I think where the calculations are breaking down is in the probability of asteroid strikes.
All the math assumes that the probabilities will follow historic trends and is relatively static. With single digit events, we really have no way in knowing what the actual likelihood of impact is. It could be 1 in 100 million, it could actually be 1 in 1 million and we've been rolling a bunch of nat 20s.
Before we build out the asteroid blaster 9000, the first step is detection. With that in place then we get actual good risk and probability calculations. If the detector tells us "There's no object that will strike earth in the next 1000 years" we can safely not put any budget into asteroid defense. If, on the other hand, the detector shows "Chicxulub 2.0 will hit in the next 100 years" then your probability of an impact is 1 and the actual budget worth it is going to be much closer to that $8e+16 number calculated earlier.
While I'm strongly supportive of survey astronomy in general...
We can already say that we have very high completion of cataloguing near-Earth objects that are anywhere near extinction-event / Chicxulub-sized (~10km), and have a majority of catastrophic / country-killer (~1km), and are digging deeper and deeper into regional / city-killer (~100m) bodies.
What we don't have is comets. Comets on long period orbits just aren't readily detectable with this sort of survey unless they're quite close in to the Sun, and I don't think we have great statistics on frequency vs size, size being something that requires very specific radar cross-checking to establish with any confidence. A long-period comet or hyperbolic body has a potential impact velocity much higher than inner system asteroids, and impact energy scales with impact velocity squared.
Will rubin detect comets? I'd assume not as it seems like they'll only really be visible as they approach the sun (or if they end up blocking a line of stars).
The problem is that the difference in optical/NIR brightness (apparent magnitude) between a long-period comet core that's going to hit us in 1000 years, and a long-period comet core that's going to hit us in six months, might be a factor 10^12 (magnitude 10 vs magnitude 40) or worse. Normally brightness drops off with distance squared for light sources, but comets without any tail or halo aren't emitting all that much light, they're reflecting it, and (except for a very brief period) they're about as far from us as they are from the sun. This means that brightness drops with distance to the fourth power. Cometary tails also only offgas a significant amount near the sun. Comet cores are expected to be extremely dark / low-reflectivity due to space weathering producing a carbon coating not unlike chimney-creosote.
You can fight this a bit by working in the thermal infrared, which you really need a specific sort of space telescope for. But long-period comets and hyperbolic impactors will be a probabilistic threat for the foreseeable future. I would say "Be thankful that they're so rare", but the data from observatories like Rubin on these bodies during points of their orbit where they're close enough to the sun to actually detect, is necessary to statistically characterize their existence with any confidence.
I agree that detection is a very helpful first step and almost enough on its own. But I'm unsure how far this can be pushed-- I think impact certainty for a century or more might be physically impossible, because of uncertainty in orbital parameters and chaotic behavior of the whole system.
I also believe the approximate bounds we have on impact probability are good enough for this estimate and quite unlikely to be off by a factor of 100, because we can guess at both size distribution and impact likelihood from craters (on earth and moon), and if the >10km object impact likelihood was over 1/million years we would expect to see a hundred times more craters of the corresponding size...
> I think impact certainty for a century or more might be physically impossible, because of uncertainty in orbital parameters and chaotic behavior of the whole system.
We already have 10s of years of certainty with the current observations. Most of the uncertainty comes from the interactions of unknown objects. As the mappings of objects increase, our predictions will become much better.
The other thing to consider is that large objects will have much better certainty. A 10km asteroid won't be influenced (much) by colliding with 100 1m asteroids. It will only be impacted if it hits or swings by something like a 1km asteroid.
Rubin should in a pretty short timeframe (a few years) give us an orbital mapping of all the >1km asteroids, which is pretty exciting.
All the math assumes that the probabilities will follow historic trends and is relatively static. With single digit events, we really have no way in knowing what the actual likelihood of impact is. It could be 1 in 100 million, it could actually be 1 in 1 million and we've been rolling a bunch of nat 20s.
Before we build out the asteroid blaster 9000, the first step is detection. With that in place then we get actual good risk and probability calculations. If the detector tells us "There's no object that will strike earth in the next 1000 years" we can safely not put any budget into asteroid defense. If, on the other hand, the detector shows "Chicxulub 2.0 will hit in the next 100 years" then your probability of an impact is 1 and the actual budget worth it is going to be much closer to that $8e+16 number calculated earlier.