[Mr. K]

That is the main problem detecting one that is going to hit us. If it is moving across the pictures than it's trajectory is somewhere else, but if it is coming right towards us it does not move- we can only tell it is coming by it growing brighter.

If one hits us I doubt we will have much more than a few days notice no matter what.

[Ditter]

Think of the panic it would have caused if they had announced it. I have seen what happens when a small part of the coast is evacuated for a hurricane, gridlock. Imagine if they announced that it was going to hit in a populated area. What a nightmare. If I can't get out of the way in time, don't even tell me about it.

[Larry Lucido]

but if it is coming right towards us it does not move- we can only tell it is coming by it growing brighter.

Is there any equivalent of doppler-radar that can detect the speed of a seemingly stationary object headed toward the earth?

[Indie]

In actuality you're right. The most likely scenario for an impact will be...impact. No warning.

[ngc6656]

but if it is coming right towards us it does not move- we can only tell it is coming by it growing brighter.

It isn't quite that simple for both the asteroid and Earth are in motion. If a just-discovered asteroid is say, three days from impact, it will strike Earth where Earth will be in its orbit 3 days hence. An asteroid approaching from directly ahead or behind along the direction of Earth's travel in its orbit would show little apparent motion; from any other direction, the asteroid's motion against the background stars would be more obvious. Think of it as two cars approaching one another on a one lane road in the first scenario and as two cars, one each on separate but crossing roads approaching a 90 degree intersection in the other.