Lots of proposed methods, but without knowing more about asteroids, we can't be sure what will work both safely and effectively. So more probes (including some soft-landers and sample missions) will be needed to tell us how durable, etc. various NEO s are. We don't want to nudge something out of the way only to have it break up and carpet-bomb us instead.

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"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

Yes, many asteroids appear to be mere rubble piles (Itokawa, for example). If we try something drastic like explosives or attaching a rocket in it the whole thing will break apart. If we have decades to act, we can use very gentle methods because all we have to do is to change the orbit very slightly in order to prevent it hitting us.

Probes are absolutely necessary in order to know the "enemy".

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Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.
-- Richard Feynman

Could a better tracking system handle these keyhole situation Apophis is in at the moment? It would be great if we had a system that could tell 30 years in advance if any asteroid with a diameter of 50 meters or larger is going to hit. But if not you'll still need a deflection system. Especially if you have a pretty good but not perfect tracking system and you get a bunch of 1:40000 chance to hit alarms.

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"The cure for boredom is curiosity. There is no cure for curiosity."

Dorothy Parker (?)

"Chance to hit" is a guesstimation based on --at present-- woefully incomplete data. The more accurate information you have, the more you can predict.

And if someone with a big brain cracks the N-body problem, that'll help too.

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

But more may not be good enough. If you want to avoid paying for a deflection system altogether you have to be pretty sure that there are no short or medium term risks. I'm just not sure if it's technically and economically feasible at the moment. It's even possible that it is cheaper to develop a way to deflect 50-300 m asteroids on a few month' notice than to build a tracking system which can reliably rule out an impact over 20 years timescales. Maybe not,I really don't know. That's why I'm asking.

__________________
"The cure for boredom is curiosity. There is no cure for curiosity."

Dorothy Parker (?)

How much might a deflection method(s) cost? How much for a better observation system?

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

yes.........well, for a while, scientists tried busting up a few icebergs.
Never made a dent in them. And...you are going to break up or move
an iron/nickel object 2000 feet in dieameter? Interesting at best.
And....most of these things are tumbling.

The last thing you'd like to do is to break it up. Instead of one big bang, there could be several smaller but still each of them devastating enough. Therefore the total damage might be much larger. Unless, of course, the impactor is small enough so that its pieces become harmless. Also, in the case of rubble piles like Itokawa or Styrofoam asteroids like Mathilde explosives make little difference. Rubble or porous structure can make the asteroid to withstand major explosions without breaking it apart (see images of Mathilde if you don't believe).

__________________
Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.
-- Richard Feynman

Breaking it up would be ludicrously dangerous. Except in movies, of course!

Only a small number of methods that I've read about would be affected by the tumbling. And deflection is simpler than moving an iceberg through water.

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

No idea. You might find some info here, esepecially the report at the start.

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"The cure for boredom is curiosity. There is no cure for curiosity."

Dorothy Parker (?)

So, the chance of Apophis hitting the earth is 1 in 45,000. Okay, but what are the chances that it would hit the US? It's not just a cost benefit analysis for the world but for the people who will actually spend the money. If we thought the asteroid was going to crash into a country that is our enemy, would we be as inclined to stop it?

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"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau

No way to be that precise ahead of time. If we can't even tell yet if it'll hit Earth, then there's certainly not enough to tell us where it might hit if it does!

(Hmm, why assume that only the US will take part in a deflection project?)

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

Can we really predict who our enemies will be 30 years into the future?

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PW -- Plant Whisperer

Probably can't get precision like the city closest to ground zero, right now but it wouldn't be hard to get the hemisphere, maybe even region. Estimate of the arrival time has precision: 2036-04-13.37. I don't know what the error bars are on that, but probably less than an hour. Since we know the direction it's coming from, it's not hard to calculate roughly which hemisphere might face impact if Earth's path actually then intersected Apophis's.

Spaceref.com: Asteroids, Comets, Meteors Meeting 2005

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Attention, California surfers; get out your boards for one BIG wave...

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

USA has enemies??!!
Govermets are bad, not people.
North Koreans are normal humans, but their govorement is a cruel monster that kills it's own people in political prisoner camps.
It is better to have no enemy.

A gravity tractor--provided it has enough fuel, might work--but you would need a good HLLV to place it by an asteroid and it not be on empty.

Yes, You have to assemble things in orbit and boost fuel up there in order to do
the "Difficult things" .
Nothing's easy. And you don't always know the results.
I had to snap the lock off my Mother-in-Law's ammunition box.
She had a $1.75 , her spice collection , and a box of Parodis cigars in there.

I remember seeing a calculation on the new series, "The Universe" on the Science Channel. I think they used the same data that 01101001 mentioned. So perhaps the US and Russia would be interested in preventing it from hitting them. But chances are that no one will divert Apophis, or any other possible impactor until it was clear that it would hit, and that might not be until a few years before that impact would occur. Therefore, by the time we would be interested in averting the threat we will have a good idea whether or not we actually want to.

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"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau