Okay, the setup: I want to take an 8-900 meter M-Type asteroid—the type that’s mostly metallic, hence the “M”—attach an engine to it, and fly it around the solar system a little.
Nevermind where I’m getting the engine to do this, or what I’m going to do with it. My question is: what kind of acceleration could I reasonably apply to such an asteroid, ballpark, without breaking it apart?
I can guess that this would at least be an easier feat than trying to move around a rocky “rubble pile,” but beyond that, it’s still beyond my wheelhouse.
And as an addendum, are there any kind of structural changes that I should or could make to such an asteroid to better withstand G-forces, short of melting it down, adding a c-type asteroid, and turning it into a giant steel bullet?
(As that, of course, would just be silly, and has no place in a serious engineering discussion about carving a space rock the size of Disneyland into an atomic Ed Roth hot rod.)
You’d actually need to know details about the composition and structure of the asteroid to answer that, but in any case it won’t be much. Even large igneous rocks with a high metallic composition are going to have low shear strength compared to even mild steel or other structural materials just because it will have natural lines of fracture where it crystallizes. Any concentrated thrust reaction is going to develop large shear loads. If you could distribute your thrust across the body (assuming, of course, that it isn’t rotating) and adjust the thrust to equalize shear stresses then you might be able to apply high thrust (on the order of Earth surface gravity or higher) but even slight imbalances will contributed to fractures. The metallic meteorites you see in museums are the residue of much, much larger meteors that fractured and burned up during descent and don’t represent what you would find in interplanetary space.
Uh…sure. I won’t ask any questions about it. I’m sure your intentions are completely benign.
There’s no need for any structural reinforcement. You can apply an arbitrarily high acceleration to any collection of rubble.
You simply have to acquire a large quantity of neutron star matter and some means of forming it into a large, thin plane.
The gravitational acceleration of an infinite plane is constant, independent of distance. Of course your plane is not infinite, but if you make it large large compared to the asteroid, it should be a reasonable approximation. There will be some residual tidal forces which scale by the mass of your plane and the resulting acceleration, so the higher the acceleration the larger it needs to be to stay within structural limits (possibly just the self-gravity of the asteroid).
Then, place the neutronium plane near the asteroid, and accelerate it around the solar system with your magical engines. The asteroid will “fall” towards the plane, which is itself accelerating away, but due to the constant acceleration field will not tend to rip apart.
You’ve translated the difficulty of applying an impulse to an asteroid without fracturing it to the impossibility of making a flat plate of neutronium, which requires compressing matter to neutron degeneracy pressure and maintaining that condition, even at the free edges of the plate that would probably be oscillating like crazy under such radical stresses and radiating away gravitational energy. How you could possibly maintain this condition without being in gravitationally compressed in the core of a neutron star is a question, as is how you would manipulate such an object is unclear because being electrically neutral means you can’t use electromagnetic forces, and any solid material you put into contact with it should be destroyed by differential tensile stresses due to the extreme gravitational gradient.
Fundamentally, if you had the command of gravitational forces to make this object, you probably wouldn’t need to do anything as crude as use it as a tractor; you could just create directional gravity waves on demand and bend space to make the asteroid go wherever you want.
But the other asteroid is likely a rubble pile too! Consider that asteroids have been playing extreme bumper cars for four and half billion years. The very largest ones may not be rubble piles, but most of the rest probably are. Except for the fast rotators where the rotation throws the rubble off.
The OP wanted to know the peak acceleration without destroying it. I doubt a net would survive more than a few milligees before rocks started leaking out the holes.
A bag would do better, but at a certain level the asteroid is going to turn to soup. Large mountains on Earth are more like 10 km tall instead of 1 km, so as a very rough ballpark, I’ll say that around 10 gees acceleration are possible before the asteroid deforms into some other shape, even assuming it’s gently cradled at the bottom.
But we can do a lot better than that, since objects in freefall can accelerate arbitrarily quickly, with the only limits being tidal forces. If we can set up a constant gravitational field, then the amount of acceleration possible is unlimited.
Well, maybe not quite unlimited. I haven’t worked out the geometric limits here. Eventually our mass will form a black hole. That might be ok, though it does prevent us from using a flat plate. We can instead use a large black hole, which will have sufficiently low tidal forces at a reasonable distance away (for really big black holes, that might even be at the event horizon).
Well, that’s fair. The neutronium plate probably needs a gravy device just to keep it in the right shape, and if you have that then there’s no need for the neutronium. Call it an art project, then.
Unless you need to get the asteroid to a high speed really fast it probably does not matter.
Given enough time you can get that asteroid up to a really fast speed.
At 1g acceleration (what you are experiencing right now reading this) you can get a mass to 0.5.c (stupidly fast…way, way, way faster than humans have ever gotten something bigger than an atom to go) in ~177 days. If you are flinging something from the outer solar system into the inner solar system you have that time. Maybe even from the asteroid belt (not sure).
There are loads of problems doing the above but the acceleration is modest and not what will break things.
I guess anything in an elliptical orbit will speed up and slow down to varying degreess. Such an asteroid that endures that natural acceleration variation stands a decent chance of remaining intact with a sustained acceleration in that range at least.
(Layman’s thoughts of course, I don’t know what sort of accelertion such a natural process imparts)
Tidal forces are proportional to the inverse of the cube of the radius, so not too large for natural orbits. Even though the gravitational acceleration is proportional to r^{-2}.
But do I take it from your fancy book-learning that trying to go much beyond such gravitational forces and natural orbits means that tidal forces on the body start to climb substantially?
Absolutely no fancy calculation elided. What I mean is, say you are in orbit around the Earth. Even though you are constantly accelerated at close to 1g, you just feel like you are floating, not ripped apart. Same thing for an asteroid. On the other hand, if you accelerate something at 1g by strapping a rocket engine to it, there will obviously be some internal stresses when you first fire it up.
Sure, that much I did know. I may not be expressing myself clearly here (that’s your reward for trying to be helpful with someone who knows vanishingly little about orbital mechanics).
I’m thinking that if an asteroid was in an elliptical orbit it wouldn’t have a constant acceleration and so would be subject to certain internal forces and stresses that come from that.
If you could put a number on that additional acceleration then could you not safely apply that acceleration constantly with reasonable expectation that the asteroid could take it without breaking up?
If that was the case then it would be interesting to know what the value of that acceleration would be and what that means in velocity after, say, a year.
Maybe, but the stress from being in a solar orbit at the distance of your typical asteroid is quite low. Even near-Earth asteroid distances don’t induce much stress. There’s lots more stress from rotation of the asteroid. However, the stress from linear acceleration is going to be in a different direction than those from either kind of rotation, so they probably don’t tell you as much as you’d like.