What are the repercussions of two asteroids in the asteroid belt colliding?

Question

As the title states, what would happen if two asteroids in the asteroid belt were to collide? Specifically, two the size of 45 Eugina impacting with each other. In my story, I am thinking about having them crash into each other because humans attempted to move one but screwed up the calculations by a few small margins causing one to be launched into the other.

I know that the impact could cause a shockwave and that smaller pieces would be launched in all directions, but I wonder how far and fast these pieces might travel. I am sure Mars would be hit by some of these pieces, but would some make their way to Earth or Jupiter? How far beyond them would they go? To the Sun or Neptune, depending on the direction? Or would the asteroid belt provide enough or a buffer that only nearby asteroids, ships, and maybe Mars would be impacted? Or would the belt cause more problems by creating a domino effect by the pieces of these first two asteroids colliding with other asteroids, creating even more projectiles?

Thank you for any help that can be provided.

Answer 1

Probably nothing

Robert Rapplean's answer is correct (upvoted) that without further information it is not possible to guess at an answer without more information, but there are some additional factors that are too long for a comment:

1. The asteroid belt is very sparse with very little mass. All of the asteroids in total have a mass only equivalent to 3% of that of Earth's moon, spread over an enormous volume of space. (The Empire Strikes Back was a fun film, but through its influence over popular culture it has miseducated generations of viewers regarding what asteroid belts are actually like.) So the asteroid belt will not provide a "buffer" for any violent fragments sent flying by a collision, because the odds of any significant fragments hitting any asteroids in less than geological timeframes are negligible. Similarly, there will not be a domino effect - Kessler Syndrome is a local concern because of how crowded Earth orbit is these days. The asteroid belt is orders of magnitude less crowded and the objects have orbital periods that are orders of magnitude longer.
2. Earth, Mars and all the other celestial bodies each only occupy one point in their orbit at any given time. Even if a large fragment intersects Earth's orbit, for example, the chance of Earth being at that point at that time is miniscule - Earth has a diameter of slightly over 12 thousand km and its orbit is 940 million km long. Over millions of years an object in an orbit that crosses Earth's may eventually have an impactful close encounter, but the odds of it happening on a fragment's first orbit - or even its first few hundred orbits - is incalculably small. Given that 45 Eugenia's orbit is about 4.5 Earth years long and fragments are likely to have comparable orbital periods, do not hold your breath waiting for a collision. (By the same token, it would take an incredibly precise miscalculation for humans to "accidentally" steer one asteroid into another, especially given how large and detectable the second is - the equivalent of "accidentally" shooting a particular ant with a sniper rifle from 3000 metres away when there are no other living things anywhere in any direction within the rifle's range.)
3. Note that the discussion in the previous paragraph assumes that the fragments remain in the ecliptic. Space is three dimensional and while most of the massive objects in solar orbit are in the plane of the ecliptic, energetic fragments from a collision could be thrown into other orbits. These would have even lower chances (per orbit) of striking other bodies.

In summary - if the collision throws fragments into the path of the orbits of other bodies then over the next few million years some collisions will occur. Any immediate collisions would only occur as required by the plot of the story.

Answer 2

There is no way to even start answering this unless you know the relative speed and direction of the two asteroids.

On the low end, they would gently merge into a single larger asteroid, with some rocks being thrown out. This presumes that one of them creeps up slowly on the other, with their direction and velocity only varying by enough that they can move closer to each other.

On the high end, both rocks would be smashed to bits. The only thing you could say about the bits is that the average energy of the resulting bits would be equal to the average energy of the incoming asteroids. Most of them would be on a trajectory similar to the sum of the forces.

From a fiction perspective, they will go wherever the story requires them to go. In real life, most of the planets would see a few fiery trails in the sky, but the odds of anything substantial hitting anything we care about would take centuries, and is the kind of low probability that defines the word astronomical. This is, of course, dependent upon where the asteroids are when they collide.

I'm not going to do calculations, because the numbers would be meaningless to a fictional setting.

Answer 3

Short version? Nothing, worth worrying about, other than those asteroids will be rearranged a bit.

The asteroids do have their own gravity, although minuscule, and if they collided after having been in relatively the same orbit for... well... ever, you're going to get basically a slight comet effect as a little ejecta trails, but a lot of the stuff that they eject will just, very slowly, fall back down. Anything in the collision point between the two asteroids is toast, but... that's about it. When Theia collided with Earth to create the moon (a much bigger impact), it comparatively didn't cause all that much damage to the rest of the solar system.