The moon has just the right speed not to crash on the Earth or escape into space. What are the odds?

Question

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?

2022 Edit: I got my "ah HA!" moment where everything makes sense after playing 10 minutes of the tutorial of the "Kerbal Space Program" game. Highly recommended.

Short version: Imagine "soccer ball sized" earth with no atmosphere . It is "soccer ball sized" because I want to make sure nothing collides with it, but it is still very heavy. It has no atmosphere because I dont want stuff to be slown down by the atmosphere.

Now imagine you are a few hundred kilometers above that soccer ball and you throw a baseball in any direction.

The baseball witll orbit the "earth" and the orbit will have some oval shape. After every orbit, the baseball will come back to the exact same point and speed/direction relative to the earth.

The speed you pick doesnt matter: it just impacts how far the baseball will travel before coming back. There is no "perfect" "goldilock" speed equilibrium speed you have to launch the ball at.

If you throw the baseball super fast and you are relatively close to the soccer-ball earth, then two interesting points in the orbit are

1. where you are relative to the earth (ball travelling super fast, but low altitude/gravitational energy) and,
2. the furthest point from the earth (ball travelling much slower as it had to "climb", but high altitude/gravitational energy).

(aka good old energy conservation)

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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 with a component 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.

Answer 6

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.