I was wondering how massive something have to be so that it it can attract moons by pop culture standards (ellipsoid/round shape).
Could a planetoid have a moon? What is the relation between the mass of a moon and planet?
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Sign up to join this communityPlanetoids can have moons and the minimum size is "pretty small". For example 2003 SS84is a small Near-Earth asteroid, with a diameter of 120m and a moon of about 60m in diameter, which orbits at a distance of 270m ever 24 hours. It probably didn't form by "attracting the moon" but the moon probably formed as a result of impact splitting a "rubble pile" asteroid. The moon, in this case, is similar in size to the main object. There is a wide distribution of size ratios from close to 1:1 to very small objects orbiting much larger ones.
However one aspect of your question is different: you ask for a "round" shape. That makes things harder, since a round shape requires a fairly large size to pull the object into a sphere. There is probably only one object except for the major planets, with a spherical moon, and that is Pluto with its moon Charon (and even Charon isn't perfectly rounded, but it is close)
So it is quite easy for a planetoid to have a moon. But it is hard for a planetoid's to be big enough to pull itself into ellipsoidal equilibrium
In Kollmeier & Raymond (2018), it is stated that a moon can have its own submoon, and that submoon can have a subsubmoon, etc. It doesn't matter if the object is round or not, and there's no minimum mass per se, provided the secondary object has $10^{−5}$ times the primary body's mass, using the rule of thumb from Reid (1973). So, for example for a submoon of the Moon, which has mass of $7.342×10^{22}$ kg, could have a maximum mass of $7.3420×10^{17}$ kg, and that submoon could have a subsubmoon of $7.3420×10^{12}$ kg. There could be, also, a subsubsubmoon, with a mass of $7.3420×10^{7}$ kg, or $10000$ tons. As you can see, there is a moment that the smallest object has very little mass, so it can be gravitationally attached to almost anything.
Edit: the smallest moon in the Solar System is Deimos, with a mass of $1.4762×10^{15}$ kg and a diameter of 12.4 km. So, theoretically, it could have a submoon of $1.4762×10^{7}$ tons.
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sidebar, and will stay there even if the comment is deleted. I think that in this case the comment is the best compromise. $\endgroup$