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

  • 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?


    I did upvoted one answer below. However, a short answer is that indeed there are odds, but just if you select an orbit a priori. There are certainly odds that exactly the moon that we have forms on its orbit, but many are available if you don't put a restrain.

    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?

    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.

    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.

    Isnt it the opposite? Faster when closer and slower when further away? If you want to orbit 1000 from the surface of the earth ya gotta go*fast*

    @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.

    For two bodies, it should be possible to work out the velocity (speed and direction) range that would be required for collision (orbit trajectory with low enough periapsis), for two body gravitation, as well as escape velocity. There may not be a closed form solution, but you could find the ranges to any desired accuracy.

    https://youtu.be/ZENSCasmBzg This video is extremely informative, with simulations of the collision

    @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..

    @Zoltan I think you have the right idea now, orbital mechanics can be incredibly non-intuitive.

    @EuroMicelli One could make an argument that it is not a coincidence that human conciousness developped at exactly the time when sun and moon are able to produce the special eye-looking solar eclipse. It is indeed, as you pointed out, a special time in Earth's life. In fact I think we cannot be 100% certain that anything is a coincidence.

    Is the orbital eccentricity of the Moon really that low compared to that of other planets and moons of the solar system? It seems to me like this is not an amazing coincidence but rather a side-effect from how star systems form.

    @Manuki yes, it is conceivable. I remember Isaac Asimov speculated about that in one of his earlier F&SF columns (I believe “The Triumph of the Moon”). The thing is (as far as I know) we don’t have any evidence or serious theory for a mechanism linking the two; so far, this idea remains just a curious possibility.

    There's also the obvious survivorship bias. Planets with moons that are prone to flying off into space or crashing back to the surface tend to not have moons for very long.

  • James K

    James K Correct answer

    one year ago

    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.


    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?

    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.

    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.

    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)

    @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).

    Question: Any ejecta from the Earth's surface that don't have escape velocity are on an Earth-intersecting trajectory, aren't they? They can only achieve an orbit when they collide with other objects (or interact gravitationally with large bodies -- but there was no Moon yet, so it's collision). This friction-like interaction may be responsible for "aligning" many orbits to a certain mean trajectory.

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