I wonder if discovering lots of tiny moons will lead to a new definition for moon like what happened with the planets.
As for the spherical shape, the term there is hydrostatic equilibrium: https://en.wikipedia.org/wiki/Hydrostatic_equilibrium.
Keep in mind it's not actually possible to just "capture" an asteroid. The object needs to lose speed somehow in order to be captured.
Most likely via collision - something large hitting the planet, or two other moons crashing.
So the story of the moons is much more complicated than just "random piece of rock".
[1] 10^65 https://en.wikipedia.org/wiki/Timeline_of_the_far_future
Even if the conjecture that sufficiently high entropy causes quantum physical effects to dominate macro-physical spacetime is correct, long before that happens there won't be any objects left which aren't already spherical.
https://en.wikipedia.org/wiki/Roche_limit
If body is in a strange orbit taking it in and out of the roche limit, it will adopt some strange middle ground between bring a round moon and a flat ring. Inside the limit, material will be ripped away from the body and flattened towards a ring. Outside the limit, that material will fall back nearer to the equator. So you get something like a ball with a belt.
Pop culture references aside, yes, a moon is defined to be a natural satellite.
A fun read about this:
- [Asimov - The Relativity of Wrong](http://chem.tufts.edu/answersinscience/relativityofwrong.htm)
From the link above:
> To put it another way, on a flat surface, curvature is 0 per mile everywhere. On the earth's spherical surface, curvature is 0.000126 per mile everywhere (or 8 inches per mile). On the earth's oblate spheroidal surface, the curvature varies from 7.973 inches to the mile to 8.027 inches to the mile.
> The correction in going from spherical to oblate spheroidal is much smaller than going from flat to spherical. Therefore, although the notion of the earth as a sphere is wrong, strictly speaking, it is not as wrong as the notion of the earth as flat.
I've seen a couple fairly decent arguments that Earth/Moon should be considered a double planet.
One is that for every moon we know of except for Earth's, the force on that moon from the planet's gravity is more than the force on that moon from the Sun's gravity.
That's not the case for the Moon. The gravitational force on the Moon from the Sun is about twice as much as the gravitation force on it from the Earth.
I could accept a requirement for moon status being that the thing you are a moon of is the thing that has the strongest gravitational hold on you. For the Moon, that is the Sun.
Another argument is based on the shape of the paths of the bodies as seen from the Sun. Planets follow convex paths. Their moons swing them in and out as the moons go around them, but that just reduces the curvature of the planet's orbit. The Moon, for example, turns the Earth's path as seen from the Sun from essentially a circle (the eccentricity of the ellipse is low enough we can ignore it for this discussion) into a regular 12-gon with broadly rounded corners.
Same goes for other planets with moons, except their convex shape is more complicated because they have multiple moons.
When you look at those other moons from the Sun's viewpoint, they are not following convex paths. They are more like something you might have made when you first played with a Spirograph as a kid.
Except for the Moon. The Moon's path as seen from the Sun has the same basic shape as Earth's, a rounded 12-gon. In other words, it looks like a planet path, not a moon path.
(I'm not sure if that is actually another argument. It may follow from the first argument, the relative gravity strength one...I've not tried to do the math to see).
I find both these arguments pretty good, with one caveat. What happens with even bigger moons relative to their planet than the Moon?
Imagine if Earth had a moon that was much closer to Earth's mass, say 70 or 80%, and much closer to Earth?
Going by either the tug-of-war with the Sun criteria, or the convexity of orbit as seen from the Sun criteria, I think we could get a situation where each body would be classified as a moon of the other! I don't think we want to allow a system that is all moons, so we'll need some fiddling so that in this case they are both planets.
(Credits: I'm reasonably convinced I got both of the above arguments from one of Isaac Asimov's books that collected the monthly science columns he wrote for The Magazine of Fantasy and Science Fiction)
It should at least be considered a planet and dwarf planet pair. After all, the Moon is larger than Pluto. The relative size of the Moon compared to Earth is enough to convince me. Binary planet or double planet would make fine nomenclature.