# Roughly how long could an 'Oumuamua type object get?

Roughly how long could an 'Oumuamua type object get if created naturally or if created artificially using fused rock? What would be the limiting factor governing the length of such objects?

Oumaumau was a strange elongated object that entered the Solar System in 2017. It is believed to have formed from a series of molten blobs of rock following a very close encounter with a star.

• An open access link to any of the papers proposing variants of the tidal fragmentation theory might be helpful, if someone can find one. I also want to remark that this particular theory of formation was published yesterday, and is by no means necessarily correct. Apr 14, 2020 at 22:14

Based on the current state of thinking, somewhere in the vicinity of a couple hundred kilometers.

This particular formation theory (Zhang & Lin 2020) is a variant of an idea that's been kicked around for a couple of years. The basic principle is that early in the history of a planetary system, newly-formed planetesimals drift too close to the star and are torn apart by tidal forces. Some of the resulting fragments are, through mechanisms like three-body interactions, ejected into interstellar space, resulting in 'Oumuamua-like objects. (See Ćuk 2018 and Raymond et al. 2018 for a start - Zhang & Lin's idea is an interesting twist on older work.)

The maximum size of these fragments is dictated by the same thing that produced them - tidal forces. After a planetesimal breaks up, tidal stresses continually act on the fragments. Some of these bodies will travel closer to the star, and therefore experience even stronger tidal forces. Each fragment will continue to break up until internal forces can resist gravity and the so-called crack propagation stops.

As part of their analysis of planetesimal fragmentation around white dwarfs, Rafikov 2018 modeled the distribution of fragment sizes. The peak sizes depend on the composition of the planetesimals; iron planetoids should produce minimum and maximum radii of $$R_f^{\text{min}}=350$$ m and $$R_f^{\text{max}}=250$$ km. Rocky planetoids should be slightly smaller, at $$R_f^{\text{min}}=100$$ m and $$R_f^{\text{max}}=200$$ km. It appears that fragmentation of either type should produce significant numbers of 'Oumuamua-sized objects, at $$R_f=100$$ m to $$1$$ km. This is partly why we think these models may be true: they produce 'Oumuamua-like objects. Our dataset is currently extremely limited; it only contains 'Oumuamua and Comet 2I/Borisov.

Most other astronomers use similar limits in their models; we can safely that say that the fragments should have maximum sizes on the order of $$\sim100$$ km. I should note that these fragments, regardless of size, will not necessarily have the same dimensions as 'Oumuamua, but I'm not aware of any authors who have also conducted that sort of analysis.

• How about if it was artificially built up? Could such an object avoid gravitational collapse by virtue of being so extended and so thin? Apr 15, 2020 at 16:01
• @Slarty Well, resistance to tidal forces depends on the structure and material of the object, so perhaps it could - I don't think I can say anything intelligent on the subject. Apr 15, 2020 at 16:15

I suspect that the only real limit is collapse under its own gravity. Of course, it would get more and more fragile as it reached this limit. But, it's floating in empty space. It might help if it was spinning about its long axis. And it's not just length but length to width ratio. I would guess that a few miles across and a hundred miles long would be possible. But very fragile. (Answer partial based on looking at the size of existing asteroids, eg Ceres is approx 1000Km, but gravitationally collapsed).

https://en.wikipedia.org/wiki/4_Vesta

https://en.wikipedia.org/wiki/Ceres_(dwarf_planet)

Rock has a tensile strength of 10 MPa and is brittle. (No, I am not going to attempt any calculation). A bending rod gets compressed on one side and stretched on the other. At some curvature, the stress on the outer edge exceeds the tensile strength, and a crack propagates suddenly across the rod. For a natural space object, the surface would already be riddled with bumps and dents, which would greatly weaken the rock.

As the rock gets longer, think of it as two halves with a center of mass at the 1/4 and 3/4 points. The mass goes up with the length, and the gravity force down with the square length, meaning that the gravity force is getting weaker. But, now think of the rock as curving slightly, with a uniform curvature that is less than the snapping point of the rock. As the rock gets longer, the lever arm of the force gets greater, and the stress on the outer edge larger in proportion to the force.

When the rock is fairly short, this is a 2nd order effect, we can dismiss. But as the rock gets long enough to bend noticeably, actually the distance between the two centers no longer goes up with the length of the rock, and the lever arm eventually does go up with the length of the rock.

Precisely what the balance is and where the breaking point is might be difficult to determine by an exact and justified calculation.

• Haumea is bigger and more massive than Ceres and egg-like shape. Apr 15, 2020 at 0:17
• @RodolfoPenteado good point. But, how thin could it be made before it collapsed? That is what is on my mind. Not 100% sure what is on the OP's mind. Apr 15, 2020 at 6:28
• But a fragment 1000km long would have a tiny gravitational field compared to a whole spherical object such as Ceres no? Apr 15, 2020 at 15:57
• Indeed, but it would be very fragile. How long could it be before a typical micro meteor collision causes vibrations that coupled with the gravitational field would cause it to snap in half. Rocks have low tensile strength. Imagine that there was a slight bowing of the rock. A 1:100 piece of rock is like an asbestos fiber. It would not take much force to bend it so that it breaks. The mass of each half would go up with length and the gravity force down with length squared, so the force between the halves is actually dropping as it get longer. But the fragility is increasing - at what rate? Apr 15, 2020 at 23:07
• And if it was set spinning, then the tensile force could be enormous compared to the tensile strength. Gravity is not the only thing I think would limit the practical length of a rock of fixed cross-sectional area. Apr 15, 2020 at 23:09