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The most accurate theory for the formation of our moon is the Giant impact hypothesis, which says that a Mars sized body collided with our early Earth and after this collision all the debris got spreaded and that debris moved in an orbit (somehow) and then recombined to form our moon.

But why didn't that debris fall back to the earth? They didn't have any perpendicular component of velocity to follow an orbit as suggested in this answer.

They were projected radially from the earth's and the collider's crust (Right ?)

So why did that debris followed a curved path to form the moon ?

Ankit
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    That is determined by the total energy of the system, geometry of the impact, and "chemistry" of the rocks. . If the ejecta can orbit, why they shall fall? – Alchimista Jan 23 '21 at 10:54
  • @Alchimista how can they orbit ? – Ankit Jan 23 '21 at 11:17
  • They orbit because "simply" had the right velocity to do so. I see from the way you asked that you do not need recalling of escape veloci and stable orbit. For ejecta to have some forwards (tang.) componenti seems intuitive enough. And for circularuzation am I am pretty sure you also know about conservation of momentum. This would require ejecta collisions or gravitational attraction. Final Moon might have formed from a more massive clump. I speak in principle, not focusing on specific detailed mechanisms for the moon formation. – Alchimista Jan 23 '21 at 12:06
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    Your premise is incorrect: You say "They didn't have any perpendicular component of velocity to follow an orbit". No encounter in the 3-D universe is perfectly radial, particularly considering how orbits intersect. Hence the moon-forming impact came in at a non-zero angle at super-orbital speeds. It is therefore no wonder that the resulting debris entered orbit around the planet. – AtmosphericPrisonEscape Jan 23 '21 at 12:21
  • Seem like probability of earth and pre moon object having zero dependent velocity is small. – marshal craft Jan 24 '21 at 11:47
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    Nitpick/ELL lesson: It's "that debris". Debris is a mass noun, not a plural. That is, "debri" is not a word :-) – jamesqf Jan 24 '21 at 18:23

7 Answers7

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A lot of debris has probably fallen back to earth. To stay in orbit you need enough angular momentum to overcome attraction. But if the collision happened at an angle a portion of the debris could have enough angular momentum to sustain orbit. Here is a nice video of how the collision could have happened.

Here are some snapshots from the video in case the link breaks

enter image description here

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Over time any debris that had enough angular momentum to stay in orbit will eventually collect into the moon (or fall back to earth).

Edit based on the comments.

If you have some experience with orbital mechanics you might expect the debris to follow an ellipse. Since an ellipse forms a closed orbit which started at the surface you might expect that after one period all the debris would have fallen exactly where it came from. This isn't the case though: ellipsoidal curves only occur in two body systems. The blob of mass that is ejected is large enough that it has a gravitational field of its own and this complicates things a lot. Combine this with the fact that the blobs can collide with other blobs and stick to each other. This give some pretty complicated interactions and to say anything meaningful you would have to run a simulation at some point. In this case the interactions make some of the matter go into orbit instead of falling back down.

AccidentalTaylorExpansion
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    In the question the following point is raised: we have that orbital motion is a closed loop; orbital motion comes back to the point where it started. Hence anything ejected from the surface will at some point of the ensuing orbit impact the surface again. In the simulation not all debris rains back on the surface. So: how has the simulation been implemented, such that some material remains in orbit? – Cleonis Jan 23 '21 at 11:50
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    @Cleonis This doesn't depend on the implementation of the simulation (If that's what you mean with implementation) it depends on the physics. This is a valid concern but closed, elliptical orbits only occur in two body systems. Many body systems can show arbitrarily complex behaviour and the blob of mass that is ejected is large enough that it can't be described by a two body system. – AccidentalTaylorExpansion Jan 23 '21 at 13:55
  • Here is why I asked: what is not feasible in simulation in general is to program an exhaustive simulation. As we know: decisions must be made on what effects are small enough to be neglected, and what effects aren't. An exhaustive simulation would require too much computer time. It could be that that this simulation only factors in gravitational interactions of the debris field, it could be that the simulation must factor in actual collisions. What is signifiant? What is negligable? Without that kind of implementation detail offering this simulation has little explanatory power. – Cleonis Jan 23 '21 at 14:25
  • More generally: let me make a comparison. Suppose someone asks about Lagrange points: why is orbital motion close to the L4 and L5 Lagrange points long term resilient? That is something that can be explained in words. Now, sometime ago I created an L4/L5 simulation. Suppose that by way of answer I would offer a video capture of that simulation? While that would present corroboration that the mathematical physics is good, it would not provide explanation. The L4/L5 resilience is among the simplest examples of emergent behavior. The task then is to explain how the L4/L5 orbit resilience emerges. – Cleonis Jan 23 '21 at 14:46
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    @Cleonis I agree that the simulation is highly dependent on the details of the implementation but you asked why the blob doesn't fall back to earth since the orbits are a closed loop. The answer is that for a general many body problem the orbits aren't closed loops. Just from looking I can see the simulation implements gravitiational interactions and some fluid mechanics which includes collisions automatically. The significant result is that from a collision at this particular angle a moon-like body can form which is enough explanatory power to answer this question. – AccidentalTaylorExpansion Jan 23 '21 at 20:07
  • Re the closed-loop discussion, wouldn't the major input to this particular many-body problem be the fact that the Earth is also moving so that it may well not be there when something comes back to that 'initial position'? Even that doesn't really seem like it makes sense in this situation as the motion of the Earth will further disturb the attempted closed-loop path. – SoronelHaetir Jan 23 '21 at 22:33
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    @AccidentalTaylorExpansion The comment on elliptical orbits only applying to two-body systems and this being a many-body system (with added fluid dynamics) is probably worth incorporating into the answer, to help explain the physics shown in the video. – BBeast Jan 25 '21 at 01:08
  • @Cleonis Newton's cannonball, which you're referring to, assumes that the cannonball did not interact with anything after having been fired. Given how much impact debris would have been dusted upwards, that is not true of the future-moon-materials we're talking about here. They bumped into each other and changed their trajectories, making it possible for this cannonball to never hit Newton in the back. – Flater Jan 25 '21 at 15:18
  • @SoronelHaetir: No. Intuitively, if this were true, the moon would suffer from this lag as well, which it does not. Regardless of the Earth, remember that this dust is orbiting the Sun just as much as the Earth is, so they're going to remain in roughly the same orbit. Just as a thought experiment, even though the Moon is influenced more by Earth than the Sun, if the Earth pops out of existence, the Moon will still orbit the Sun. It will slightly alter its orbital trajectory, but that difference is negligible when zooming out to solar system scale. – Flater Jan 25 '21 at 15:25
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    @AccidentalTaylorExpansion I concur with the comment by BBeast. Stating the following explicitly is worthwhile: the simulation features gravitational interaction and fluid mechanics. Your answer and mine were posted within minutes of each other. In my answer I discuss collisions between pieces of debris as a possible mechanism of circularization. Sure: gravitational interaction most likely important too. To investigate how important: run multiple simulation versions, implemented with and without gravitational interaction. – Cleonis Jan 25 '21 at 20:54
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Theories of the moon's formation are hypothetical and a subject of active research. While the impact theory is the most popular at the moment, it's not a done deal. So the true answer is that we don't know.

But proposals for how it might have happened generally suggest a glancing collision, where the second body (Theia) ploughs through the mantle of the Earth, missing the iron core. This explains why the moon has no iron core and has much the same mineral content as the Earth's mantle. This means the debris would start off in a range of elliptical orbits grazing the surface, major axes of the ellipses spread out across the hemisphere that suffered the collision (and thus crossing over in high orbit). There are then a couple of mechanisms commonly proposed for circularising the orbits - tidal circularisation, and collision.

When a body in elliptical orbit is subject to tidal forces, the force is different when it is close to the planet than when it is further away. This applies a repetitive torque on the body that tends to make the orbit more circular, and also drags it towards the rotation of the planet. Tidal forces are stronger and more non-linear if the planet has a non-spherical mass distribution, as might be expected after a planetary collision.

The other mechanism is collisions between bodies in orbit. Initially, the particles have a range of energies and angular momenta, are of different sizes and masses, ranging from huge lumps to vaporised rock (lots of heat, so rock will be boiling off, which will push the bits around like tiny rockets). When chunks collide in orbit, they exchange a part of their energy and angular momentum depending on the parameters of the collision, but given the random properties of the bits, may be considered to be at random. It will spread out in all directions from the point of impact. Some of it will be dropped into even more elliptical orbits and collide with the Earth. Some of it will be knocked into a more circular orbit. A certain proportion enters circular-ish orbit outside the Roche limit and stays there, the rest falls back to Earth.

Initial orbits of debris forming moon

SoupDragon
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    In my opinion, this diagram does the best job of any answers of showing plausible cancellation of radial momentum leading to a stable orbit. – Oscar Smith Jan 25 '21 at 03:15
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I agree you raise a valid point.

It is of course the case that material that is thrown up will not enter circular orbit automatically. Compare launching of satellites. The rocket sets its payload up such that the payload will reach an orbital apogee near the intended altitude, and then some more propulsion is needed to circularize the orbit.

So the question becomes: in the case of the proto-Moon, what effect caused circularization of the orbital motion of the material that went on to form the Moon?

My guess is that the material that was thrown up extended over such a large angle (relative to the Earth), that some debris that was starting to fall down again encounted debris that was still moving upwards.

I imagine that statistically this can have a circularizing effect: the more eccentric the orbit of a particular piece of debris, the larger the probability of a collision with some other piece of debris. Conversely, the more circular the orbits of a population of pieces of debris the lower the probability of a high speed collision within that population.

For comparison: the rings of Saturn. In the case of Saturn's rings the supposition is that tidal effects from other Saturn moons tend to randomize the motion of the particles of the rings, preventing those particles from assembling to another moon. But the rings are very close to circular because any piece not in circular orbit has an elevated probability to collide with other pieces.

In the case of the proto-moon of the Earth there were no other moons to prevent aggregation of the proto-moon to the eventual Moon.

[Later edit]
I recommend the answer by SoupDragon
More details than in my answer, and the picture makes precicely the point I was trying to make in my answer.

Cleonis
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  • The rings of Saturn are within its Roche limit. If you want moons it has to be outside that limit and within the Hill sphere. "Inside the Roche limit, orbiting material disperses and forms rings, whereas outside the limit material tends to coalesce." - " Beyond that distance, a third object in orbit around the second (e.g. the Moon) would spend at least part of its orbit outside the Hill sphere, and would be progressively perturbed by the tidal forces of the central body (e.g. the Sun), eventually ending up orbiting the latter." – Mazura Jan 23 '21 at 20:36
  • @Mazura Yeah, I didn't consider the Roche limit, and I should have. It's interesting; there are small moons inside the ring system (these moons are described as acting as 'shepherds') – Cleonis Jan 25 '21 at 21:06
  • "It is of course the case that material that is thrown up will not enter circular orbit automatically. Compare launching of satellites. The rocket delivers the payload at altitude, and then some more propulsion is needed to circularize the orbit." I feel this is misleading, it's quite the opposite. Most fuel is spent getting up to orbit velocity, and then some more is needed to get the altitude. – orlp Jan 26 '21 at 12:36
  • @orlp I have edited the answer, to bring it into line with my original intention. I wrote 'altitude', but my actual thinking was in terms of an orbital apogee. – Cleonis Jan 26 '21 at 16:15
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Hypersonic collisions of solid matter results in vapor. Much of the "debris" must have been in the gas state. Gas doesn't generally follow Keplerian orbits: instead it collapses into a disk. The subsequent evolution of the disk, condensation and accretion, formed the Moon in a process similar to the formation of planets. At least that's the current understanding...

John Doty
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    but why do gases form a disc ? – Ankit Jan 24 '21 at 03:36
  • Seem like minimal energy distribution of the gas would be disc, if the gravitating object is an oblate spheroid. – marshal craft Jan 24 '21 at 11:50
  • @marshalcraft: Do you have a reference for your claim? – Hans Jan 25 '21 at 01:21
  • @Astudent: Other answers already noted "collisions". In a gas, the colliding bits are the individual molecules. That means there are a lot of collisions. The whole notion of gas pressure is based on the observation that even in a gram of gas, there are so many molecules and so many collisions that the statistical variation in collisions per second can be ignored. Now space is a bit unusual in this respect, as it's effectively a vacuum. But molecules still need to achieve escape velocity to escape, so many heavy molecules didn't. – MSalters Jan 25 '21 at 09:58
  • @Hans, the nature of my statement doesn't seem like a scientific observation which can meaningfully be backed up by an citation referencing some journal or academic institution. So I fully interpret your attack as two possibilities – marshal craft Jan 25 '21 at 16:21
  • The only one that means anything in terms of physics, is that you doubt the possibility of an equilibrium that is trivially phrased as a "ring". Well, that is interesting. I do know mars atmosphere is thinner at the poles. I think Earths may be as well. Both are oblate spheroids approximately. Both I think is attributed to being oblate spheroids. It seems gas giants typically have rings. They are usually oblate spheroids, I believe the rings orientate themselves with the plane of their oblateness. I believe the oblateness, plane of rotation, and ring orientation all agree. – marshal craft Jan 25 '21 at 16:28
  • I believe all of these are purely due to the oblated nature of the distribution of mass. It is an interesting question, the exact nature of the solutions to the gravitational fields, the topology in question, oblate spheroids, and rings, and their solution space in classical gravitation. But I think your comment isn't out of curiosity, only to mindlessly attack thought. I fully believe it deserves to be here. Yours likely does not, attacking citation. I could have not said anything, but your irrational nature is interesting to me. – marshal craft Jan 25 '21 at 16:30
  • @marshalcraft: Why does "minimal energy distribution of the gas would be disc, if the gravitating object is an oblate spheroid" not sound like a falsifiable statement that can be mathematically verified? Do you actually mean to say "attack"? What are the two possibilities? Rather than examining the general oblate spheroid, we can just start with a sphere which can be effectively represented as a point. Will the gas equilibrium state be a disc? – Hans Jan 25 '21 at 16:43
  • I'm not saying I'm right, just doesn't have nothing to do with citations – marshal craft Jan 25 '21 at 17:27
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The Giant Impact might have liquified and even vaporized a large part of both the impactor and the Earth. If this was the case, gas expansion may have added velocity to ejecta post-ejection, to alter the orbits of the ejecta.

Lock et. Al propose the possibility that the impact that created the Moon imparted so much energy that the resultant system exceeded the corotation limit (CoRoL), which is the hottest, highest AM system possible. They theorize the result would be a rapidly spinning vaporized torus of gas called a synestia instead of a planet. Here is a figure from their paper:

enter image description here

They talk about the synestia contracting and shedding angular momentum similar to how the accretion disk of our solar system is thought to have shed momentum as the Sun and planets were formed. The formation of the Moon would then be analogous to the formation of the planets in the Solar System.

Note: I took some of the material for this answer from another answer of mine here: https://astronomy.stackexchange.com/questions/26253/how-fast-was-the-earth-spinning-directly-after-the-moon-formed/40781#40781

Connor Garcia
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Newton's cannonball seemingly applies here, which I suspect is the basis for your question.

enter image description here

An unpowered orbiting body will revisit its position, so anything that got shot off from the surface of the Earth must revisit the Earth. That is correct.

However, unpowered is the issue here. If something interferes with this object mid-orbit, it can alter its trajectory.

As a simple thought example: if I throw a ball up, it will come down again. It will not "bounce" in the air. Launch, upwards, downwards, landing. That is the sequence of events.

But if I throw a second ball and manage to hit the first ball with it, I can alter its trajectory, potentially changing it from moving downward to moving upward again. Given the right force and the right timing (and non-atmospheric altitude), the first ball could change trajectory into a sustainable orbit.

It's important to realize that all these bits of debris were bumping into each other, constantly altering the trajectory. The bits that came up hit the bits that came down. While the odds of hitting the other bit with the exact force for one (or both) to achieve orbits is rather low, there was a lot of debris.

Given the law of big numbers, it's statistically likely for a subset of the debris to achieve a stable enough orbit. Everything else fell back down or escaped Earth's gravity well.

Note also that the dust didn't need to achieve an orbit that's close to circular. What is more correct is to say that the Moon's current orbit is basically an averaging out of all of the dust particle's trajectories, which very basically averaged out as they impacted each other and became a single object.

These original dust trajectories could have all been wildly different, and it is a fair presumption that they indeed were, before forming the Moon.

Flater
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I can see where you're getting this question from: If you fire a cannon from the surface of an airless planet with enough velocity to achieve some sort of orbit, then that cannonball will inevitably come back around and hit the cannon in the back.

But the situation gets a lot more complicated when you have vast amounts of debris flying into space, because the debris field isn't just a single cannonball in a nice neat gravitational field. Each speck of debris is gravitationally bound by the planet it just left, but also to all the other debris around it. A low-flying grain of sand might not have launched with enough velocity to make more than a long arc through the sky, but it's being pulled upward by a trillion grains that nearly acquired escape velocity, and meanwhile the sand grains that got close to escape velocity are being pulled back down by the grains that are below them. It's almost a fluid in the vacuum, drawn together by gravity rather than surface tension. Much of the mass would fall back down or be launched into an independent solar orbit, but as the smear of mess interacts with itself and congeals, a lot of it is going to find a more or less stable orbit, which will lead to coalescence into as single body over many million years.

Or to put it another way, the impact threw up so much debris that the planet's barycenter moved during the impact, so that orbits that previously would have intersected the surface of the planet were now pointing at empty space all the way around.

But even that's not the whole story. I think you're vastly underestimating the effect on the Earth itself. The formation of the Moon is less "blasting a lot of debris off the surface" and more that the planet itself got completely re-melted and stretched into a blobby oblong by the impact. Don't even think of it like bits of rock flying off the surface into space; think of it like stretching a ball of Play-Doh. So much of the planet went 'up there' that concepts like stable orbits didn't even make a lot of sense for a while. It's like the whole planet got spread out into a protoplanetary disc and reformed into a different shape. (Technically it wasn't really a disc, just a long blob, but still.)

Darth Pseudonym
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