[jacquesm]

That's because Earth has gravity, and an asteroid that comes close enough can get deflected onto the planet even if right now it seems to be on a trajectory to miss it entirely. The closer they get and the lower the relative speeds the larger the chance that they will collide and that's not a linear relationship. Beyond a certain boundary impact is certain, then the question is what the time of the impact is and how precise the observations up to that point are in order to figure out where and when exactly it will come down. That won't happen very long before the impact itself happens even if you could say some time in advance roughly in which hemisphere and roughly when. But not precise enough to be very useful.

[fouc]

I wouldn't expect earth gravity to affect it sufficiently enough to cause it to crash unless it was moving very slowly, but I'm not sure asteroids ever move that slowly?

[Fatnino]

We're not talking about the asteroid stopping with a screech of tires and then taking a hard left turn to crash into earth.

It's just that anything traveling through the earth/moon gravitational sphere of influence will have it's trajectory tweaked just a bit. How close to the center of gravity the pass is determines exactly how much of a tweak. There is a small section of space, we'll call it the keyhole, where if the asteroid happens to pass exactly through that area the tweak will result in a collision next time the asteroid comes around. That could be decades hence.

There could even be a case where an unlucky keyhole pass this time lines up another unlucky keyhole pass the next time to an eventual collision in the distance future.

The technology to nudge the asteroid just far enough to miss a critical keyhole pass is within the realm of possibility with today's knowhow. We just need to have these missions ready to go on short (order of a few months to a year) notice.

[jacquesm]

We see big ones with a few days to hours of notice, sometimes we see them when they hit.

Most likely: this will never come up.

Less likely: if it does we're fucked.

Even less likely: if it does and surprisingly we see it in time we will act for the good of all and not bicker about who pays and we'll make things better rather than worse. If not, see above.

[jacquesm]

Like the moon is moving slowly? About 1 km/second for an object that weighs ~10^18 tons at a distance of 300,000 km?

Now think of what that kind of force would do on a much lighter object that moves faster.

[MauranKilom]

I'm not sure I understand your point... The object mass does not impact its trajectory (unless it either touches our atmosphere or is so massive as to measurably change earth's orbit). The gravitational force earth exerts on the moon and some asteroid is also very different, because the force is proportional to both object masses.

[jacquesm]

Think 'gravitational slingshot' but without missing the planet. The object will change direction and accelerate into us. It could end up grazing the atmosphere or it could go from grazing the atmosphere or even non-impact to impact.