I can see your logic, but I have to disagree. You need an insurance that the thing has a certain mass when it arrives at target. So, a certain mass of the vehicle can be labeled "payload", as it is indespensible if the mission objective is to be achieved.
Then you need the fuel to get that mass there. Even if the "payload"-mass would be in actual fuel, you'd still not be allowed to tap it too much. You'll need that mass when you get there. So the problem is not different than any other flight: "have payload, need fuel". And as we all know, you need more fuel per ton payload the more fuel you need.
Even if the thruster was conventional and used conventional fuel, you'd still arrive at your destination with enough fuel to complete the mission. If I planned the mission, I'd make sure of that.
Of course, if the whole mass would be provided in fuel, you'd have a reasonable error-margin. If the thing weights 100 tons, one ton less wouldn't really matter. use 5 to 10 tons too much, and you might get in trouble. Of course, fuel savings would work in favour, since you'd had more mass on the site than you actually planned. But you can't really say that fuel mass isn't a problem, especially if you have to pull of a high DV manouver to catch the bastard.
Again, I highly doubt that such a mission would use conventional thrusters. I think Ion based thrusters are more likely because they can provide high efficiency at long firing durations. You'd need closer to 100 kg of fuel then 100 tons. That means that the mass of the fuel would be rather negligible compared to the payload mass.
Or, let it pass within 600 km and jump it when it flies by, then correct it within the seven years remaining. I could imagine that, because you'd only have to match velocity at flyby, and not first spend DV to intercept, and then some more to match.
That is doubtful at best.
The asteroid will accelerate to insane speeds, while passing by Earth at slightly lower then geostationary orbits... delta-V for that would be quite large.
That, of course, is true. But if we don't just ram it but try for some "nuclear propulsion" (i.e. nuking it out of orbit), we might get a hell of a lot of shots for that mass. More than we'd need, so maybe we could reduce the mass to reasonable amounts and still have enough shots left.
We can't even get a 200 RTG into space without huge public fear. Nuclear warheads wouldn't just spark public protests. I fear international distrust could cause a war.
Besides, once we break the ice, what's there to stop us? Do we really wanna be a civilization that nukes every threat to our existence, despite having alternative means to deal with the problem?
I'd say the gravity tractor is not a very feasible option unless we really conquer and hold LEO first. With sufficiently cheap surface to LEO ( or to GSO) transport, it might become an option.
And you still want to catch up with the thing at GSO altitude?
Ok, so assuming we won't nuke the thing, we have two options. Ram it or tow it.
So here are some numbers:
99942 Apophis:
Mass M = 2.7 * 10^10 kg
Diameter d = 270 m
The ship:
Mass m = 2 * 10^5 kg (200 tons)
Impact velocity RelV = 10 km/s
Construction time + getting to the asteroid = 6 years.
Assuming a huge impact velocity:
m * RelV = M * delta-v (we can assume that the mass of the asteroid won't change much)
delta-v = (m * RelV) / M = 0.07 m/s on impact.
The diameter of the asteroid is some 270 m, meaning we can hover around 200 m from the surface.
a * M = m * M * G / r^2
a = m * G / r^2 = 3.3 * 10^-10 m/s^2
With a hover time of 20 years:
delta-v = 0.2 m/s with 0.01 m/s change per year.
The force required to keep the ship from falling onto the asteroid is around 0.5 N. At around 45° angle, that would mean around 0.7 N. I would say that would be split up between at least 4 thrusters, giving a workload of less then 0.2 N per thruster. I think this is entirely doable.
Granted, there's still the trouble of launching the thing, but I think we can all agree that the most fuel efficient approach is to eject it from Earth's orbit at like 4 km/s or something (once in LEO) and rendezvous with the asteroid in outer space and not trying to catch it at flyby of Earth.
I also think that a relative velocity of 10 km/s will be difficult to achieve, however, maybe a sling around Jupiter into a retrograde orbit and then hitting the asteroid when it's mid way from it's perihelion to aphelion could do the trick.
Still, the total delta-v of the asteroid resulting from parking the ship next to the asteroid will be greater then that of an impact. It would take an impact of more then 25 km/s relative velocity.
The advantage of the impact is that it changes velocity of the asteroid right away, while it takes some years before the parked ship can do the same... and the earlier you change the velocity the better, but the ship can provide a far larger delta v after that and I think it might compensate for the time it took.
I know these numbers are just rough estimates but they clearly show that we'd get more bang for the buck from gravitational tether.
---------- Post added at 02:00 PM ---------- Previous post was at 01:22 PM ----------
One more thing...
Assuming an impact delta-v of 0.07 m/s and an acceleration of 3.3 * 10^-10 m/s^2 for 20 years, the impact moves the asteroid a total of 44 000 km and the ship moves it a total of 65 000 km. Of course, that doesn't directly translate to the flyby, but it does give a measure of which is more powerful.