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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?

Thanks

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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 yesterday
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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 yesterday
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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 19 hours ago
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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 7 hours ago
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    $\begingroup$ @Zoltan I think you have the right idea now, orbital mechanics can be incredibly non-intuitive. $\endgroup$ – Connor Garcia 6 hours ago
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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 momentum and a certain amount of energy. The 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 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 yesterday
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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 yesterday
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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 yesterday
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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 yesterday
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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 9 hours ago
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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 yesterday
  • $\begingroup$ @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 8 hours ago
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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 1 hour ago
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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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