What is the danger for Ceres of collision with other asteroids?

Question

In the context of possible colonization of Ceres, would not such colony be totally impossible because of high probability of collision of Ceres with other asteroids in the Asteroid Belt?

Answer 1

There are a few common misconceptions about the main belt's density and relative velocities between its members that seem to cause quite many of such questions similar to yours even on our site. This seems to boil down to how asteroid belt (aka main belt, because it isn't really the only asteroid belt in the Solar system) is often visually represented in media, greatly exaggerating its density for visualisation purposes. I'd first like to invite you to read through a few answers to these related questions that discuss main belt density from various perspectives:

• What's the (particle) density of the asteroid belt?
• How do spacecraft navigate through the Asteroid belt to avoid collision?
• How frequently do asteroids collide with each other?

You'll notice that, while the chance of a collision is never zero, it is indeed astronomically slim. But it gets better, at least as far as collisions between main belt members are concerned. You see, Ceres' mass, despite being the largest member of the main belt, is only about 1.3% that of our own Moon's mass. That means it's gravitationally a lot less attractive body, which further reduces the chance that it would gravitationally perturb orbits of other asteroids in the main belt sufficiently enough to cause them to destabilize and potentially intersect with Cerean own some orbits around the Sun later. With Cerean orbital period of 4.6 Julian years, even if that happened, it would take many, many years for such orbits to intersect and for both bodies to be at exactly the same time at exactly the same place in their orbital position for all of this to result in impact.

Better still, relative velocities between main belt objects are small, and all the rest of them are much less massive than Ceres, both facts substantially reducing kinetic potential of such collision events. So if we indeed colonized it, and we'd first have to have the technology to do so, we'd also have means to predict future collisions, and have sufficient time to redirect any threatening objects away from its intersecting orbit with Ceres. Do that many years in advance and it becomes a trivial matter even for today's technology.

Edit: Actually, come to think of it, considering the rarity of some of the other main belt objects getting relatively close to Ceres, they could be considered a blessing rather than a curse. You get to mine them for likely much needed resources relatively cheaply in the region where there's nearly no other significant mass to be found for millions of kilometers in any direction.

For some numbers, refer to Collision rates and impact velocities in the main asteroid belt, Paolo Farinella, Dipartimento di Matematica, Università di Pisa and Donald R. Davis, Planetary Science Institute, Tucson, Arizona paper that, while not exactly recent (came out in my college years) and is sadly paywalled, in its abstract does give some relevant numbers to our problem. Reproducing the abstract of the mentioned paper here for convenience:

We have computed, using G.W. Wetherill's (1967, J. Geophys. Res. 72, 2429–2444) algorithm, mutual collision probabilities and impact velocities for a set of 682 asteroids of diameter > 50 km, intended to represent a bias-free sample of asteroid orbits.

For every asteroid, we have obtained the intrinsic collision probability, $P_i$, the average collision velocity, $V$, and the number of projectile orbits which can intersect the target asteroid's orbit, Ncross, using the proper orbital elements of A. Milani and Z. Knežević (1990, Celest. Mech. 49, 247–411). The average values and the corresponding standard deviations for the whole asteroid sample are:

• $〈P_i〉 = 2.85 ± 0.66 \cdot 10^{−18} \text{ km}^{−2} \text{ year}^{−1}$,

• $〈V〉 = 5.81 ± 1.88 \text{ km/sec}$,

• $〈N_{cross}〉 = 601$ (88% of the existing orbit pairs).

No significant differences were found in the average values of $P_i$, $V$, or $N_{cross}$ using osculating elements instead of proper elements, although results for individual asteroids could change by $\approx 10\%$.

A running box mean of the intrinsic collision probability with semimajor axis shows a peak near $2.7 \text{ AU}$ with $〈Pi〉= 3.4 \cdot 10^{−18} \text{ km}^{−2} \text{ year}^{−1}$ followed by a nearly monotonic decrease to $〈Pi〉 = 1.8 \cdot 10^{−18} \text{ km}^{−2} \text{ year}^{−1}$ at $3.3 \text{ AU}$.

Collision probabilities are nearly independent of eccentricities but show a significant decrease with larger inclinations. As expected, collisional velocities grow rapidly with increasing orbital eccentricities and inclinations, but they show surprisingly little variation across the asteroid belt.

Family asteroids undergo collisions with other members of the same family two to three times more frequently than with nonfamily projectiles, but the relative speed of these intrafamily impacts is comparatively low for the Koronis and Themis families.

So, even generously overestimating the number of colony threatening mass asteroids in the main belt that intersect Cerean orbit, let's for the sake of argument say there's one million of them, and taking the whole Cerean surface area into account ($2,850,000 \text{ km}^2$), the average time period between two such civilisation ending events (assuming nothing would be done to thwart against it), comes out at one such event every roughly 125 thousand years. Remember, this is a rough, generous estimate and in reality should happen orders of magnitude less frequently than that (read: millions of years).

Non-civilisation ending collisions would happen a lot more frequently though. Not exactly cloudy with a chance of meatballs, but in one of my calculations roughly two collisions with over one thousand metric ton (about 10 times less massive than the Chelyabinsk meteor) object per year at mentioned speeds (which are over five times smaller, so roughly 26.7 times less kinetic potential per same mass objects, than what the Earth and the Moon scoop by their own orbital speeds around the Sun alone).

Now, a chance of a collision with other objects that are not members of the main belt is also non zero, and could potentially be much more threatening with higher relative velocities involved and some of the trans-Neptunian objects (such as Kuiper belt or Oort cloud objects) could be hurled by other collisions between them towards the inner Solar system. But, as stated, Ceres is a really small target to hit, and the area is also protected by the gas and icy giants (Jupiter, Saturn, Uranus and Neptune) between the main belt and TNO and that are much, much stronger attractors clearing the neighborhood through the process known as accretion.

So, TL;DR - however you look at it, the chance of a collision with an object of significant mass is orders of magnitude smaller than if we set a colony on our own Moon, for example. And it would be many times easier in terms of required energy, to protect parts or even whole of the Cerean surface from such events.