please excuse my ineptitube at not knowing how to use the quote button.

Apparently, sides are being taken: one for the Lagrangian impactor and one for early solar system chaos and bombardment. I have interesting issues with both sides. I already expressed my doubts about the Lagrangian impactor. And I have my serious doubts about major impacts in the early solar system within the first few hundred million years after most accretion is completed, but before the Late Bombardment estimated at 3.9 bya. The overwhelming trends of today's solar system such as co-planar orbits, similar spin axis directions and nearly round similar orbital directions leads me to believe the initial solar system formation was quite organized and not very chaotic. To introduce any chaotic orbits and spins and extra massive bodies into a computer simulation of a newly formed solar system will not lead to the known existing trends.

This opinion has no relation to the Later Bombardment which has a plausible explanation in the nice Nice Theory. But, the Nice Theory needs to tell me the origin of the Kuiper Belt ice balls. And, I am not sure about how resonance causes the exchange of orbits. Perhaps resonance can exhange angular momentum by affecting velocities, but once orbits are crossing major havoc will occur.

My contention is that the Moon is still an enigma. Why do the Moon and Earth share the same orbit and why are both held in their orbits by the Sun's gravity field?

[Chris Peterson]

The overwhelming trends of today's solar system such as co-planar orbits, similar spin axis directions and nearly round similar orbital directions leads me to believe the initial solar system formation was quite organized and not very chaotic. To introduce any chaotic orbits and spins and extra massive bodies into a computer simulation of a newly formed solar system will not lead to the known existing trends.

I don't think that's the case. Pretty much all the numerical models of early solar system development show a chaotic environment. What that means is that orbital radii were not stable, due mainly to changing resonances. Angular momentum considerations still explain the coplanar orbits and common spin directions. "Chaotic" doesn't mean everything was going everywhere. Even today, our solar system is at best metastable. Except for some special cases, all multiple body systems are chaotic. The difference is that today the system is much simpler than it was in the first few million years.

[dougettinger]

The overwhelming trends of today's solar system such as co-planar orbits, similar spin axis directions and nearly round similar orbital directions leads me to believe the initial solar system formation was quite organized and not very chaotic. To introduce any chaotic orbits and spins and extra massive bodies into a computer simulation of a newly formed solar system will not lead to the known existing trends.

I don't think that's the case. Pretty much all the numerical models of early solar system development show a chaotic environment. What that means is that orbital radii were not stable, due mainly to changing resonances. Angular momentum considerations still explain the coplanar orbits and common spin directions. "Chaotic" doesn't mean everything was going everywhere. Even today, our solar system is at best metastable. Except for some special cases, all multiple body systems are chaotic. The difference is that today the system is much simpler than it was in the first few million years.

I think I understand angular momentum and how it must be conserved. But how do angular momentum laws create common spins for planets and satellites in our solar system as they are being formed by accretion (which has been somewhat discredited due to recent observations especially for the outer planets) ?

I make an interesting point which I am sure you will amend. The orbiting dust that supposely accretes to make planets moves faster at smaller radii than at larger radii. This scenario should actually create spins in the opposite direction of the orbits for accreting bodies. It is like one rotating gear meshing with another external gear; they rotate in opposite directions.

[dougettinger]

I wish to address issues with the Asteroid Belt once again. If Jupiter's gravity field perturbs and prevents the asteroids from combining, then why did Saturn in the next adjacent orbit form without being disturbed by Jupiter's gravity field?

It isn't just Jupiter's gravity that's the factor. What you get with a complex system of orbiting planets is resonance zones- specific orbital regions that are stable or unstable, depending on the distance from the Sun, distance from other planets, and the orbital periods of those planets. Even within the asteroid belt today it is possible to see radial zones that are completely clear of debris, and other zones where debris accumulates- all because of resonances with Jupiter.

The situation is further confused by the fact that planetary orbits appear not to have been constant over the lifetime of the Solar System. The planets have moved considerably from where they were originally formed- including extreme situations such as the possible switching of position of planetary orbits (see the Nice Model). All of this early action involved planets transferring angular momentum between each other, changing their orbital radii, and creating and breaking various resonances.

Thank you for referring me to the Nice Model. It is a nice invention to explain many solar system anomalies. Wikipedia made a statement that this model's limitations are its inability in producing the outer-system satellites and the Kuiper belt. Do you know why? I would think that outer-system satellites and Kuiper belt bodies would normally be the remnants of such a planetesimal belt that is mentioned in the Nice model.

Doug Ettinger
Pittsburgh, PA

[Chris Peterson]

I make an interesting point which I am sure you will amend. The orbiting dust that supposely accretes to make planets moves faster at smaller radii than at larger radii. This scenario should actually create spins in the opposite direction of the orbits for accreting bodies. It is like one rotating gear meshing with another external gear; they rotate in opposite directions.

I think you are visualizing what happens based on the angular velocities of material at different radii. The conserved property isn't angular velocity, but angular momentum. You need to consider the sum of the angular momenta of all the particles that accrete into a planet. I think if you approach the problem that way, you'll see that the sign of the angular momentum vector is the same for both the orbital direction and the rotational direction.

[dougettinger]

I make an interesting point which I am sure you will amend. The orbiting dust that supposely accretes to make planets moves faster at smaller radii than at larger radii. This scenario should actually create spins in the opposite direction of the orbits for accreting bodies. It is like one rotating gear meshing with another external gear; they rotate in opposite directions.

I think you are visualizing what happens based on the angular velocities of material at different radii. The conserved property isn't angular velocity, but angular momentum. You need to consider the sum of the angular momenta of all the particles that accrete into a planet. I think if you approach the problem that way, you'll see that the sign of the angular momentum vector is the same for both the orbital direction and the rotational direction.

I presume in a protostar disk that the density increases as the radius decreases similar to the velocity of the particles. As a lump is formed in the circulating mass, eddy currents are created to spin the lump in the opposite direction. Then, for conservation of momentum to occur the lumps of accreted mass must slow down. Where does my system of logic fail me?

Douglas Ettinger
Pittsburgh, PA

[Chris Peterson]

I presume in a protostar disk that the density increases as the radius decreases similar to the velocity of the particles. As a lump is formed in the circulating mass, eddy currents are created to spin the lump in the opposite direction. Then, for conservation of momentum to occur the lumps of accreted mass must slow down. Where does my system of logic fail me?

Well, assuming that the logic is flawed, I think it's likely in treating the accretion disc as if it were a fluid. The actual material densities are still quite low- probably close to what we'd call a vacuum in the lab. It isn't clear that you realistically get what could be called "eddy currents", and to the extent they might exist, that they would have the necessary mass to actually transfer significant momentum. I think it is the initial angular momentum of each particle forming the protoplanet that dominates the final angular momentum of the accreted body.

[dougettinger]

Let's assume a vacuum and similar lateral motions for three particles (keeping it simple) and a curvilinear trajectory that is imperceptible at orbital ranges at AU distances. If these particle's changing distances develop so that they attract and cling to each other, the sum of the momentum vectors should only result in randomly different momentum vectors. In other words, initial angular momentums should not show any special trend. Does this make any sense?

I know that planets and satellites generally have the same momentum vector directions. I am only suggesting that there may be a hidden mechanism for causing this trend that is not being considered currently.

Doug Ettinger
Pittsburgh, PA

[bystander]

ScienceShot: Moon Formed From Head-On Collision
Science NOW | Bruce Dorminey | 2012 Aug 03

[url=http://www.nasa.gov/multimedia/imagegallery/image_feature_268_prt.htm][b][i]Credit: NASA/JPL-Caltech[/i][/b][/url]

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Some 4.53 billion years ago, a Mars-sized impactor slammed into Earth, forming a young, molten moon. But was it a head-on collision or a glancing blow? New computer simulations argue for the former, indicating that the impactor scored a direct hit, crashing into Earth at a steeper angle and with a higher velocity than previously thought. The resulting smashup would have ejected far more Earth debris into space than other models have indicated, with much hotter temperatures. And that would mean the moon formed from more Earthlike material than previously thought. The origin of the impactor itself remains an open question. The slow impact velocity of previous models requires it to have originated from an orbit very near Earth, while the new model allows for an origin from more far-flung parts of the solar system, researchers report in an upcoming issue of Icarus.

A hit-and-run Giant Impact scenario - Andreas Reufer et al

• arXiv.org > astro-ph > arXiv:1207.5224 > 22 Jul 2012

Findings Cast Doubt on Moon Origins
Science NOW | Tim Wogan | 2012 Mar 25

[i]Spectacular. New research sheds light on how the moon formed. Credit: Cosmic Collisions Space Show/Rose Center for Earth and Space/AMNH[/i]

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The moon, that giant lump of rock that has fascinated poets and scientists alike, may be about to get even more interesting. A new analysis of isotopes found in lunar minerals challenges the prevailing view of how Earth's nearest neighbor formed.

Most scientists believe Earth collided with a hypothetical, Mars-sized planet called Theia early in its existence, and the resulting smash-up produced a disc of magma orbiting our planet that later coalesced to form the moon. This is called the giant impact hypothesis. Computer models indicate that, for the collision to remain consistent with the laws of physics, at least 40% of the magma would have had to come from Theia.

One way to test the hypothesis is to look at the isotopes of particular elements in rocks returned from the moon. Atoms of most elements can occur in slightly different forms, called isotopes, with slightly different masses. Oxygen, for example, has three isotopes: ¹⁶O, ¹⁷O and ¹⁸O, indicating differences in the number of neutrons each nucleus contains. Compare any two samples of oxygen found on Earth and you'll find the proportions of ¹⁶O, ¹⁷O and ¹⁸O isotopes are almost identical in the two samples. The proportions found in samples from meteorites and other planets like Mars, however, are usually different. So if you find that a sample has the same oxygen isotope composition as one from Earth, then it's very likely the sample came from our world.

Previous research has established that the oxygen isotope composition of lunar samples is indistinguishable from that of Earth. Since 40% of the moon is supposed to have come from Theia (which presumably would have had a different isotope composition), this might spell trouble for the giant impact hypothesis. But it's possible that Earth may have exchanged oxygen gas with the magma disk that later formed the Moon shortly after the collision, explaining why the results are the same.

In the new research, published online today in Nature Geoscience, geochemists led by Junjun Zhang at the University of Chicago in Illinois, together with a colleague at the University of Bern in Switzerland, looked at titanium isotopes in 24 separate samples of lunar rock and soil. The proportion of ⁵⁰Ti to ⁴⁷Ti is another good indicator of whether a sample came from Earth, and, just as with oxygen, the researchers found the moon's proportion was effectively the same as Earth's and different from elsewhere in the solar system. Zhang explains that it's unlikely Earth could have exchanged titanium gas with the magma disk because titanium has a very high boiling point. "The oxygen isotopic composition would be very easily homogenized because oxygen is much more volatile, but we would expect homogenizing titanium to be very difficult."

So, if the giant impact hypothesis doesn't explain the moon, how did it get there? One possibility is that a glancing blow from a passing body left Earth spinning so rapidly that it threw some of itself off into space like a shot put, forming the disk that coalesced into the moon. This would explain why the moon seems to be made entirely of Earth material. But there are problems with this model, too, such as the difficulty of explaining where all the extra angular momentum went after the moon formed, and the researchers aren't claiming to have refuted the giant impact hypothesis.

Planetologist Matthias Meier of Lund University in Sweden, who was not involved in the new study, finds the research persuasive, but he's not ready to give up on the giant impact hypothesis either. "I think the general idea of having an impact forming a disk and this disk then forming a moon is probably right," he says, "but this paper shows us that we still don't understand exactly what the mechanism is, and there is a lot of work to be done in that field."

The proto-Earth as a significant source of lunar material - Junjun Zhang et al

• Nature Geoscience 5(4) 251 (25 Mar 2012) DOI: 10.1038/ngeo1429

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