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My understanding is that the moon was created a long time ago when Earth was hit by a big asteroid.

The debris then agglomerated into the Moon, which happens to be orbiting at the exact speed required to neither crash back into the Earth, nor escape into space.

Having the exact correct speed seems extremely unlikely. Yet, our moon is there, and many other planets have moons.

Are these just the few survivors out of thousands of events that didnt have the « goldilock » speed?

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    $\begingroup$ The odds are 100%, or we wouldn't be here to make the observation. What are the minimum set of physical characteristics to define an Earth like planet? $\endgroup$ – Mazura Jan 30 at 20:01
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    $\begingroup$ The key is that the speed is not special. If the moon had formed with a bit higher traveling speed, it would simply be orbiting a bit farther; if it had formed with a lower speed, it would be orbiting closer. There is a huge range of speeds that would have resulted in some moon, at some distance and some speed. $\endgroup$ – Euro Micelli Jan 30 at 20:59
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    $\begingroup$ There exists one Goldilocks coincidence though: the Moon currently has such an orbital distance and size combination, just right so that it has about the same visual disk size as the Sun. This makes the beautiful solar eclipses we experience possible. This is temporary; the Moon slowly gains orbital speed (and distance) through a tidal interaction with the Earth and in less than a million years it will be too far and visually small to fully block the Sun’s disk, and after that there will never be another total solar eclipse. This is definitely just a lucky coincidence. $\endgroup$ – Euro Micelli Jan 30 at 21:15
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    $\begingroup$ @Zoltan Orbits farther away have lower orbital speeds, but they have more orbital energy. So initial speed has to be higher to inject an object into a higher orbit than into a lower orbit. $\endgroup$ – Connor Garcia Jan 31 at 4:58
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    $\begingroup$ @ConnorGarcia OOOh that's the bit I hadnt thought about. If you are too fast then you will indeed move further away to an orbit where the "equilibrium" speed is lower. My first thought was "then you will keep moving further away", but I had forgot about the part where moving up also means slowing down.. $\endgroup$ – Zoltan Jan 31 at 17:36
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There isn't a "Goldilocks speed" for orbit. If you put two objects in space, and give them a velocity relative to each other, then provided that velocity is less than the escape velocity (at their relative distance) the two objects will orbit each other.

Those orbits will be elliptical, and it is possible that the ellipse is skinny and "eccentric" enough for the two bodies to collide when they are closest to each other. But for an object that is several hundred thousand km from Earth, there is a quite a wide range of possible elliptical orbits.

So when (and if) the grand collision happened, there was a huge amount of matter that was ejected up into space. Some probably was moving so fast that it escaped, Some certainly went into orbits that didn't have enough energy and so were small skinny ellipses and the matter fell back to Earth. But there was a lot that ended up in some kind of elliptical orbit. This matter was not all in the same orbit, but it started to coalesce, and form into a single ball, under its own gravity.

Other moons weren't formed like this, they either formed at the same time as their planets as a "mini solar system" (such as the four major moons of Jupiter) or they were captured from the asteroid or Kuiper belts). Initially, the captured moons may have had rather elliptical orbits.

But most moons are in rather circular orbits. Even if the moon was originally in an elliptical orbit, tidal effects will tend to make the orbit more circular. A planet and moon system has a certain amount of angular momentum and a certain amount of energy. The angular momentum can't change, but energy can be converted into heat and since tides dissipate some energy as heat, the orbit will tend to change to a shape that minimizes energy, for a given amount of angular momentum. That shape is a circle. (See Is the moon's orbit circularizing? Why does tidal heating circularize orbits?)

So the effect of tides is to give moons the "Goldilocks speed" that keeps them in a circular orbit.

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    $\begingroup$ Thanks for replying! I think this answers my point of « having the just right speed » by saying « there is a wide range of speeds that will neither crash nor escape, correct? $\endgroup$ – Zoltan Jan 30 at 13:09
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    $\begingroup$ Basically, that means that the odds of a moon « staying put » are higher than I thought and you dont need to generate thousands of moons to keep one. $\endgroup$ – Zoltan Jan 30 at 13:15
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    $\begingroup$ Now that I think of it, isnt it simply because billions of rocks were thrown into orbit each at a different speed, and those that were at the « just right » speed eventually gathered while the others either escaped or fell back? That way I dont even need a wide range of « just right » speed. $\endgroup$ – Zoltan Jan 30 at 13:51
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    $\begingroup$ Lots of stuff would have been thrown into space, once out in space it all would start to orbit, on lots of different orbits (there are animations of this) Some of those orbits would intersect with the ground, but there is quite a range of orbits that don't. Those rocks then joined up to make a moon. If the moon's orbit was not circular then tides would make it circular. There is quite a range of speeds that are potenially stable. For an orbit of the moon its roughly between 200m/s and 1400 m/s (transverse velocity at lunar distance) $\endgroup$ – James K Jan 30 at 15:07
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    $\begingroup$ @Zoltan: "those that were at the « just right » speed eventually gathered while the others either escaped or fell back" -- that wouldn't account for why the Moon is a large-ish proportion of the mass that could plausibly have been ejected by the collision. You could perhaps see the Moon's speed as the average of all the stuff that was in the large range of "good enough" speeds. To see for sure that there isn't a "just right" speed, you could perhaps look up the actual orbital speeds in systems with multiple satellites (such as the moons of Jupiter, or the planets in the Solar system). $\endgroup$ – Steve Jessop Jan 31 at 15:21
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My understanding is that the moon was created a long time ago when Earth was hit by a big asteroid.

A big asteroid? If you want to call Mars a "big asteroid", then yes, the giant impact hypothesis says that the Earth was hit by a big asteroid. If the giant impact hypothesis is correct, the mass of the impactor was significantly larger (by a factor of eight to ten) than the mass of the Moon. The vast majority of the impactor's mass fell back onto the proto-Earth. A very small amount may have escaped.

The rest of the debris, roughly a tenth of the impactor's original mass, had enough energy to orbit but not enough energy to escape. The debris cloud then circularized, and then attracted itself.

This might be too pretty of a picture, which leads to my next point:

This seems extremely unlikely.

That this may be extremely unlikely is one of the proposed solutions to the Fermi Paradox, which asks why alien beings haven't colonized the Earth: Where are the aliens? If intelligent life requires a planet in the Goldilocks zone, a Goldilocks collision that creates a massive moon that stabilizes the planet's orientation, a Goldilocks amount of water, and a Goldilocks climate that keeps the climate relatively stable for over a billion years, then perhaps intelligent life is extremely rare. We humans may be here because our planet was one of the few winners in an intergalactic lottery in which almost every planet is a loser.

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    $\begingroup$ Thanks for replying! Re: goldilock zone for life, I should have used a different word, because I really meant the « just right speed to orbit without escaping ». My new understanding is that there is a wide range of speeds that will neither crash nor escape, which means that the odds of a moon ´staying put’ are higher than I expected. $\endgroup$ – Zoltan Jan 30 at 13:14
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    $\begingroup$ @Zoltan The key thing you might not have realized is that orbital speed and distance are tied together. The average Earth-Moon distance is ~385,000 km; to stay at that distance, the Moon must maintain the orbital speed it has. But there's a wide range of distances the Moon could be orbiting at, stably, and so also a wide range of speeds. $\endgroup$ – zwol Jan 31 at 16:17
  • $\begingroup$ A simpler explanation to the Fermi Paradox could be that time and space are too big compared to our own small neighborhood and a few thousand years of written history or millions years of archaeology. Life could have started and vanished, or will start after we are no longer here. $\endgroup$ – Rsf Feb 2 at 13:38
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I just want to add some numbers. The International Space Station orbits with the speed of 7.66 km/s (27,600 km/h). On the other hand, Earth's escape velocity is around 11 km/s (40,000 km/h). This means that anything with the speed in that range will orbit Earth. So it doesn't need to be some kind of a precise speed for objects to remain in Earth's orbit. Granted, the orbits of fragments from the Giant impact had different shapes, but over millions of years they started to clump together and eventually the largest object cleaned the smaller fragments because orbits of different shapes are not sustainable in the long term.

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  • $\begingroup$ Can you clarify why you can compare the orbital speed (which is tangential, i.e. sideways) with escape velocity (which you might assume is radial, i.e. straight up)? $\endgroup$ – gidds Jan 31 at 22:38
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    $\begingroup$ @gidds Escape velocity might actually be better named escape speed, since the direction does not matter. If you are moving at 11km/s relative to earth in any direction (so long as it's not one that results in a collision with earth itself), you have sufficient kinetic energy to go as far as you want from earth (i.e. escape). $\endgroup$ – Nuclear Hoagie Feb 1 at 13:37
  • $\begingroup$ Obligatory XKCD: xkcd.com/1356 $\endgroup$ – I'm with Monica Feb 2 at 7:28
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You might reasonably assume that the result of the collision was a big cloud of debris of various sizes. Some bits will have come rapidly back to what was left of Earth, other bits will have gone flying out into space, and some bits stayed more or less in orbit for long enough to coalesce into the Moon. At this scale, solids behave more or less like liquids and so both Earth and Moon formed into roughly spherical shapes. Mars' moons, being somewhat smaller and (IIRC) newer, are rather less spherical.

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I"m not sure if I understood your question or I just didn't answer your question right. However, the earth has been bombarded by many debris floating around in the early solar system. This was due to the fact that in the belt around the sun various aggregations of material happened through mutual attraction of smaller materials, that grew. This is how all the planets formed in star systems. At a certain period in time the diverse clumped together debris where big enough to be called proto planets and the rest was still called debris or asteroids.

The theory you are mentioning is called the giant impact theory or the Theia impact. Earth was not struck by an asteroid, but by another proto planet called Theia. It is assumed that this has happening a lot, also in other star systems. The fact that from this impact the earth and the moon formed in the form they currently have, is unique in our solar system. We only see it with the earth. However, impacts between proto planets is not considered to be rare in the early solar system, so the chance that the Theia impact could happen might have been small, but considering the chance of colliding proto planets was very high, the possibility was there.

Now back to your remark that the moon has exactly the right speed to stay in orbit with the earth. This is not true. The moon actually has a speed too high to stay in orbit and the distance between the earth and the moon is getting bigger each year. High precision measurements are made and suggest that the moon is spiraling away from the earth with a speed of about 4 centimeter per year. Of there the course of the last 4 billion years, this has thus been quite a distance and it suggests the speed is not exactly right, but a bit too high.

Still, a Theia-like collision between Venus and another proto planet would not have resulted in a planet moon system, due to the tidal forces from the sun. A similar thing would apply for Mars, but here Jupiter is the reason for the absence of such a pair. The outer planets are too big and would have not resulted in material being able to escape the planet's gravity.

So, yes, the existence of the earth moon can be seen as a unique situation, but this is not because the kind of impacts didn't happen. It is because the earth was just at the right distance from the sun and Jupiter to result in such a pair. Impacts like the Theia impact were not rare. Do, however, understand that the Theia-impact is a theory that has good acceptance, but is not undoubted. There are several questions about the validity of this theory.

Kind regards, MacUserT

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    $\begingroup$ Thanks for replying! I also read about the 4cm distance increase, I ´ll argue that if it is slow enough for the moon to still be around after 4bn years then it is pretty much at the ideal speed:). My newfound understanding is that a wide range of speeds will lead to a moon that isnt going too slow or fast, so a moon is much more likely to stay in place than I thought $\endgroup$ – Zoltan Jan 30 at 13:18
  • $\begingroup$ Is it really correct to say that the moon is going faster then a certain value? The fact that the Moon goes slowly away isn't really because it has a speed exceeding that of a special orbit. It cannot even be spelled... Isn't? I would say that being the orbiting bodies not rigid than there is acceleration /transfer of momentum...... Just to say that the sentence "thus is not true. The moon actually...." seems - although I somehow understand what you mean - suggesting something untrue to OP, or just is not a very happy formulation. $\endgroup$ – Alchimista Jan 30 at 13:53
  • $\begingroup$ The additional 4cm per year is due to tidal effects. The energy comes from slowing the Earth's rotation. Eventually the Earth and Moon will keep the same face to each other, meaning that there will be no tides - provided nothing happens to disturb the system before then. $\endgroup$ – Rich Farmbrough Feb 1 at 14:03
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A point not mentioned above is that the primordial swarm of material that would eventually form the Moon would, on average, have the same direction of orbit around the Earth as the Moon does today. In that case, we shouldn't ignore collisions between that material where the radial momenta are cancelled and leave only, or mostly, the tangential momenta (possibly with coaleced material). Similarly, collisions parallel to the axis of the orbit would generally reduce momenta parallel to the axis of the orbit and lead to a disk of material (as seen for Saturn's rings). Self-gravity would then create 'lumpiness' in the disk and the dominant lump would preferentially attract material to itself and form a single body. It's not jut an orbital dynamics problem but also one of momentum exchange and aggregation statistics.

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