To have enough of an effect, you have to do your thing while it's quite a ways away.
That means you have to go pretty fast to get out to it before it gets too close to you.
You can blow up a bomb while the ship has a large difference in velocity with the asteroid.
You cannot attach a rocket engine when you're traveling 1000m/s past what you're trying to attach it to.
So if you take Earth to be your stationary velocity, you need to slow down, stop, and accelerate backwards to catch up to the asteroid's velocity.
Acceleration/deceleration requires fuel, or specifically mass.
More mass at the same acceleration requires even more fuel.
So either you send up a bomb to hit the asteroid with a glancing blow, or you launch a very complicated bit of machinery atop a very very large ship, have it do its delta-V stuff, delicately land on the surface, not so delicately drill in and and anchor to an unpredictable surface, and then start burning the even more fuel that you carried along (at a cost of yet more fuel). All while hoping desperately that no bit of sand or gravel gets into something and sticks it in place while setting things up.
I'm liking the bomb approach. I imagine you'd even make use of the speed of impact rather than paying for it. You're essentially installing a rocket engine on the asteroid this way anyway, using its mass as propulsion mass, and you can even send up multiple redundant attempts because you've supposedly calculated the trajectory so precisely that it's enough to add some force in pretty much any direction. (Or the rest of the swarm could disarm themselves when they detect the first successful hit.)
To have enough of an effect, you have to do your thing while it's quite a ways away.
That means you have to go pretty fast to get out to it before it gets too close to you.
You can blow up a bomb while the ship has a large difference in velocity with the asteroid.
You cannot attach a rocket engine when you're traveling 1000m/s past what you're trying to attach it to.
So if you take Earth to be your stationary velocity, you need to slow down, stop, and accelerate backwards to catch up to the asteroid's velocity.
Acceleration/deceleration requires fuel, or specifically mass.
More mass at the same acceleration requires even more fuel.
So either you send up a bomb to hit the asteroid with a glancing blow, or you launch a very complicated bit of machinery atop a very very large ship, have it do its delta-V stuff, delicately land on the surface, not so delicately drill in and and anchor to an unpredictable surface, and then start burning the even more fuel that you carried along (at a cost of yet more fuel). All while hoping desperately that no bit of sand or gravel gets into something and sticks it in place while setting things up.
I'm liking the bomb approach. I imagine you'd even make use of the speed of impact rather than paying for it. You're essentially installing a rocket engine on the asteroid this way anyway, using its mass as propulsion mass, and you can even send up multiple redundant attempts because you've supposedly calculated the trajectory so precisely that it's enough to add some force in pretty much any direction. (Or the rest of the swarm could disarm themselves when they detect the first successful hit.)