We know and track many asteroids similar in size to the Russian meteorite.So it depends on its orbit. If you look at the upcoming close approaches table, there are many around 20 meters or so, the size of the Russian meteorite.
If it has done flybys of Earth before and been spotted when it did it, we might know of it decades in advance. If it is a new one, that's never come close to Earth, then we'd normally know of it a few days in advance depending what direction it comes from.
But the Russian meteorite came from the direction of the sun and in that direction we have a blindspot for the very small asteroids. Even up to 1 kilometer, it would be hard to detect if coming from that direction, we'd have some warning, a week or so if I remember right, but not a lot. And there are 10% of the population of 1 kilometer asteroids still to be found though we expect to find 90% of those remaining ones by the 2020s - are currently discovering one of them every month.
We already know all the ten kilometer asteroids out to Jupiter's orbit - and our telescopes are sensitive enough to spot them well beyond Jupiter actually at that size, and none of them are headed for us. So a 10 kilometer asteroid will be detected at least six months before encounter - and given that an asteroid / comet from beyond Jupiter is likely to do flybys first, then we'd probably have decades of warning. Anyway those are very unlikely, 1 chance in 10 million that any come this way in the next century.
It would be fairly easy to fix this. The Sentinel telescope designed by the B612 foundation costs $450. Less than half the amount that Bloomberg would spend on his presidential campaign if he decides to run. A two hundredth of the amount the UK plans to spend on renewing the Trident submarines.
Almost any country except the very poorest, and any billionaire could afford to pay for this telescope. It would orbit between Venus and Earth and look outwards, detect even small asteroids down to 20 meter diameter in the infrared. It would find most of the small asteroids within 6.5 years.
It wouldn't find all of the 20 meter asteroids. But it would make a good dent on it. And find most of the more dangerous larger asteroids.
As for what we could do if we could use that $100 billion the UK plans to spend on Trident for asteroid detection, goodness knows, probably be able to detect them all. Trident is of course capable of firing its nuclear weapons into space on its way to its target, like an ICBM so it is a space technology of a sort.
I think an ET looking at Earth would be astonished at our priorities - that we spend so much effort and space technology on weapons, also spy satellites, huge telescopes as big as Hubble but all pointed towards Earth - probably much more expensive thanthe B623 idea - focused at ourselves (rival countries but ETs would see them all as just us) as the threat, meanwhile pretty much ignoring asteroids as if they don't exist, although we know they do.
There is a major effort amongst astronomers with the Pan-STARRS telescope in Hawaii particularly looking at a large area of the sky several times a minute and doing a complete sky survey of the area of sky visible to it at the time every month or so. But we could do so much more, though major for astronomy, it's a tiny amount compared to the amount we spend on spy satellites and weapons of mass destruction all aimed at ourselves.
For more on this see my Giant Asteroid Headed Your Way? - How We Can Detect And Deflect Them
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